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Q1:

2025 Slot 3

Logical Reasoning > Grids

Hard

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators - Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing. <img src="https://balti.aftergrad.in/questions/lf88lEOj8Hmp56a" width="500px"/> It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the duration of calls (in minutes) from Bijay to Anu?

Entered answer:

Correct Answer

50

Correct Answer

Explanation →

Q2:

2025 Slot 3

Logical Reasoning > Grids

Hard

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators - Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing. <img src="https://balti.aftergrad.in/questions/lf88lEOj8Hmp56a" width="500px"/> It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the total duration of calls (in minutes) made by Anu to friends having mobile numbers from Operator Yocel?

Entered answer:

Correct Answer

525

Correct Answer

Explanation →

Q3:

2025 Slot 3

Logical Reasoning > Grids

Hard

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators - Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing. <img src="https://balti.aftergrad.in/questions/lf88lEOj8Hmp56a" width="500px"/> It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the total duration of calls (in minutes) made by Faruq to friends having mobile numbers from Operator Yocel?

Entered answer:

Correct Answer

350

Correct Answer

Explanation →

Q4:

2025 Slot 3

Logical Reasoning > Grids

Hard

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators - Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing. <img src="https://balti.aftergrad.in/questions/lf88lEOj8Hmp56a" width="500px"/> It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the duration of calls (in minutes) from Deepak to Chetan?

0

100

50

125

Correct Answer

Option 2

Correct Answer

Explanation →

Q5:

2025 Slot 2

Logical Reasoning > Grids

Medium

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a "ping". Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

What was the total number of pings made by B1, B2, and B3?

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q6:

2025 Slot 2

Logical Reasoning > Grids

Medium

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a "ping". Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

Which of the following statements about the relative sizes of the balls is NOT NECESSARILY true?

B1 < B5 < B3

B4 < B5 < B3

B1 < B6 < B3

B2 < B1 < B5

Correct Answer

Option 3

Correct Answer

Explanation →

Q7:

2025 Slot 2

Logical Reasoning > Grids

Medium

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a "ping". Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

Which of the following statements about the relative sizes of the hoops is true?

H2 < H4 < H3 < H1

H2 < H3 < H4 < H1

H1 < H4 < H3 < H2

H1 < H3 < H4 < H2

Correct Answer

Option 2

Correct Answer

Explanation →

Q8:

2025 Slot 2

Logical Reasoning > Grids

Medium

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a "ping". Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

What BEST can be said about the total number of pings from all the tests undertaken?

12 or 13

At least 9

12 or 13 or 14

13 or 14

Correct Answer

Option 1

Correct Answer

Explanation →

Q9:

CAT 2024 Slot 3

Logical Reasoning > Grids

Hard

The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs. $$\newline$$ The following additional information is known. $$\newline$$ <ol><li>The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.</li> $$\newline$$ <li>The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.</li></ol> $$\newline$$ <img src="https://balti.aftergrad.in/questions/cw2dATs2y7USZ41" width="400px"/>

Which of the following statements is correct?

The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 9 Lakhs.

The cash requirement of the ATM placed at the (R-C, V2) intersection cannot be uniquely determined.

The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 8 Lakhs.

There is no ATM placed at the (R-C, V2) intersection.

Correct Answer

Option 1

Correct Answer

Explanation →

Q10:

CAT 2024 Slot 3

Logical Reasoning > Grids

Hard

The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs. $$\newline$$ The following additional information is known. $$\newline$$ <ol><li>The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.</li> $$\newline$$ <li>The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.</li></ol> $$\newline$$ <img src="https://balti.aftergrad.in/questions/cw2dATs2y7USZ41" width="400px"/>

How many ATMs have cash requirements of Rs. $10$ Lakhs or more?

Entered answer:

Correct Answer

3

Correct Answer

Explanation →

Q11:

CAT 2024 Slot 3

Logical Reasoning > Grids

Hard

The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs. $$\newline$$ The following additional information is known. $$\newline$$ <ol><li>The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.</li> $$\newline$$ <li>The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.</li></ol> $$\newline$$ <img src="https://balti.aftergrad.in/questions/cw2dATs2y7USZ41" width="400px"/>

Which of the following two statements is/are DEFINITELY true? $\newline$ $\newline$ Statement A: Each of R-A, R-B, and R-C has two ATMs. $\newline$ Statement B: Each of V1, V2, and V3 has two ATMs.

Only Statement B

Neither Statement A nor Statement B

Both Statement A and Statement B

Only Statement A

Correct Answer

Option 4

Correct Answer

Explanation →

Q12:

CAT 2024 Slot 3

Logical Reasoning > Grids

Hard

The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs. $$\newline$$ The following additional information is known. $$\newline$$ <ol><li>The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.</li> $$\newline$$ <li>The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.</li></ol> $$\newline$$ <img src="https://balti.aftergrad.in/questions/cw2dATs2y7USZ41" width="400px"/>

What best can be said about the road distance (in km) between the ATMs having the second highest and the second lowest cash requirements?

4 km

5 km

Either 4 km or 7 km

7 km

Correct Answer

Option 3

Correct Answer

Explanation →

Q13:

CAT 2024 Slot 3

Logical Reasoning > Grids

Hard

The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs. $$\newline$$ The following additional information is known. $$\newline$$ <ol><li>The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.</li> $$\newline$$ <li>The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.</li></ol> $$\newline$$ <img src="https://balti.aftergrad.in/questions/cw2dATs2y7USZ41" width="400px"/>

What is the number of ATMs whose locations and cash requirements can both be uniquely determined?

Entered answer:

Correct Answer

3

Correct Answer

Explanation →

Q14:

CAT 2024 Slot 2

Logical Reasoning > Grids

Hard

<img src="https://balti.aftergrad.in/questions/2KjUjzHyvcSe9HW" width="400px"/> $$\newline$$ The above is a schematic diagram of walkways (indicated by all the straight lines) and lakes (3 of them, each in the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m. $$\newline$$ The following additional information about the facilities in the area is known. $$\newline$$ <ol><li>The only entry/exit point is at C. $$\newline$$ </li><li>There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L. $$\newline$$ </li><li>The post office is located at P and the bank is located at B.</li></ol>

One resident whose house is located at L, needs to visit the post office as well as the bank. What is the minimum distance (in m) he has to walk starting from his residence and returning to his residence after visiting both the post office and the bank?

3200

3000

3000

2700

Correct Answer

Option 1

Correct Answer

Explanation →

Q15:

CAT 2024 Slot 2

Logical Reasoning > Grids

Hard

<img src="https://balti.aftergrad.in/questions/2KjUjzHyvcSe9HW" width="400px"/> $$\newline$$ The above is a schematic diagram of walkways (indicated by all the straight lines) and lakes (3 of them, each in the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m. $$\newline$$ The following additional information about the facilities in the area is known. $$\newline$$ <ol><li>The only entry/exit point is at C. $$\newline$$ </li><li>There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L. $$\newline$$ </li><li>The post office is located at P and the bank is located at B.</li></ol>

One person enters the gated area and decides to walk as much as possible before leaving the area without walking along any path more than once and always walking next to one of the lakes. Note that he may cross a point multiple times. How much distance (in m) will he walk within the gated area?

3200

2800

3000

3800

Correct Answer

Option 4

Correct Answer

Explanation →

Q16:

CAT 2024 Slot 2

Logical Reasoning > Grids

Hard

<img src="https://balti.aftergrad.in/questions/2KjUjzHyvcSe9HW" width="400px"/> $$\newline$$ The above is a schematic diagram of walkways (indicated by all the straight lines) and lakes (3 of them, each in the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m. $$\newline$$ The following additional information about the facilities in the area is known. $$\newline$$ <ol><li>The only entry/exit point is at C. $$\newline$$ </li><li>There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L. $$\newline$$ </li><li>The post office is located at P and the bank is located at B.</li></ol>

One resident takes a walk within the gated area starting from A and returning to A without going through any point (other than A) more than once. What is the maximum distance (in m) she can walk in this way? $\newline$ $\square$

Entered answer:

Correct Answer

5100

Correct Answer

Explanation →

Q17:

CAT 2024 Slot 2

Logical Reasoning > Grids

Hard

<img src="https://balti.aftergrad.in/questions/2KjUjzHyvcSe9HW" width="400px"/> $$\newline$$ The above is a schematic diagram of walkways (indicated by all the straight lines) and lakes (3 of them, each in the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m. $$\newline$$ The following additional information about the facilities in the area is known. $$\newline$$ <ol><li>The only entry/exit point is at C. $$\newline$$ </li><li>There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L. $$\newline$$ </li><li>The post office is located at P and the bank is located at B.</li></ol>

Visitors coming for morning walks are allowed to enter as long as they do not pass by any of the residences and do not cross any point (except C) more than once. What is the maximum distance (in m) that such a visitor can walk within the gated area?

Entered answer:

Correct Answer

3500

Correct Answer

Explanation →

Q18:

CAT 2023 Slot 2

Logical Reasoning > Grids

Hard

There are nine boxes arranged in a $3\times3$ array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. <img src="https://balti.aftergrad.in/questions/elh0rATpTbK599P" width="500px"/> Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a, if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by. if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9.

What is the total number of coins in all the boxes in the 3rd row?

15

45

36

30

Correct Answer

Option 2

Correct Answer

Explanation →

Q19:

CAT 2023 Slot 2

Logical Reasoning > Grids

Hard

There are nine boxes arranged in a $3\times3$ array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. <img src="https://balti.aftergrad.in/questions/elh0rATpTbK599P" width="500px"/> Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a, if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by. if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9.

How many boxes have at least one sack containing 9 coins?

3

8

4

5

Correct Answer

Option 4

Correct Answer

Explanation →

Q20:

CAT 2023 Slot 2

Logical Reasoning > Grids

Hard

There are nine boxes arranged in a $3\times3$ array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. <img src="https://balti.aftergrad.in/questions/elh0rATpTbK599P" width="500px"/> Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a, if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by. if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9.

For how many boxes are the average and median of the numbers of coins contained in the three sacks in that box the same?

Entered answer:

Correct Answer

4

Correct Answer

Explanation →

Q21:

CAT 2023 Slot 2

Logical Reasoning > Grids

Hard

There are nine boxes arranged in a $3\times3$ array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. <img src="https://balti.aftergrad.in/questions/elh0rATpTbK599P" width="500px"/> Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a, if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by. if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9.

How many sacks have exactly one coin?

Entered answer:

Correct Answer

9

Correct Answer

Explanation →

Q22:

CAT 2023 Slot 2

Logical Reasoning > Grids

Hard

There are nine boxes arranged in a $3\times3$ array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. <img src="https://balti.aftergrad.in/questions/elh0rATpTbK599P" width="500px"/> Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a, if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by. if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9.

In how many boxes do all three sacks contain different numbers of coins?

Entered answer:

Correct Answer

5

Correct Answer

Explanation →

Q23:

CAT 2023 Slot 1

Logical Reasoning > Grids

Hard

The schematic diagram below shows 12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are located in six columns – Column-A through Column-F, and two rows – Row-1 and Row-2. The houses are divided into two blocks - Block XX and Block YY. The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GYjFBOy9OLsFNw4" width="400px"/> $$\newline$$ Some of the houses are occupied. The remaining ones are vacant and are the only ones available for sale. $$\newline$$ The road adjacency value of a house is the number of its sides adjacent to a road. For example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupied houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively. $$\newline$$ The base price of a vacant house is Rs. 10 lakhs if the house does not have a parking space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house is calculated as (base price) + 5 $\times$ (road adjacency value) + 3 $\times$ (neighbour count). $$\newline$$ The following information is also known. $$\newline$$ <ol> $\newline$ <li>The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimum quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.</li> $$\newline$$ <li>Row-1 has two occupied houses, one in each block.</li> $$\newline$$ <li>Both houses in Column-E are vacant. Each of Column-D and Column-F has at least one occupied house.</li> $$\newline$$ <li>There is only one house with parking space in Block YY.</li> $\newline$ </ol>

How many houses are vacant in Block XX? (in numerial value)

Entered answer:

Correct Answer

3

Correct Answer

Explanation →

Q24:

CAT 2023 Slot 1

Logical Reasoning > Grids

Hard

The schematic diagram below shows 12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are located in six columns – Column-A through Column-F, and two rows – Row-1 and Row-2. The houses are divided into two blocks - Block XX and Block YY. The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GYjFBOy9OLsFNw4" width="400px"/> $$\newline$$ Some of the houses are occupied. The remaining ones are vacant and are the only ones available for sale. $$\newline$$ The road adjacency value of a house is the number of its sides adjacent to a road. For example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupied houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively. $$\newline$$ The base price of a vacant house is Rs. 10 lakhs if the house does not have a parking space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house is calculated as (base price) + 5 $\times$ (road adjacency value) + 3 $\times$ (neighbour count). $$\newline$$ The following information is also known. $$\newline$$ <ol> $\newline$ <li>The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimum quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.</li> $$\newline$$ <li>Row-1 has two occupied houses, one in each block.</li> $$\newline$$ <li>Both houses in Column-E are vacant. Each of Column-D and Column-F has at least one occupied house.</li> $$\newline$$ <li>There is only one house with parking space in Block YY.</li> $\newline$ </ol>

Which of the following houses is definitely occupied?

B1

D1

F2

A1

Correct Answer

Option 1

Correct Answer

Explanation →

Q25:

CAT 2023 Slot 1

Logical Reasoning > Grids

Hard

The schematic diagram below shows 12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are located in six columns – Column-A through Column-F, and two rows – Row-1 and Row-2. The houses are divided into two blocks - Block XX and Block YY. The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GYjFBOy9OLsFNw4" width="400px"/> $$\newline$$ Some of the houses are occupied. The remaining ones are vacant and are the only ones available for sale. $$\newline$$ The road adjacency value of a house is the number of its sides adjacent to a road. For example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupied houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively. $$\newline$$ The base price of a vacant house is Rs. 10 lakhs if the house does not have a parking space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house is calculated as (base price) + 5 $\times$ (road adjacency value) + 3 $\times$ (neighbour count). $$\newline$$ The following information is also known. $$\newline$$ <ol> $\newline$ <li>The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimum quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.</li> $$\newline$$ <li>Row-1 has two occupied houses, one in each block.</li> $$\newline$$ <li>Both houses in Column-E are vacant. Each of Column-D and Column-F has at least one occupied house.</li> $$\newline$$ <li>There is only one house with parking space in Block YY.</li> $\newline$ </ol>

Which of the following options best describes the number of vacant houses in Row-2?

Either 3 or 4

Either 2 or 3

Exactly 3

Exactly 2

Correct Answer

Option 2

Correct Answer

Explanation →

Q26:

CAT 2023 Slot 1

Logical Reasoning > Grids

Hard

The schematic diagram below shows 12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are located in six columns – Column-A through Column-F, and two rows – Row-1 and Row-2. The houses are divided into two blocks - Block XX and Block YY. The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GYjFBOy9OLsFNw4" width="400px"/> $$\newline$$ Some of the houses are occupied. The remaining ones are vacant and are the only ones available for sale. $$\newline$$ The road adjacency value of a house is the number of its sides adjacent to a road. For example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupied houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively. $$\newline$$ The base price of a vacant house is Rs. 10 lakhs if the house does not have a parking space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house is calculated as (base price) + 5 $\times$ (road adjacency value) + 3 $\times$ (neighbour count). $$\newline$$ The following information is also known. $$\newline$$ <ol> $\newline$ <li>The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimum quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.</li> $$\newline$$ <li>Row-1 has two occupied houses, one in each block.</li> $$\newline$$ <li>Both houses in Column-E are vacant. Each of Column-D and Column-F has at least one occupied house.</li> $$\newline$$ <li>There is only one house with parking space in Block YY.</li> $\newline$ </ol>

What is the maximum possible quoted price (in lakhs of Rs.) for a vacant house in Column-E? (in numerial value)

Entered answer:

Correct Answer

21

Correct Answer

Explanation →

Q27:

CAT 2023 Slot 1

Logical Reasoning > Grids

Hard

The schematic diagram below shows 12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are located in six columns – Column-A through Column-F, and two rows – Row-1 and Row-2. The houses are divided into two blocks - Block XX and Block YY. The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GYjFBOy9OLsFNw4" width="400px"/> $$\newline$$ Some of the houses are occupied. The remaining ones are vacant and are the only ones available for sale. $$\newline$$ The road adjacency value of a house is the number of its sides adjacent to a road. For example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupied houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively. $$\newline$$ The base price of a vacant house is Rs. 10 lakhs if the house does not have a parking space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house is calculated as (base price) + 5 $\times$ (road adjacency value) + 3 $\times$ (neighbour count). $$\newline$$ The following information is also known. $$\newline$$ <ol> $\newline$ <li>The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimum quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.</li> $$\newline$$ <li>Row-1 has two occupied houses, one in each block.</li> $$\newline$$ <li>Both houses in Column-E are vacant. Each of Column-D and Column-F has at least one occupied house.</li> $$\newline$$ <li>There is only one house with parking space in Block YY.</li> $\newline$ </ol>

Which house in Block YY has parking space?

F1

E2

E1

F2

Correct Answer

Option 3

Correct Answer

Explanation →

Q28:

CAT 2020 Slot 3

Logical Reasoning > Grids

Easy

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered $1$ through $16$, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient's blood sample is distributed. $$\newline$$ <table class="question-table"> $\newline$ <thead> $\newline$ <tr><th>Patient</th><th>Vials</th><th>Patient</th><th>Vials</th></tr> $\newline$ </thead> $\newline$ <tbody> $\newline$ <tr><td>1</td><td>B, D, F, H</td><td>9</td><td>A, D, F, H</td></tr> $\newline$ <tr><td>2</td><td>B, D, F, G</td><td>10</td><td>A, D, F, G</td></tr> $\newline$ <tr><td>3</td><td>B, D, E, H</td><td>11</td><td>A, D, E, H</td></tr> $\newline$ <tr><td>4</td><td>B, D, E, G</td><td>12</td><td>A, D, E, G</td></tr> $\newline$ <tr><td>5</td><td>B, C, F, H</td><td>13</td><td>A, C, F, H</td></tr> $\newline$ <tr><td>6</td><td>B, C, F, G</td><td>14</td><td>A, C, F, G</td></tr> $\newline$ <tr><td>7</td><td>B, C, E, H</td><td>15</td><td>A, C, E, H</td></tr> $\newline$ <tr><td>8</td><td>B, C, E, G</td><td>16</td><td>A, C, E, G</td></tr> $\newline$ </tbody> $\newline$ </table> $$\newline$$ If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose blood samples were mixed in the vial has the disease.

Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?

Patient 2

Patient 6

Patient 14

Patient 8

Correct Answer

Option 2

Correct Answer

Explanation →

Q29:

CAT 2020 Slot 3

Logical Reasoning > Grids

Easy

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered $1$ through $16$, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient's blood sample is distributed. $$\newline$$ <table class="question-table"> $\newline$ <thead> $\newline$ <tr><th>Patient</th><th>Vials</th><th>Patient</th><th>Vials</th></tr> $\newline$ </thead> $\newline$ <tbody> $\newline$ <tr><td>1</td><td>B, D, F, H</td><td>9</td><td>A, D, F, H</td></tr> $\newline$ <tr><td>2</td><td>B, D, F, G</td><td>10</td><td>A, D, F, G</td></tr> $\newline$ <tr><td>3</td><td>B, D, E, H</td><td>11</td><td>A, D, E, H</td></tr> $\newline$ <tr><td>4</td><td>B, D, E, G</td><td>12</td><td>A, D, E, G</td></tr> $\newline$ <tr><td>5</td><td>B, C, F, H</td><td>13</td><td>A, C, F, H</td></tr> $\newline$ <tr><td>6</td><td>B, C, F, G</td><td>14</td><td>A, C, F, G</td></tr> $\newline$ <tr><td>7</td><td>B, C, E, H</td><td>15</td><td>A, C, E, H</td></tr> $\newline$ <tr><td>8</td><td>B, C, E, G</td><td>16</td><td>A, C, E, G</td></tr> $\newline$ </tbody> $\newline$ </table> $$\newline$$ If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose blood samples were mixed in the vial has the disease.

Suppose vial A tests positive and vials D and G test negative. Which of the following vials should we test next to identify the patient with the disease?

Vial C

Vial H

Vial B

Vial E

Correct Answer

Option 4

Correct Answer

Explanation →

Q30:

CAT 2020 Slot 3

Logical Reasoning > Grids

Easy

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered $1$ through $16$, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient's blood sample is distributed. $$\newline$$ <table class="question-table"> $\newline$ <thead> $\newline$ <tr><th>Patient</th><th>Vials</th><th>Patient</th><th>Vials</th></tr> $\newline$ </thead> $\newline$ <tbody> $\newline$ <tr><td>1</td><td>B, D, F, H</td><td>9</td><td>A, D, F, H</td></tr> $\newline$ <tr><td>2</td><td>B, D, F, G</td><td>10</td><td>A, D, F, G</td></tr> $\newline$ <tr><td>3</td><td>B, D, E, H</td><td>11</td><td>A, D, E, H</td></tr> $\newline$ <tr><td>4</td><td>B, D, E, G</td><td>12</td><td>A, D, E, G</td></tr> $\newline$ <tr><td>5</td><td>B, C, F, H</td><td>13</td><td>A, C, F, H</td></tr> $\newline$ <tr><td>6</td><td>B, C, F, G</td><td>14</td><td>A, C, F, G</td></tr> $\newline$ <tr><td>7</td><td>B, C, E, H</td><td>15</td><td>A, C, E, H</td></tr> $\newline$ <tr><td>8</td><td>B, C, E, G</td><td>16</td><td>A, C, E, G</td></tr> $\newline$ </tbody> $\newline$ </table> $$\newline$$ If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose blood samples were mixed in the vial has the disease.

Which of the following combinations of test results is NOT possible?

Vial B positive, vials C, F and H negative

Vials B and D positive, vials F and H negative

Vials A and E positive, vials C and D negative

Vials A and G positive, vials D and E negative

Correct Answer

Option 3

Correct Answer

Explanation →

Q31:

CAT 2020 Slot 3

Logical Reasoning > Grids

Easy

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered $1$ through $16$, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient's blood sample is distributed. $$\newline$$ <table class="question-table"> $\newline$ <thead> $\newline$ <tr><th>Patient</th><th>Vials</th><th>Patient</th><th>Vials</th></tr> $\newline$ </thead> $\newline$ <tbody> $\newline$ <tr><td>1</td><td>B, D, F, H</td><td>9</td><td>A, D, F, H</td></tr> $\newline$ <tr><td>2</td><td>B, D, F, G</td><td>10</td><td>A, D, F, G</td></tr> $\newline$ <tr><td>3</td><td>B, D, E, H</td><td>11</td><td>A, D, E, H</td></tr> $\newline$ <tr><td>4</td><td>B, D, E, G</td><td>12</td><td>A, D, E, G</td></tr> $\newline$ <tr><td>5</td><td>B, C, F, H</td><td>13</td><td>A, C, F, H</td></tr> $\newline$ <tr><td>6</td><td>B, C, F, G</td><td>14</td><td>A, C, F, G</td></tr> $\newline$ <tr><td>7</td><td>B, C, E, H</td><td>15</td><td>A, C, E, H</td></tr> $\newline$ <tr><td>8</td><td>B, C, E, G</td><td>16</td><td>A, C, E, G</td></tr> $\newline$ </tbody> $\newline$ </table> $$\newline$$ If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose blood samples were mixed in the vial has the disease.

Suppose one of the lab assistants accidentally mixed two patients' blood samples before they were distributed to the vials. Which of the following correctly represents the set of all possible numbers of positive test results out of the eight vials?

{5,6,7,8}

{4,5}

{4,5,6,7,8}

{4,5,6,7}

Correct Answer

Option 3

Correct Answer

Explanation →

Q32:

CAT 2020 Slot 3

Logical Reasoning > Grids

Hard

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below: <img src="https://balti.aftergrad.in/questions/yKAXrPpqXtphWM8" width="300px"/> The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known: <ol> <li>Abha got 20 trees more than Chitra but 6 trees less than Dipti.</li> <li>The largest number of trees in a plot was 32, but it was not with Abha.</li> <li>The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.</li> <li>Both Abha and Bina got a higher number of plots than Dipti.</li> <li>Only Bina, Chitra and Dipti got corner plots.</li> <li>Dipti got two adjoining plots in the same row.</li> <li>Bina was the only one who got a plot in each row and each column.</li> <li>Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).</li> <li>The number of mango trees was double the number of teak trees.</li> </ol>

How many mango trees were there in total?

49

98

126

84

Correct Answer

Option 2

Correct Answer

Explanation →

Q33:

CAT 2020 Slot 3

Logical Reasoning > Grids

Hard

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below: <img src="https://balti.aftergrad.in/questions/yKAXrPpqXtphWM8" width="300px"/> The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known: <ol> <li>Abha got 20 trees more than Chitra but 6 trees less than Dipti.</li> <li>The largest number of trees in a plot was 32, but it was not with Abha.</li> <li>The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.</li> <li>Both Abha and Bina got a higher number of plots than Dipti.</li> <li>Only Bina, Chitra and Dipti got corner plots.</li> <li>Dipti got two adjoining plots in the same row.</li> <li>Bina was the only one who got a plot in each row and each column.</li> <li>Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).</li> <li>The number of mango trees was double the number of teak trees.</li> </ol>

Which of the following is the correct sequence of trees received by Abha, Bina, Chitra and Dipti in that order?

60, 39, 40, 66

50, 69, 30, 56

44, 87, 24, 50

54, 57, 34, 60

Correct Answer

Option 2

Correct Answer

Explanation →

Q34:

CAT 2020 Slot 3

Logical Reasoning > Grids

Hard

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below: <img src="https://balti.aftergrad.in/questions/yKAXrPpqXtphWM8" width="300px"/> The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known: <ol> <li>Abha got 20 trees more than Chitra but 6 trees less than Dipti.</li> <li>The largest number of trees in a plot was 32, but it was not with Abha.</li> <li>The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.</li> <li>Both Abha and Bina got a higher number of plots than Dipti.</li> <li>Only Bina, Chitra and Dipti got corner plots.</li> <li>Dipti got two adjoining plots in the same row.</li> <li>Bina was the only one who got a plot in each row and each column.</li> <li>Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).</li> <li>The number of mango trees was double the number of teak trees.</li> </ol>

How many pine trees did Chitra receive?

18

15

21

30

Correct Answer

Option 1

Correct Answer

Explanation →

Q35:

CAT 2020 Slot 3

Logical Reasoning > Grids

Hard

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below: <img src="https://balti.aftergrad.in/questions/yKAXrPpqXtphWM8" width="300px"/> The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known: <ol> <li>Abha got 20 trees more than Chitra but 6 trees less than Dipti.</li> <li>The largest number of trees in a plot was 32, but it was not with Abha.</li> <li>The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.</li> <li>Both Abha and Bina got a higher number of plots than Dipti.</li> <li>Only Bina, Chitra and Dipti got corner plots.</li> <li>Dipti got two adjoining plots in the same row.</li> <li>Bina was the only one who got a plot in each row and each column.</li> <li>Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).</li> <li>The number of mango trees was double the number of teak trees.</li> </ol>

Who got the plot with the smallest number of trees and how many trees did that plot have?

Bina, 3 trees

Dipti, 6 trees

Abha, 4 trees

Bina, 4 trees

Correct Answer

Option 1

Correct Answer

Explanation →

Q36:

CAT 2020 Slot 3

Logical Reasoning > Grids

Hard

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below: <img src="https://balti.aftergrad.in/questions/yKAXrPpqXtphWM8" width="300px"/> The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known: <ol> <li>Abha got 20 trees more than Chitra but 6 trees less than Dipti.</li> <li>The largest number of trees in a plot was 32, but it was not with Abha.</li> <li>The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.</li> <li>Both Abha and Bina got a higher number of plots than Dipti.</li> <li>Only Bina, Chitra and Dipti got corner plots.</li> <li>Dipti got two adjoining plots in the same row.</li> <li>Bina was the only one who got a plot in each row and each column.</li> <li>Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).</li> <li>The number of mango trees was double the number of teak trees.</li> </ol>

Which of the following statements is NOT true?

Bina got $32$ pine trees

Dipti got $56$ mango trees

Chitra got $12$ mango trees

Abha got $41$ teak trees

Correct Answer

Option 1

Correct Answer

Explanation →

Q37:

CAT 2020 Slot 3

Logical Reasoning > Grids

Hard

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below: <img src="https://balti.aftergrad.in/questions/yKAXrPpqXtphWM8" width="300px"/> The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known: <ol> <li>Abha got 20 trees more than Chitra but 6 trees less than Dipti.</li> <li>The largest number of trees in a plot was 32, but it was not with Abha.</li> <li>The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.</li> <li>Both Abha and Bina got a higher number of plots than Dipti.</li> <li>Only Bina, Chitra and Dipti got corner plots.</li> <li>Dipti got two adjoining plots in the same row.</li> <li>Bina was the only one who got a plot in each row and each column.</li> <li>Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).</li> <li>The number of mango trees was double the number of teak trees.</li> </ol>

Which column had the highest number of trees?

2

4

3

Cannot be determined

Correct Answer

Option 2

Correct Answer

Explanation →

Q38:

CAT 2020 Slot 2

Logical Reasoning > Grids

Hard

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. $$\newline$$ <p>While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:</p><ol> $$\newline$$ <li>Two adjacent beads along the same row or column are always of different colours.</li> $$\newline$$ <li>There is at least one Green bead between any two Blue beads along the same row or column.</li> $$\newline$$ <li>There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.</li> $\newline$ </ol> $$\newline$$ <p>Every unique, complete arrangement of twenty five beads is called a configuration.</p>

The total number of possible configurations using beads of only two colors is:

Entered answer:

Correct Answer

2

Correct Answer

Explanation →

Q39:

CAT 2020 Slot 2

Logical Reasoning > Grids

Hard

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. $$\newline$$ <p>While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:</p><ol> $$\newline$$ <li>Two adjacent beads along the same row or column are always of different colours.</li> $$\newline$$ <li>There is at least one Green bead between any two Blue beads along the same row or column.</li> $$\newline$$ <li>There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.</li> $\newline$ </ol> $$\newline$$ <p>Every unique, complete arrangement of twenty five beads is called a configuration.</p>

What is the maximum possible number of Red beads that can appear in any configuration?

Entered answer:

Correct Answer

9

Correct Answer

Explanation →

Q40:

CAT 2020 Slot 2

Logical Reasoning > Grids

Hard

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. $$\newline$$ <p>While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:</p><ol> $$\newline$$ <li>Two adjacent beads along the same row or column are always of different colours.</li> $$\newline$$ <li>There is at least one Green bead between any two Blue beads along the same row or column.</li> $$\newline$$ <li>There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.</li> $\newline$ </ol> $$\newline$$ <p>Every unique, complete arrangement of twenty five beads is called a configuration.</p>

What is the minimum number of Blue beads in any configuration?

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q41:

CAT 2020 Slot 2

Logical Reasoning > Grids

Hard

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. $$\newline$$ <p>While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:</p><ol> $$\newline$$ <li>Two adjacent beads along the same row or column are always of different colours.</li> $$\newline$$ <li>There is at least one Green bead between any two Blue beads along the same row or column.</li> $$\newline$$ <li>There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.</li> $\newline$ </ol> $$\newline$$ <p>Every unique, complete arrangement of twenty five beads is called a configuration.</p>

Two Red beads have been placed in 'second row, third column' and 'third row, second column'. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration?

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q42:

CAT 2019 Slot 2

Logical Reasoning > Grids

Medium

<img src="https://balti.aftergrad.in/questions/ld8AksUcxLgW4hI" width="300px"/> $\newline$ <img src="https://balti.aftergrad.in/questions/eLBw9WSiTxqmsl3" width="300px"/> $\newline$ Three pouches (each represented by a filled circle) are kept in each of the nine slots in a $3 \times 3$ grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8. $$\newline$$ <p>There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. Hence the sum of nine pouches in any row or column should be a multiple of 9. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.</p>

What is the total amount of money (in rupees) in the three pouches kept in the first column of the second row?

Entered answer:

Correct Answer

13

Correct Answer

Explanation →

Q43:

CAT 2019 Slot 2

Logical Reasoning > Grids

Medium

<img src="https://balti.aftergrad.in/questions/ld8AksUcxLgW4hI" width="300px"/> $\newline$ <img src="https://balti.aftergrad.in/questions/eLBw9WSiTxqmsl3" width="300px"/> $\newline$ Three pouches (each represented by a filled circle) are kept in each of the nine slots in a $3 \times 3$ grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8. $$\newline$$ <p>There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. Hence the sum of nine pouches in any row or column should be a multiple of 9. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.</p>

How many pouches contain exactly one coin?

Entered answer:

Correct Answer

8

Correct Answer

Explanation →

Q44:

CAT 2019 Slot 2

Logical Reasoning > Grids

Medium

<img src="https://balti.aftergrad.in/questions/ld8AksUcxLgW4hI" width="300px"/> $\newline$ <img src="https://balti.aftergrad.in/questions/eLBw9WSiTxqmsl3" width="300px"/> $\newline$ Three pouches (each represented by a filled circle) are kept in each of the nine slots in a $3 \times 3$ grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8. $$\newline$$ <p>There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. Hence the sum of nine pouches in any row or column should be a multiple of 9. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.</p>

What is the number of slots for which the average amount (in rupees) of its three pouches is an integer?

Entered answer:

Correct Answer

2

Correct Answer

Explanation →

Q45:

CAT 2019 Slot 2

Logical Reasoning > Grids

Medium

<img src="https://balti.aftergrad.in/questions/ld8AksUcxLgW4hI" width="300px"/> $\newline$ <img src="https://balti.aftergrad.in/questions/eLBw9WSiTxqmsl3" width="300px"/> $\newline$ Three pouches (each represented by a filled circle) are kept in each of the nine slots in a $3 \times 3$ grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8. $$\newline$$ <p>There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. Hence the sum of nine pouches in any row or column should be a multiple of 9. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.</p>

The number of slots for which the total amount in its three pouches strictly exceeds Rs. 10 is

Entered answer:

Correct Answer

3

Correct Answer

Explanation →

Q46:

CAT 2018 Slot 2

Logical Reasoning > Grids

Hard

Each of the 23 boxes in the picture below represents a product manufactured by one of the following three companies: Alfa, Bravo and Charlie. The area of a box is proportional to the revenue from the corresponding product, while its centre represents the Product popularity and Market potential scores of the product (out of 20). The shadings of some of the boxes have got erased. <img src="https://balti.aftergrad.in/questions/pUXgY1WCNWOSNQI" width="400px"/> The companies classified their products into four categories based on a combination of scores (out of 20) on the two parameters - Product popularity and Market potential as given below: <table class="question-table"><thead><tr><th></th><th>Promising</th><th>Blockbuster</th><th>Doubtful</th><th>No-hope</th></tr></thead><tbody><tr><td>Product popularity score</td><td>> 10</td><td>> 10</td><td>≤ 10</td><td>≤ 10</td></tr><tr><td>Market potential score</td><td>> 10</td><td>≤ 10</td><td>> 10</td><td>≤ 10</td></tr></tbody></table> The following facts are known: <ol> <li>Alfa and Bravo had the same number of products in the Blockbuster category.</li> <li>Charlie had more products than Bravo but fewer products than Alfa in the No-hope category.</li> <li>Each company had an equal number of products in the Promising category.</li> <li>Charlie did not have any product in the Doubtful category, while Alfa had one product more than Bravo in this category.</li> <li>Bravo had a higher revenue than Alfa from products in the Doubtful category.</li> <li>Charlie had a higher revenue than Bravo from products in the Blockbuster category.</li> <li>Bravo and Charlie had the same revenue from products in the No-hope category.</li> <li>Alfa and Charlie had the same total revenue considering all products.</li> </ol>

Considering all companies' products, which product category had the highest revenue?

Blockbuster

Doubtful

No-hope

Promising

Correct Answer

Option 1

Correct Answer

Explanation →

Q47:

CAT 2018 Slot 2

Logical Reasoning > Grids

Hard

Each of the 23 boxes in the picture below represents a product manufactured by one of the following three companies: Alfa, Bravo and Charlie. The area of a box is proportional to the revenue from the corresponding product, while its centre represents the Product popularity and Market potential scores of the product (out of 20). The shadings of some of the boxes have got erased. <img src="https://balti.aftergrad.in/questions/pUXgY1WCNWOSNQI" width="400px"/> The companies classified their products into four categories based on a combination of scores (out of 20) on the two parameters - Product popularity and Market potential as given below: <table class="question-table"><thead><tr><th></th><th>Promising</th><th>Blockbuster</th><th>Doubtful</th><th>No-hope</th></tr></thead><tbody><tr><td>Product popularity score</td><td>> 10</td><td>> 10</td><td>≤ 10</td><td>≤ 10</td></tr><tr><td>Market potential score</td><td>> 10</td><td>≤ 10</td><td>> 10</td><td>≤ 10</td></tr></tbody></table> The following facts are known: <ol> <li>Alfa and Bravo had the same number of products in the Blockbuster category.</li> <li>Charlie had more products than Bravo but fewer products than Alfa in the No-hope category.</li> <li>Each company had an equal number of products in the Promising category.</li> <li>Charlie did not have any product in the Doubtful category, while Alfa had one product more than Bravo in this category.</li> <li>Bravo had a higher revenue than Alfa from products in the Doubtful category.</li> <li>Charlie had a higher revenue than Bravo from products in the Blockbuster category.</li> <li>Bravo and Charlie had the same revenue from products in the No-hope category.</li> <li>Alfa and Charlie had the same total revenue considering all products.</li> </ol>

Which of the following statements is NOT correct?

Alfa's revenue from Blockbuster products was the same as Bravo's revenue from Promising products.

The total revenue from No-hope products was less than the total revenue from Doubtful products.

Bravo's revenue from Blockbuster products was greater than Alfa's revenue from Doubtful products.

Bravo and Charlie had the same revenues from No-hope products.

Correct Answer

Option 3

Correct Answer

Explanation →

Q48:

CAT 2018 Slot 2

Logical Reasoning > Grids

Hard

Each of the 23 boxes in the picture below represents a product manufactured by one of the following three companies: Alfa, Bravo and Charlie. The area of a box is proportional to the revenue from the corresponding product, while its centre represents the Product popularity and Market potential scores of the product (out of 20). The shadings of some of the boxes have got erased. <img src="https://balti.aftergrad.in/questions/pUXgY1WCNWOSNQI" width="400px"/> The companies classified their products into four categories based on a combination of scores (out of 20) on the two parameters - Product popularity and Market potential as given below: <table class="question-table"><thead><tr><th></th><th>Promising</th><th>Blockbuster</th><th>Doubtful</th><th>No-hope</th></tr></thead><tbody><tr><td>Product popularity score</td><td>> 10</td><td>> 10</td><td>≤ 10</td><td>≤ 10</td></tr><tr><td>Market potential score</td><td>> 10</td><td>≤ 10</td><td>> 10</td><td>≤ 10</td></tr></tbody></table> The following facts are known: <ol> <li>Alfa and Bravo had the same number of products in the Blockbuster category.</li> <li>Charlie had more products than Bravo but fewer products than Alfa in the No-hope category.</li> <li>Each company had an equal number of products in the Promising category.</li> <li>Charlie did not have any product in the Doubtful category, while Alfa had one product more than Bravo in this category.</li> <li>Bravo had a higher revenue than Alfa from products in the Doubtful category.</li> <li>Charlie had a higher revenue than Bravo from products in the Blockbuster category.</li> <li>Bravo and Charlie had the same revenue from products in the No-hope category.</li> <li>Alfa and Charlie had the same total revenue considering all products.</li> </ol>

Which of the following is the correct sequence of numbers of products Bravo had in No-hope, Doubtful, Promising and Blockbuster categories respectively?

2 , 3 , 1 , 2

1 , 3 , 1 , 2

3 , 3 , 1 , 2

1 , 3 , 1 , 3

Correct Answer

Option 2

Correct Answer

Explanation →

Q49:

CAT 2018 Slot 2

Logical Reasoning > Grids

Hard

Each of the 23 boxes in the picture below represents a product manufactured by one of the following three companies: Alfa, Bravo and Charlie. The area of a box is proportional to the revenue from the corresponding product, while its centre represents the Product popularity and Market potential scores of the product (out of 20). The shadings of some of the boxes have got erased. <img src="https://balti.aftergrad.in/questions/pUXgY1WCNWOSNQI" width="400px"/> The companies classified their products into four categories based on a combination of scores (out of 20) on the two parameters - Product popularity and Market potential as given below: <table class="question-table"><thead><tr><th></th><th>Promising</th><th>Blockbuster</th><th>Doubtful</th><th>No-hope</th></tr></thead><tbody><tr><td>Product popularity score</td><td>> 10</td><td>> 10</td><td>≤ 10</td><td>≤ 10</td></tr><tr><td>Market potential score</td><td>> 10</td><td>≤ 10</td><td>> 10</td><td>≤ 10</td></tr></tbody></table> The following facts are known: <ol> <li>Alfa and Bravo had the same number of products in the Blockbuster category.</li> <li>Charlie had more products than Bravo but fewer products than Alfa in the No-hope category.</li> <li>Each company had an equal number of products in the Promising category.</li> <li>Charlie did not have any product in the Doubtful category, while Alfa had one product more than Bravo in this category.</li> <li>Bravo had a higher revenue than Alfa from products in the Doubtful category.</li> <li>Charlie had a higher revenue than Bravo from products in the Blockbuster category.</li> <li>Bravo and Charlie had the same revenue from products in the No-hope category.</li> <li>Alfa and Charlie had the same total revenue considering all products.</li> </ol>

If the smallest box on the grid is equivalent to revenue of Rs.1 crore, then what approximately was the total revenue of Bravo in Rs. crore?

30

24

40

34

Correct Answer

Option 4

Correct Answer

Explanation →

Q50:

CAT 2018 Slot 1

Logical Reasoning > Grids

Easy

You are given an $n \times n$ square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

What is the minimum number of different numerals needed to fill a $ 3\times 3$ square matrix?

Entered answer:

Correct Answer

4

Correct Answer

Explanation →

Q51:

CAT 2018 Slot 1

Logical Reasoning > Grids

Easy

You are given an $n \times n$ square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

What is the minimum number of different numerals needed to fill a $5 \times 5$ square matrix?

Entered answer:

Correct Answer

4

Correct Answer

Explanation →

Q52:

CAT 2018 Slot 1

Logical Reasoning > Grids

Easy

You are given an $n \times n$ square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?

4

16

9

25

Correct Answer

Option 1

Correct Answer

Explanation →

Q53:

CAT 2018 Slot 1

Logical Reasoning > Grids

Easy

You are given an $n \times n$ square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a $5 \times 5$ square matrix?

25

4

16

9

Correct Answer

Option 4

Correct Answer

Explanation →