CAT (QA) PYQs

Arun's present age in years is $40\%$ of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?

A person can complete a job in $120$ days. He works alone on Day $1$. On Day $2$, he is joined by another person who also can complete the job in exactly $120$ days. On Day $3$, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?

An elevator has a weight limit of $630$ kg. It is carrying a group of people of whom the heaviest weighs $57$ kg and the lightest weighs $53$ kg. What is the maximum possible number of people in the group?

A man leaves his home and walks at a speed of $12$ km per hour, reaching the railway station $10$ minutes after the train had departed. If instead he had walked at a speed of $15$ km per hour, he would have reached the station $10$ minutes before the train's departure. The distance (in km) from his home to the railway station is

Ravi invests $50\%$ of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs. $59500$, then Ravi's total monthly savings (in Rs.) is

If a seller gives a discount of $15 \%$ on retail price, she still makes a profit of $2 \%$. Which of the following ensures that she makes a profit of $20\%$?

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by $75\%$. The ratio of the original speed of the motor boat to the speed of the river is

Suppose, $C1, C2, C3, C4,$ and $C5$ are five companies. The profits made by $C1, C2,$ and $C3$ are in the ratio $9: 10: 8$ while the profits made by $C2, C4,$ and $C5$ are in the ratio $18:19:20$. If $C5$ has made a profit of Rs $19$ crore more than $C1$, then the total profit (in Rs) made by all five companies is

The number of girls appearing for an admission test is twice the number of boys. If $30\%$ of the girls and $45\%$ of the boys get admission, the percentage of candidates who do not get admission is

A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio $7: 17: 16$ for popcorn and $6: 15: 14$ for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio

In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys $80 \mathrm{~kg}$ good mangoes and $40 \mathrm{~kg}$ medium quality mangoes from the market and then sells all these at a common price which is $10 \%$ less than the price at which he bought the good ones. His overall profit is

If Fatima sells $60$ identical toys at a $40\%$ discount on the printed price, then she makes $20\%$ profit. Ten of these toys are destroyed in a fire. While selling the rest, how much discount$\%$ should be given on the printed price so that she can make the same amount of profit?

If $a$ and $b$ are integers of opposite signs such that $(a+3)^{2}: b^{2}=9: 1$ and $(a-1)^{2}:(b-1)^{2}=4: 1$, then the ratio $a^{2}: b^{2}$ is

A class consists of $20$ boys and $30$ girls. In the mid-semester examination, the average score of the girls was $5$ higher than that of the boys. In the final exam, however, the average score of the girls dropped by $3$ while the average score of the entire class increased by $2$. The increase in the average score of the boys is

The area of the closed region bounded by the equation $| x | + | y | = 2$ in the two-dimensional plane is

From a triangle $ABC$ with sides of lengths $40$ ft, $25$ ft and $35$ ft, a triangular portion $GBC$ is cut off where $G$ is the centroid of $ABC$. The area, in sq ft, of the remaining portion of triangle $ABC$ is

Let $ABC$ be a right-angled isosceles triangle with hypotenuse $BC$. Let $BQC$ be a semi-circle, away from $A$, with diameter $BC$. Let $BPC$ be an arc of a circle centred at $A$ and lying between $BC$ and $BQC$. If $AB$ has length $6$ cm ,then the area, in sq. cm, of the region enclosed by $BPC$ and $BQC$ is:

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio $1: 1 : 8: 27: 27$. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to :

A ball of diameter $4$ cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is $3$ cm, while its volume is $9 \pi$ cm$^3$. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is

Let $A B C$ be a right-angled triangle with $B C$ as the hypotenuse. Lengths of $A B$ and AC are $15 \mathrm{~km}$ and $20 \mathrm{krn}$, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of $30 \mathrm{~km}$ per hour is

Suppose, $\log_3 x = \log_{12} y = a$, where $x, y$ are positive numbers. If $G$ is the geometric mean of x and y, and $\log_6 G$ is equal to

If $x + 1 = x^2$ and $x > 0$, then $2x^4$ is

The value of $\log_{0.008} \sqrt{5} + \log_{\sqrt{3}} 81 - 7$ is equal to

If $9^{2 x-1}-81^{x-1}=1944$, then $x$ is

The number of solutions $(x, y, z)$ to the equation $x - y - z = 25$, where $x, y$, and $z$ are positive integers such that $x \le 40, y \le 12$, and $z \le 12$ is

For how many integers $n$, will the inequality $(n - 5) (n - 10) - 3(n − 2) \leq 0$ be satisfied?

If $f_{1}(x)=x^{2}+11 x+n$ and $f_{2}(x)=x$, then the largest positive integer $n$ for which the equation $f_{1}(x)=f_{2}(x)$ has two distinct real roots, is

If $a, b, c,$ and $d$ are integers such that $a + b + c + d = 30$, then the minimum possible value of $(a - b)^2 + (a - c)^2 + (a - d)^2$ is

Let $AB, CD, EF, GH,$ and $JK$ be five diameters of a circle with center at $O$. In how many ways can three points be chosen out of $A, B, C, D, E, F, G, H, J, K,$ and $O$ so as to form a triangle?

The shortest distance of the point $\left(\frac{1}{2}, 1\right)$ from the curve $y=|x-1|+|x+1|$ is

If the square of the $7$th term of an arithmetic progression with positive common difference equals the product of the $3$rd and $17$th terms, then the ratio of the first term to the common difference is

In how many ways can $7$ identical erasers be distributed among $4$ kids in such a way that each kid gets at least one eraser but nobody gets more than $3$ erasers?

If $f(x) = \frac{5x + 2}{3x - 5}$ and $g(x) = x^2 - 2x - 1$, then the value of $g(f(f(3)))$ is

Let $a_{1}, a_{2}, \ldots \ldots . . . a_{3 n}$ be an arithmetic progression with $a_{1}=3$ and $a_{2}=7$. If $a_{1}+a_{2}+\ldots .+a_{3 n}=1830$, then what is the smallest positive integer $m$ such that $m\left(a_{1}+a_{2}+\ldots .+a_{n}\right)>1830$ ?