List of top Quantitative Aptitude Questions asked in CAT

Based on the figure, what is the value of x, if y = 10?

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

Ujakar and Keshab attempted to solve a quadratic equation.
- Ujakar made a mistake in writing down the constant term and got roots (4, 3).
- Keshab made a mistake in writing down the coefficient of $x$ and got roots (3, 2).
What will be the exact roots of the original quadratic equation?

Fresh grapes contain 90% water by weight while dried grapes contain 20% water. What is the weight of dry grapes available from 20 kg of fresh grapes?

If $a, b, c, d$ are four positive real numbers such that $abcd = 1$, what is the minimum value of $(1+a)(1+b)(1+c)(1+d)$?

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom's steps. Shyama gets to the top after taking 25 steps, while Vyom takes 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

The batting average (BA) of a Test batsman is computed from runs scored and innings played — completed innings and incomplete innings (not out) in the following manner:

\[ r_1 = \text{Number of runs scored in completed innings} \] \[ n_1 = \text{Number of completed innings} \] \[ r_2 = \text{Number of runs scored in incomplete innings} \] \[ n_2 = \text{Number of incomplete innings} \]

\[ BA = \frac{r_1 + r_2}{n_1} \]

To better assess a batsman’s accomplishments, the ICC is considering two other measures MBA1 and MBA2, defined as follows:

\[ MBA_1 = \frac{r_1}{n_1} + \frac{n_2}{n_1} \max \left( 0, \left( \frac{r_2}{n_2} - \frac{r_1}{n_1} \right) \right) \]

\[ MBA_2 = \frac{r_1 + r_2}{n_1 + n_2} \]

The petrol consumption rate of a new model car ’Palto’ depends on its speed and may be described by the graph below

There are five machines A, B, C, D, and E situated on a straight line at distances of 10 metres, 20 metres, 30 metres, 40 metres and 50 metres respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw material is located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is received.

Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the first second, and C has sent a message at the beginning of the 5th second and B at the beginning of the 6th second, and E at the beginning of the 10th second. How much distance in metres has the robot travelled since the beginning of the day, when it notices the message of E? Assume that the speed of movement of the robot is 10 metres per second.

Directions for the next 2 questions: There are three bottles of water, A, B, C, whose capacities are 5 litres, 3 litres, and 2 litres respectively. For transferring water from one bottle to another and to drain out the bottles, there exists a piping system. The flow through these pipes is computer controlled. The computer that controls the flow through these pipes can be fed with three types of instructions, as explained below:

Instruction type	Explanation for the instruction
FILL (X, Y)	Fill bottle labeled X from the water in bottle labeled Y, where the remaining capacity of X is less than or equal to the amount of water in Y.
EMPTY (X, Y)	Empty out water in bottle labeled X into bottle labeled Y, where the amount of water in X is less than or equal to remaining capacity of Y.
DRAIN (X)	Drain out all the water contained in bottle labeled X.

Initially, A is full with water, and B and C are empty.

Directions for the next 3 questions: For three distinct real positive numbers x, y and z, let

$f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$

$g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$

$h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$

$j(x, y, z) = \min(\min(x, y), \min(y, z), \min(z, x))$

$m(x, y, z) = \max(x, y, z)$

$n(x, y, z) = \min(x, y, z)$

Directions for the next 2 questions:

For real numbers x, y, let

f(x, y) = Positive square-root of (x + y), if $(x+y)^{0.5}$ is real
f(x, y) = $(x+y)^2$; otherwise

g(x, y) = $(x+y)^2$, if $\sqrt{(x+y)}$ is real
g(x, y) = $-(x+y)$ otherwise