List of top Quantitative Aptitude Questions asked in CAT

Four cities are connected by roads as shown. In how many ways can you start at a city and come back to it without travelling the same road more than once?

Find the maximum value of \( y = \min\left(\frac{1}{2} - \frac{3x^2}{4}, \frac{5x^2}{4}\right) \) for \( 0<x<1 \)
If a spherical ball is placed on a hollow cone with same diameter, what portion will be outside?

@ (A,B) = average of A and B
*(A,B) = product of A and B
/(A,B) = A divided by B

Which expression gives the sum of A and B?

Is the average of the largest and the smallest of four given numbers greater than the average of the four numbers? I. The difference between the largest and the second largest numbers is greater than the difference between the second smallest and the smallest numbers.
I II. The difference between the largest and the second largest numbers is less than the difference between the second largest and the second smallest numbers.
ABC is an equilateral triangle with AB = AC, and B is 2 km north of A. A person walks from B parallel to AC, stops when directly east of C (point D). Where is D with respect to A?

@ (A,B) = average of A and B
*(A,B) = product of A and B
/(A,B) = A divided by B

If A = 2 and B = 4, what is the value of \(@(/(*(A, B), B), A)\)?

How many more hours would P take compared to Q to complete the journey?
A group of workers starts a job. From Day 2 onward, 1 worker is removed each day. The job ends when the last worker is withdrawn. If all had worked full time, the work would’ve been done in 2/3 time. How many workers were initially in the group?
Minimum value of \( K \) for which \( x + y + z = K \), \( x<y<z \) does NOT uniquely determine the triplet?
Given: \( x<0 \), \( 0<y<1 \), \( z>1 \). Which of the following may be false?
A girl counts fingers: 1 = thumb, 2 = index, ..., 5 = little finger, then reverses. Count reaches 1994. Which finger does she end on?
P and Q start from opposite ends, with Q starting an hour later and at twice the speed. When P has covered 1/6th the distance, Q has also covered the same. Where do they meet?
In a locality of 100 families: 45 have radios, 75 have TVs, 25 have VCRs. 10 have all three. Every VCR owner has TV. 25 have radio only. How many families have only TV?
What is the total distance walked by the person (from B to D to E)?
A slab of ice 8 in × 11 in × 2 in is melted and recast into a cylinder of 8 in diameter. What is the length of the cylinder?
Let \( x<0.50 \), \( 0<y<1 \), \( z>1 \). What is the median of x, y, z?
A five-digit number is formed using digits 1, 3, 5, 7, and 9 without repetition. What is the sum of all such possible numbers?
The function given by \( f(x) = |x|^3 \) is
The sum of two odd functions
John bought 5 mangoes and 10 oranges for Rs. 40. He then returned 1 mango and got 2 oranges in exchange. What is the price of one orange?
85 children went to an amusement park with 3 rides. Each ride costs Re.1. 20 children took all 3 rides, 55 took at least 2 rides, and the total receipt was Rs.145. How many children did not take any rides?
Based on the same amusement park data, how many children took exactly one ride?

The line AB is 6 metres and is tangent to the inner of two concentric circles at point C. Radii of the two circles are integers. What is the radius of the outer circle?

Three identical cones with base radius \( r \) are placed so each touches the other two. What is the radius of the circle drawn through their vertices?