List of top Questions asked in CAT

Six students (A, B, C, D, E, F) are seated in a circle. A is not adjacent to B, and C is adjacent to D. How many arrangements are possible?
Four teams (P, Q, R, S) play a tournament. Each team plays every other team once. P wins 2 matches, Q wins 1, R wins 0. How many matches did S win?
Using the same table, what is the percentage increase in sales of Product B from January to February?

The following table shows the sales (in thousands) of four products over three months. What is the total sales of Product A across all months? 

If $\log_2 (x) + \log_4 (x) = 5$, what is $x$? 
 

A pie chart shows expenses: Rent (40%), Food (25%), Transport (20%), Others (15%). If total expenses are Rs. 20,000, what is the amount spent on Food?
Five friends (A, B, C, D, E) sit in a row. A is to the left of B, and C is not at an end. How many arrangements are possible?

If the sum of two numbers is 15 and their product is 56, what is the sum of their reciprocals? 
 

A shopkeeper sells an item at a 20% discount but still makes a 20% profit. If the cost price is Rs. 100, what is the marked price? 
 

A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. If no digit is to be repeated, in how many ways can the student do so?

What is the area of a triangle with vertices at (0,0), (3,0), and (0,4)? 
 

Find the complete set of values that satisfy the relations \[ |x - 3|<2 \quad \text{and} \quad |x| - 2|<3 \]
If \( x \) is a real number and \( \lfloor x \rfloor \) is the greatest integer \( \leq x \), then \[ 3\lfloor x \rfloor + 2 - \lfloor x \rfloor = 0 \] Will the above equation have any real root?

A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both are open, how long will it take to fill the tank? 
 

What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8?

What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, ........? 
 

\( A, B, C \) can independently do a work in 15, 20, and 30 days respectively. They work together for some time after which \( C \) leaves. A total of ₹18000 is paid for the work and \( B \) gets ₹6000 more than \( C \). For how many days did \( A \) work?

A rectangle's length is twice its breadth. If the perimeter is 60 cm, what is its area? 
 

A car \( A \) starts from a point \( P \) towards another point \( Q \). Another car \( B \) starts (also from \( P \)) 1 hour after the first car \( A \), and overtakes it after covering 30% of the distance \( PQ \). After that, the cars continue. On reaching \( Q \), car \( B \) reverses and meets car \( A \), after covering \( 2\frac{1}{3} \) of the distance \( QP \). Find the time taken by car \( B \) to cover the distance \( PQ \) (in hours).

A train travels 360 km at a uniform speed. If the speed is increased by 5 km/h, the journey takes 1 hour less. Find the original speed. 
 

A rectangle is drawn such that none of its sides has length greater than ‘\( a \)’. All lengths less than ‘\( a \)’ are equally likely. The chance that the rectangle has its diagonal greater than ‘\( a \)’ (in terms of %) is:
The side of an equilateral triangle is 10 cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same, the triangle is divided into smaller equilateral triangles, each of which has sides of length 1 cm. How many such small triangles are formed?
Consider a sequence \( S \) whose \( n \)th term \( T_n \) is defined as \( T_n = 1 + \frac{3}{n} \), where \( n = 1, 2, \ldots \). Find the product of all the consecutive terms of \( S \) starting from the 4th term to the 60th term.

A number is divisible by 3 and 5. What is the smallest such number greater than 100? 
 

Find the remainder when \( 2^{1040} \) is divided by 131.