List of top Questions asked in CAT

Gopal went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of oranges he can buy is:

If $x$ is a positive integer such that $2x + 12$ is divisible by $x$, then the number of possible values of $x$ is:

A sum of money compounded annually becomes Rs.625 in two years and Rs.675 in three years. The rate of interest per annum is:

In a six-node network, two nodes are connected to all the other nodes. Of the remaining four, each is connected to four nodes. What is the total number of links in the network?

In Sivakasi, each boy’s quota of matchsticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him. Which of the following is the possible number of sticks assigned to each boy?

A third standard teacher gave a simple multiplication exercise to the kids. But one kid reversed the digits of both the numbers and carried out the multiplication and found that the product was exactly the same as the one expected by the teacher. Only one of the following pairs of numbers will fit in the description. Which one is that?

Let $k$ be a positive integer such that $k + 4$ is divisible by 7. Then the smallest positive integer $n>2$ such that $k + 2n$ is also divisible by 7 equals:

Find the minimum integral value of $n$ such that the division $55n/124$ leaves no remainder.

What is the greatest power of 5 which can divide $80!$ exactly?

A one rupee coin is placed on a table. The maximum number of similar one rupee coins which can be placed on the table, around it, with each one of them touching it and only two others is:

$x, y, z$ are three positive integers such that $x>y>z$. Which of the following is closest to the product $xyz$?

A calculator has two memory buttons, A and B. Value 1 is initially stored in both memory locations. The following sequence of steps is carried out five times:
- Add 1 to B
- Multiply A to B
- Store result in A
What is the value stored in memory location A after this procedure?

Let $Y = \min((x + 2), (3 - x))$. What is the maximum value of $Y$ for $0 \le x \le 1$?

Three machines, A, B and C can be used to produce a product. Machine A takes 60 hours to produce a million units. Machine B is twice as fast as A. Machine C takes the same time as A and B together. How much time will be required to produce a million units using all three machines?

What was the ratio of schools having laboratory to those having library?

A player rolls a die and receives the same number of rupees as the number of dots on the face that turns up. What should the player pay for each roll if he wants to make a profit of one rupee per throw of the die in the long run?

There are 3 clubs A, B \& C in a town with 40, 50 \& 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?

A square piece of cardboard of side 10 inches is taken and four equal square pieces are removed at the corners, such that the side of this square piece is also an integer value. The sides are then turned up to form an open box. Then the maximum volume such a box can have is:

Let the consecutive vertices of a square S be A, B, C \& D. Let E, F \& G be the mid-points of the sides AB, BC \& AD respectively of the square. Then the ratio of the area of the quadrilateral EFDG to that of the square S is nearest to:

A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?

The number of integers $n$ satisfying $-n + 2 \ge 0$ and $2n \ge 4$ is:

How many schools had none of the three viz., laboratory, library or play-ground?

The sum of two integers is 10 and the sum of their reciprocals is $\frac{5}{12}$. Then the larger of these integers is:

If $y = f(x)$ and $f(x) = \dfrac{1 - x}{1 + x}$, which of the following is true?

$2^{73} - 2^{72} - 2^{71}$ is the same as: