List of top Questions asked in CAT

A dealer deals only in colour TVs and VCRs. He wants to spend up to Rs.12 lakhs to buy 100 pieces. He can purchase a colour TV at Rs.10,000 and a VCR at Rs.15,000. He can sell a colour TV at Rs.12,000 and a VCR at Rs.17,500. His objective is to maximize profits. Assume that he can sell all the items that he stocks

In a game played by two people there were initially N match sticks kept on the table. A move in the game consists of a player removing either one or two matchsticks from the table. The one who takes the last matchstick loses. Players make moves alternately. The player who will make the first move is A. The other player is B.

$\left[ \frac{x^{-1} - y^{-1}}{x^2 - y^2} \right]>1$?
I. $x + y>0$
II. $x$ and $y$ are positive integers and each is greater than 2.

Saira, Mumtaz, and Zeenat have a ball, a pen and a pencil, and each girl has just one object in hand. Among the following statements, only one is true and the other two are false.
I. Saira has a ball.
II. Mumtaz does not have the ball.
III. Zeenat does not have the pen.
Who has the ball?

Albert, David, Jerome and Tommy were plucking mangoes in a grove to earn some pocket money during the summer holidays. Their earnings were directly related to the number of mangoes plucked and had the following relationship:
Jerome got less money than Tommy. Jerome and Tommy together got the same amount as Albert and David taken together. Albert and Tommy together got less than David and Jerome taken together.
Who earned the most pocket money? Who plucked the least number of mangoes?

If \( xy + yz + zx = 0 \), then \( (x + y + z)^2 \) equals

If equal numbers of people are born on each day, find the approximate percentage of the people whose birthday will fall on 29\(^\text{th}\) February (if we are to consider people born in the 20\(^\text{th}\) century and assuming no deaths).

The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50, and Rs.5.00 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupee notes on the counter payment. How many notes did Rahul give?

A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got Rs. 94.60 in all. When they divide the money among themselves, A, B and C will respectively get (in Rs.):

The set of natural numbers is partitioned into subsets $S_1 = \{1\}$, $S_2 = \{2, 3\}$, $S_3 = \{4, 5, 6\}$, $S_4 = \{7, 8, 9, 10\}$ and so on. The sum of the elements of subset $S_{50}$ is:

A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the same way and this process is continued indefinitely. If a side of the first square is 8 cm, the sum of the areas of all the squares thus formed (in sq.cm) is:

The roots of the equation $a x^2 + 3x + 6 = 0$ will be reciprocal to each other if the value of $a$ is:

A car after traveling 18 km from a point A developed some problem in the engine and speed became $\frac{4}{5}$ of its original speed. As a result, the car reached point B 45 minutes late. If the engine had developed the same problem after traveling 30 km from A, then it would have reached B only 36 minutes late. The original speed of the car (in km/h) and the distance between points A and B (in km) is:

If $n$ is any positive integer, then $n^3 - n$ is divisible:

The value of $\frac{(1 - d^3)}{(1 - d)}$ is:

Gopal went to a fruit market with a 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:

Consider the following steps:
1. Put $x = 1$, $y = 2$
2. Replace $x$ by $xy$
3. Replace $y$ by $y + 1$
4. If $y = 5$ then go to step 6 otherwise go to step 5
5. Go to step 2
6. Stop
Then the final value of $x$ equals:

In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective products in the stockpile?

From any two numbers $x$ and $y$, we define $x * y = x + 0.5y - xy$. Suppose that both $x$ and $y$ are greater than 0.5. Then $x * x>y$ if:

Consider a function $f(k)$ defined for positive integers $k = 1, 2, $; the function satisfies the condition
$f(1) + f(2) + + f(k) = p( p^{k-1} )$ Where $p$ is a fraction i.e. $0<p<1$. Then $f(k)$ is given by:

116 people participated in a singles tennis tournament of knockout format. The players are paired up in the first round, winners of the first round are paired in the second round, and so on till the final is played between two players. If after any round, the number of players is odd, one player is given a bye (he skips that round and plays the next round with the winners). Find the total number of matches played in the tournament.

There were $x$ pigeons and $y$ mynahs in a cage. One fine morning $p$ of them escaped to freedom. If the bird keeper, knowing only that $p = 7$, was able to figure out without looking into the cage that at least one pigeon had escaped, then which of the following does not represent a possible $(x, y)$ pair?

The remainder when $26^{60}$ is divided by 5 equals:

Mr. X enters a positive integer Y in an electronic calculator and then goes on pressing the square repeatedly. Then:

What is the sum of the following series:
$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + + \frac{1}{100 \times 101}$