List of top Questions asked in CAT

What is the value of ‘a’?
[I.] Ratio of \( a \) and \( b \) is 3 : 5, where \( b \) is positive.
[II.] Ratio of \( 2a \) and \( b \) is \( \dfrac{12}{10} \), where \( a \) is positive.
There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4. If an even rack has to contain an odd-numbered book and an odd rack contains an even-numbered book, then what is the position of book 4?
[I.] Second book has been put in third rack.
[II.] Third book has been put in second rack.
There are two concentric circles \( C_1 \) and \( C_2 \) with radii \( r_1 \) and \( r_2 \). The circles are such that \( C_1 \) fully encloses \( C_2 \). Then what is the radius of \( C_1 \)?
[I.] The difference of their circumference is \( k \) cm.
[II.] The difference of their areas is \( m \) sq. cm.
What is the price of tea?
[I.] Price of coffee is Rs. 5 more than that of tea.
[II.] Price of coffee is Rs. 5 less than the price of a cold drink which costs three times the price of tea.
In a group of 150 students, find the number of girls.
[I.] Each girl was given 50 paise, while each boy was given 25 paise to purchase goods totaling Rs. 45.
[II.] Girls and boys were given 30 paise each to buy goods totaling Rs. 45.
Find the value of X in terms of ‘a’.
[I.] Arithmetic mean of X and Y is ‘a’ while the geometric mean is also ‘a’.
[II.] $\dfrac{X}{Y} = R$; $X - Y = D$
Is \( n \) odd?
[I.] \( n \) is divisible by 3, 5, 7, and 9.
[II.] \( 0 < n < 400 \)
Find \( 2 \otimes 3 \), where \( 2 \otimes 3 \) need not be equal to \( 3 \otimes 2 \)
[I.] \( 1 \otimes 2 = 3 \)
[II.] \( a \otimes b = \dfrac{a + b}{a} \), where \( a \) and \( b \) are positive.

Find the length of AB if $\angle YBC = \angle CAX = \angle YOX = 90^\circ$.
[I.] Radius of the arc is given.
[II.] \( OA = 5 \)

Radha and Rani appeared in an examination. What was the total number of questions?
[I.] Radha and Rani together solved 20% of the paper.
[II.] Radha alone solved \( \dfrac{3}{5} \) of the paper solved by Rani.
There are two containers: the first contains 500 ml of alcohol, while the second contains 500 ml of water. Three cups of alcohol from the first container is taken out and is mixed well in the second container. Then three cups of this mixture is taken out and is mixed in the first container. Let A denote the proportion of water in the first container and B denote the proportion of alcohol in the second container. Then
What is the digit in the unit’s place of 251?
A, B, C, D, ..., X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 point. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, a ranking list is published which is in accordance with the alphabetical order. Then
A number is formed by writing first 54 natural numbers in front of each other as 12345678910111213... Find the remainder when this number is divided by 8.

Answer the questions based on the following information.
Mr Bankatlal acted as a judge for the beauty contest. There were four participants, viz. Ms Andhra Pradesh, Ms Uttar Pradesh, Ms West Bengal and Ms Maharashtra. Mrs Bankatlal, who was very anxious about the result, asked him about it as soon as he was back home. Mr Bankatlal just told that the one who was wearing the yellow saree won the contest. When Mrs Bankatlal pressed for further details, he elaborated as follows: All of them were sitting in a row.
All of them wore sarees of different colours, viz. green, yellow, white, red. There was only one runner-up and she was sitting beside Ms. Maharashtra. The runner-up was wearing the green saree. Ms West Bengal was not sitting at the ends and was not the runner up. The winner and the runner-up are not sitting adjacent to each other. Ms Maharashtra was wearing white saree. Ms Andhra Pradesh was not wearing the green saree. Participants wearing yellow saree and white saree were at the ends.
Who wore the red saree?

Answer the questions based on the following information.
Mr Bankatlal acted as a judge for the beauty contest. There were four participants, viz. Ms Andhra Pradesh, Ms Uttar Pradesh, Ms West Bengal and Ms Maharashtra. Mrs Bankatlal, who was very anxious about the result, asked him about it as soon as he was back home. Mr Bankatlal just told that the one who was wearing the yellow saree won the contest. When Mrs Bankatlal pressed for further details, he elaborated as follows: All of them were sitting in a row.
All of them wore sarees of different colours, viz. green, yellow, white, red. There was only one runner-up and she was sitting beside Ms. Maharashtra. The runner-up was wearing the green saree. Ms West Bengal was not sitting at the ends and was not the runner up. The winner and the runner-up are not sitting adjacent to each other. Ms Maharashtra was wearing white saree. Ms Andhra Pradesh was not wearing the green saree. Participants wearing yellow saree and white saree were at the ends.
Ms. West Bengal was sitting adjacent to

Answer the questions based on the following information.
Mr Bankatlal acted as a judge for the beauty contest. There were four participants, viz. Ms Andhra Pradesh, Ms Uttar Pradesh, Ms West Bengal and Ms Maharashtra. Mrs Bankatlal, who was very anxious about the result, asked him about it as soon as he was back home. Mr Bankatlal just told that the one who was wearing the yellow saree won the contest. When Mrs Bankatlal pressed for further details, he elaborated as follows: All of them were sitting in a row.
All of them wore sarees of different colours, viz. green, yellow, white, red. There was only one runner-up and she was sitting beside Ms. Maharashtra. The runner-up was wearing the green saree. Ms West Bengal was not sitting at the ends and was not the runner up. The winner and the runner-up are not sitting adjacent to each other. Ms Maharashtra was wearing white saree. Ms Andhra Pradesh was not wearing the green saree. Participants wearing yellow saree and white saree were at the ends.
Which saree was worn by Ms Andhra Pradesh?

Answer the questions based on the following information.
Mr Bankatlal acted as a judge for the beauty contest. There were four participants, viz. Ms Andhra Pradesh, Ms Uttar Pradesh, Ms West Bengal and Ms Maharashtra. Mrs Bankatlal, who was very anxious about the result, asked him about it as soon as he was back home. Mr Bankatlal just told that the one who was wearing the yellow saree won the contest. When Mrs Bankatlal pressed for further details, he elaborated as follows: All of them were sitting in a row.
All of them wore sarees of different colours, viz. green, yellow, white, red. There was only one runner-up and she was sitting beside Ms. Maharashtra. The runner-up was wearing the green saree. Ms West Bengal was not sitting at the ends and was not the runner up. The winner and the runner-up are not sitting adjacent to each other. Ms Maharashtra was wearing white saree. Ms Andhra Pradesh was not wearing the green saree. Participants wearing yellow saree and white saree were at the ends.
Who was the runner-up?

I started climbing up the hill at 6 a.m. and reached the top of the temple at 6 p.m. Next day I started coming down at 6 a.m. and reached the foothill at 6 p.m. I walked on the same road. The road is so short that only one person can walk on it. Although I varied my pace on my way, I never stopped on my way. Then which of the following must be true?
What is the maximum current gain possible?
If the USA dollar becomes cheap by 12% over its original cost and the cost of German mark increased by 20%, what will be the gain? (The selling price is not altered.)
You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg and each emerald weighs 0.4 kg. Your bag can carry at most 12 kg. What should you collect to get the maximum wealth?
How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?
I have one-rupee coins, 50-paisa coins and 25-paisa coins. The number of coins are in the ratio 2.5 : 3 : 4. If the total amount with me is Rs. 210, find the number of one-rupee coins.
My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates as he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate costs Rs. 1. The cost of an apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if the number of chocolates, biscuits, and apples bought were all integers?