List of top Questions asked in CAT

Three boys had a few Coffee Bite toffees with them. The number of toffees with the second were four more than those with the first and the number of toffees with the third were four more than those with the second. How many toffees were there in all?
I. The number of toffees with each of them is a multiple of 2.
II. The first boy ate up four toffees from what he had and the second boy ate up six toffees from what he had and the third boy gave them two toffees each from what he had and the number of toffees remaining with each of them formed a geometric progression.

If the selling price were to be increased by $10%$, the sales would reduce by $10%$. In what ratio would profits change?
I. The cost price remains constant.
II. The cost price increased $10%$.

What is the average weight of the 3 new team members who are recently included into the team?
I. The average weight of the team increases by $20$ kg.
II. The 3 new men substitute earlier members whose weights are $64$ kg, $75$ kg and $66$ kg.

If twenty sweets are distributed among some boys and girls such that each girl gets $2$ sweets and each boy gets $3$ sweets, what is the number of boys and girls?
I. The number of girls is not more than five.
II. If each girl gets $3$ sweets and each boy gets $2$ sweets, the number of sweets required for the children will still be the same.

A and B work at digging a ditch alternately for a day each. If A can dig a ditch in $a$ days and B can dig that ditch in $b$ days, will work get done faster if A begins the work?
I. $n$ is a positive integer such that $n\left(\frac{1}{a} + \frac{1}{b}\right) = 1$.
II. $b>a$.

Is segment $PQ$ greater than segment $RS$?
I. $PB>RE$, $BQ = ES$.
II. $B$ is a point on $PQ$, $E$ is a point on $RS$.

Is the distance from the office to home less than the distance from the cinema hall to home?
I. The time taken to travel from home to office is as much as the time taken from home to the cinema hall, both distances being covered without stopping.
II. The road from the cinema hall to home is bad and speed reduces, as compared to that on the road from home to the office.

The winning relay team in a high school sports competition clocked $48$ minutes for a distance of $13.2$ km. Its runners A, B, C, and D maintained speeds of $15$ kmph, $16$ kmph, $17$ kmph, and $18$ kmph respectively. What is the ratio of the time taken by B to that taken by D?

A dealer offers a cash discount of $20%$ and still makes a profit of $20%$, when he further allows $16$ articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?

There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits $6$ litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?

Which is the least number that must be subtracted from $1856$, so that the remainder when divided by $7$, $12$, and $16$ is $4$?

A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?

$\log_{6} 216 \sqrt{6}$ is:

Along a road lie an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then the number of stones is:

Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after travelling distances of 40, 50 and 60 metres. The maximum distance that the fourth could have traveled is (approximately)….

Fourth term of an arithmetic progression is $8$. What is the sum of the first $7$ terms of the arithmetic progression?

What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?

It takes the pendulum of a clock 7 seconds to strike 4 o’clock. How much time will it take to strike 11 o’clock?

A man buys spirit at Rs. 60 per litre, adds water to it and then sells it at Rs. 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?

Shyam went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is $\frac{3}{4}$ times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Shimla. If the average speed for the entire journey was 49 kmph, what was the average speed from Chandigarh to Shimla?

Given that $a>b$ then the relation $Ma[md(a), \ mn(a, b)] = mn[a, \ md(Ma(a, b))]$ does not hold if:

If one root of $x^{2} - 7 + 12 = 0$ is $4$, while the equation $x^{2} - 7x + q = 0$ has equal roots, then the value of $q$ is:

If the harmonic mean between two positive numbers is to their geometric mean as $12 : 13$, then the numbers could be in the ratio:

Value of $Ma \left[ md(a), \ mn(md(b), a), \ mn(ab, md(ac)) \right]$ where $a = -2$, $b = -3$, $c = 4$ is:

A water tank has three taps A, B, and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour, and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?