CAT Questions

Fresh grapes contain 90% water while dry grapes contain 20% water. What is the weight of dry grapes obtained from 20 kg fresh grapes?

1. 2 kg
2. 2.4 kg
3. 2.5 kg
4. 10 kg

A can contains a mixture of two liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?

1. 10
2. 20
3. 21
4. 25

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

1. 1/4
2. 1/3
3. 1/7
4. 1/5

In what ratio must a grocer mix two varieties of tea worth Rs.60 a kg and Rs.65 a kg so that by selling the mixture at Rs.68.20 a kg, he may gain 10%?

1. 3 : 2
2. 3 : 5
3. 3 : 4
4. 4 : 5

The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel C consisting half milk and half water?

1. 8 : 3
2. 4 : 3
3. 2 : 3
4. 7 : 5

A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?

1. Rs. 1,200
2. Rs. 1,500
3. Rs. 1,700
4. Rs. 2,000

A jar contains a mixture of two liquids A and B in the ratio 4:1. When 10 litres of the liquid B is poured into the jar, the ratio becomes 2:3. How many litres of liquid A were contained in the jar?

Nine litres of solution are drawn from a cask containing water. It is replaced with a similar quantity of pure milk. This operation is done twice. The ratio of water to milk in the cask now is 16:9. How much does the cask hold?

There are two containers A and B of milk solution. The ratio of milk and water in container A is 3 : 1 and in container B, it is 4 : 1. How many liters of container B solution has to be added to 20 lts of container A solution such that in the resulting solution the ratio of milk to water should be 19 : 6?

There are two alloys P and Q made up of silver, copper and aluminium. Alloy P contains 45% silver and rest aluminum. Alloy Q contains 30% silver, 35% copper and rest aluminium. Alloys P and Q are mixed in the ratio of 1 : 4.5. The approximate percentages of silver and copper in the newly formed alloy is

1. 33% and 29%
2. 29% and 26%
3. 35% and 30%
4. None of the above

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

1. 27 : 14
2. 27 : 13
3. 27 : 16
4. 27 : 18

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1: 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

1. The same amount of water and liquid B
2. The same amount of liquids B and C
3. More water than liquid B
4. More water than liquid A

The surface area of a sphere is 616 square cm. If its radius is changed so that the area gets reduced 75% then the radius becomes

1. 1.6 cm
2. 2.3 cm
3. 2.5 cm
4. 3.5 cm

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be

1. 20 cm
2. 25 cm
3. 35 cm
4. 50 cm

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is

1. 8960
2. 5120
3. 4830
4. 6420

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder equal their diameters. Then their volumes are proportional, respectively to

1. 2 : 1 : 3
2. 3 : 2 : 1
3. 1 : 2 : 3
4. 1 : 3 : 1

A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and re-solidified into the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to

1. 3
2. 3.5
3. 3
4. 4.5

A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and the frustum are in the ratio

1. 1 : 4
2. 1 : 7
3. 8 : 19
4. 1 : 3

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

1. 2 : 5
2. √3 : 2
3. 3 : 4
4. 1 : √3

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.

1. 168 m2
2. 84 m2
3. 42 m2
4. 22 m2

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

1. 4 : 3
2. 4 : 1
3. 3 : 1
4. 1 : 3

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

1. 17.05
2. 22.45
3. 26.25
4. 27.85

If a right circular cylinder of height 14 is inscribed in a sphere of radius 8, then the volume of the cylinder is

1. 110
2. 220
3. 440
4. 660

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

1. 3√2
2. 3
3. 4
4. √3

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

1. 1300
2. 1340
3. 1480
4. 1520

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?

1. 2 : 3
2. 3 : 4
3. 1 : 2
4. 1 : 4

A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm) will be:

1. 32 π
2. 40.5 π
3. 50 π
4. 81 π

Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer then how many such triangles exist?

1. 5
2. 10
3. 15
4. 21

If in the figure below, angle XYZ = 90° and the length of the arc XZ = 10π, then the area of the sector XYZ is 1. 10π
2. 25π
3. 100π
4. None of the above

AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm. then what will be the length of PN?

1. 17 cm
2. 18 cm
3. 19 cm
4. 20 cm
5. 21 cm

AB, CD and EF are three parallel lines, in that order. Let d1 and d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1 : d2 = 2 : 1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

1. slightly less than 10 units
2. 10 units
3. slightly greater than 10 units
4. slightly less than 20 units
5. slightly greater than 20 units

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

1. -5
2. -6
3. -7
4. -8

If n is a positive integer, then (√3+1)2n - (√3−1)2n is

1. An even positive integer
2. A rational number other than positive integers
3. An odd positive integer
4. An irrational number

The last digit of the number 32015 is

1. 1
2. 3
3. 5
4. 7

When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits, we get 486. Find the number?

1. 81
2. 45
3. 36
4. 54

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p2 - 1) is

1. always divisible by 6, and may or may not be divisible by 12
2. always divisible by 24
3. never divisible by 6
4. always divisible by 12, and may or may not be divisible by 24

Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

1. 1
2. 2
3. 3
4. 4

The number of integers n satisfying -n+2 ≥ 0 and 2n ≥ 4 is

1. 0
2. 1
3. 2
4. 3

What is the right most non-zero digit of the number 302720?

1. 1
2. 3
3. 7
4. 9

The product of all integers from 1 to 100 will have the following numbers of zeros at the end?

1. 19
2. 20
3. 22
4. 24

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

1. 21
2. 25
3. 41
4. 67

The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

1. 55
2. 57
3. 58
4. 59

What are the last two digits of 72008?

1. 01
2. 21
3. 41
4. 61

What is the digit in the unit’s place of 251?

1. 1
2. 2
3. 4
4. 8

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

1. 5
2. 6
3. 7
4. 8

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

1. 16
2. 15
3. 14
4. 13

What is the number of all possible positive integer values of n for which n2 + 96 is a perfect square?

1. 2
2. 4
3. 5
4. Infinite

If N = (11p + 7)(7q – 2)(5r + 1)(3s) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

1. 5
2. 6
3. 7
4. 8
5. 9

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

1. 1777
2. 1785
3. 1875
4. 1877

Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

1. 16
2. 18
3. 36
4. 40