**Note:**These Quant questions have been selected from

**1000+**CAT Quant Practice Problems with video solutions of Bodhee Prep’s Online CAT Quant Course

Question 1:

Question 1:

ABC is an isosceles triangle with sides AB=AC=5. D is a point in between B and C such that BD=2 and DC=4.5. Find the length of AD.

Topic: triangles

[1] \(2\sqrt 2 \)

[2] \(3\)

[3] \(4\)

[4] \(2\sqrt 3 \)

Question 2:

Question 2:

Let \(P=\frac{1}{{{10}^{2}}+1}+\frac{2}{{{10}^{2}}+2}+\frac{3}{{{10}^{2}}+3}+...+\frac{10}{{{10}^{2}}+10}\) then which of the following is the best approximate value of P.

Topic: series

[1] \(0.42\)

[2] \(0.52\)

[3] \(0.57\)

[4] \(0.62\)

Question 3:

Question 3:

How many rectangles can be formed by taking the four vertices of 18-sided regular polygon.

Topic: permutation and combination

Question 4:

Question 4:

Find the smallest number which has 6 distinct factors

Topic: factors

Question 5:

Question 5:

If Rohit drives at 20kmph, he reaches office at 3 pm. If he drives at 30kmph, he reaches office at 11 am. At what speed he should drive if he wishes to reach office at 1 pm.

Topic: speed time and distance

[1] 25 kmph

[2] 24 kmph

[3] 27 kmph

[4] None of these

Question 6:

Question 6:

A five digit number N has all digits different and contains digits 1,3,4,5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens place digit of N.

Topic: divisibility

[1] 1

[2] 3

[3] 4

[4] 5

Question 7:

Question 7:

If \(\alpha \) and \( - \alpha \) are the roots of the equation \(2{x^3} - 5{x^2} - 8x + n = 0\) . Find the value of n?

Topic: equations

Question 8:

Question 8:

The bases of a trapezoid have lengths 10 and 15. A segment parallel to the bases passes through the point of intersection of the diagonals and extends from one side to the other. Find the length of the segment

Topic: quadrilaterals

[1] 5

[2] \(\sqrt {150} \)

[3] \(\frac{{25}}{{\sqrt 2 }}\)

[4] 12

Question 9:

Question 9:

The value of a fraction represented in base n is \(0.\overline {111} \) while in base 2n it takes the simpler form 0.2n. What is n?

Topic: base system

Question 10:

Question 10:

If Gopal and Harish can complete a work together in 20 days, and Gopal alone can do the same work in 32 days. When both work together their efficiencies reduce by 20% compare to the efficiency when they would have worked alone. Find the number of days Harish alone takes to complete the same work.

Topic: work and time

Question 11:

Question 11:

In a survey done across 115 people about their favorite TV Serials: Sathiya, Kumkum, and Balika.

The following results were found

A) 80 prefer Sathiya, 60 prefer Kumkum and 50 prefer Balika.

B) 30 prefer both Sathiya and Kumkum, 40 prefer both Kumkum and Balika. 25 prefer Sathiya and Balika

Find the maximum number of people who could prefer all three serials.

Topic: set theory

[1] 25

[2] 50

[3] 15

[4] 20

Question 12:

Question 12:

In how many different ways can we change the sign * with + or -, such that the following equation is true? 1*2*3*4*5*6*7*8*9*10*11 = 42?

Topic: properties of numbers

[1] 6

[2] 7

[3] 8

[4] 10

Question 13:

Question 13:

Nishant, Rakesh, Brijesh, and Rohit bought a house for Rs.40 lakhs. The contribution of Nishant is 3/5

^{th}of the contribution of Rakesh, Brijesh, and Rohit taken together. The contribution of Rakesh is 2/3rd of the contribution of Brijesh and Rohit taken together. Brijesh and Rohit contributed equal amount. What is the ratio of their respective contributions?

Topic: ratio and proportion

[1] 6:4:3:1

[2] 8:4:2:2

[3] 6:4:3:3

[4] 5:4:3:4

Question 14:

Question 14:

The area of a triangle is 48 and the two sides of the triangle are 8 and 15. Let x be the length of largest possible third side. What is the value of [x], where [x] is a greatest integer less than equal to x.

Topic: triangles

[1] 12

[2] 17

[3] 19

[4] None of these

Question 15:

Question 15:

Find sum of all the real roots of the equation \(\sqrt[3]{x} + \sqrt[3]{{20 - x}} = 2\)

Topic: equations

Question 16:

Question 16:

Let \(N = 1! \times 2! \times 3! \times ..... \times 99! \times 100!\), and if \(\frac{N}{{p!}}\) is a perfect square for some positive integer \(p \le 100\), then find the value of p.

Topic: factorials

Question 17:

Question 17:

If \({x^2} + {y^2} = 1\) , find the maximum value of \({x^2} + 4xy - {y^2}\)

Topic: maxima minima

[1] \(1\)

[2] \(\sqrt 2 \)

[3] \(\sqrt 5 \)

[4] \(4\)

Question 18:

Question 18:

The compound interest on a certain amount for two years is Rs. 291.2 and the simple interest on the same amount is Rs. 280. If the rate of interest is same in both the cases, find the Principal amount

Topic: sici

[1] 1200

[2] 1400

[3] 1700

[4] 1750

Question 19:

Question 19:

In the diagram given below, the circle and the square have the same center O and equal areas. The circle has radius 1 and intersects one side of the square at P and Q. What is the length of PQ?

Topic: circles

[1] 1

[2] 3/2

[3] \(\sqrt {4 - \pi } \)

[4] \(\sqrt {\pi - 1} \)

Question 20:

Question 20:

What is the remainder when \({{x}^{276}}+12\) is divided by \({{x}^{2}}+x+1\) given that the remainder is a positive integer?

Topic: remainders

Question 21:

Question 21:

A, B, C, D, and E are five friends. The sums of the weights of each group of four of them are 132, 138, 113, 131, and 126. What is the positive difference of the weights of the heaviest and lightest among them?

Topic: averages

[1] 25

[2] 26

[3] 27

[4] None of these

Question 22:

Question 22:

In the figure given below, O is the center and AB is the diameter of the circle of radius 15. From point D, two tangents DC and DB are drawn to the circle. If AC is parallel to OD and AC+OD=43, find the length of CD given CD is positive integer

Topic: circles

Question 23:

Question 23:

If \(x+y+z=2,\ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}=6,\ and\ {{x}^{3}}+{{y}^{3}}+{{z}^{3}}=8\), find the value of \({{x}^{4}}+{{y}^{4}}+{{z}^{4}}\) ?

Topic: basic algebra

[1] \(8\sqrt{5}\)

[2] 18

[3] \(18\sqrt{3}\)

[4] 16

Question 24:

Question 24:

Two friends Ankit and Brijesh are approaching towards each other, each one at 1 kmph. Ankit is walking with a dog, which can run at speed of 9 kmph. The dog leaves Ankit and runs towards Brijesh when Ankit and Brijesh are 10 km apart. After reaching Brijesh the dog immediately runs back to Ankit. Find the distance travelled by Ankit between the time the dog leaves him and comes back to him.

Topic: speed time and distance

[1] 1.6 km

[2] 1.8 km

[3] 1.2 km

[4] 1.4 km

Question 25:

Question 25:

The lines \(x = \frac{1}{4}y + a\) and \(y = \frac{1}{4}x + b\) intersect at the point \(\left( 1,2 \right)\). What is a + b?

Topic: coordinate geometry

[1] 0

[2] \(\frac{3}{4}\)

[3] 1

[4] \(\frac{9}{4}\)

Question 26:

Question 26:

For any three positive real numbers x, y and z,\(9\left( {25{x^2} + {y^2}} \right) + 25\left( {{z^2} - 3zx} \right) = 15y\left( {3x + z} \right)\) Then :

Topic: progressions

[1] x, y and z are in G.P.

[2] y, z and x are in G.P.

[3] y, z and x are in A.P.

[4] x, y and z are in A.P.

Question 27:

Question 27:

Circles with center A and B are externally tangent to each other and to line m. If the radii of circle A and B are 3 and 1 respectively, Find the area of the shaded region.

Topic: area

[1] \(4\sqrt{3}-\frac{7\pi }{3}\)

[2] \(3\sqrt{3}-\frac{11\pi }{7}\)

[3] \(2\sqrt{3}-\frac{\pi }{3}\)

[4] \(4\sqrt{3}-\frac{11\pi }{6}\)

Question 28:

Question 28:

13 married couples attended a wedding ceremony, each woman gave a pack of chocolates to everyone except her spouse, and no exchange of gifts took place between men. How many gifts were exchanged among these people?

Topic: permutation and combination

[1] 78

[2] 312

[3] 468

[4] 624

Question 29:

Question 29:

Let \(f\left( x \right)=a{{x}^{2}}+bx+c\) and \(f\left( {x + y} \right) = f\left( x \right) + f\left( y \right) + xy\). Given a+b+c=3 , find the value of \(f\left( 10 \right)\)

Topic: functions

Question 30:

Question 30:

Let \(x={{\log }_{4}}9+{{\log }_{9}}28\) then which of the following is true:

Topic: logarithm

[1] 2<x<3

[2] 3<x<4

[3] 4<x<5

[4] None of these

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## 8 Responses

do you have exclusive PACKAGE OF video solutions of last 10-15 years CAT EXAMS? I AM INTERESTED IN JUST THAT. I AM HELPING A GIRL APPEARING FOR CAT 2019 EXAM

We have already included all the good questions from CAT and other MBA entrance exams in our course.

All these questions are with Video explanations

If f is 3

F(3)

6+3+2 is 11

Can you tell the name of the theorem that you said in the first quetion

stewarts theorem

Sir, for question no. 23:- we can do as x+y=2-z

=> cubing both sides:- x3+y3+z3=8-(2-z)(6z+3xy)

=>as given that x3+y3+z3=8, then (2-z)(6z+3xy)=0 => z=2(considering an integer value for easy output) ,now putting z value in every eqn given :- x+y=0

x2+y2=2

x3+y3=0

from the above three eqns we find that if one of x or y is +ve then another ll be -ve but both ll be of same magnitude i.e. (+-)1….thus x4+y4+z4=18

Set 1 Question 5.

I want to know the below logic would be wrong.

Distance is constant. If the Speed increases by 10km/hr, the time decreases by 4 hours.

So to decrease time by 2 hours, Speed can be increased by 5km/hr.

20 + 5= 25 kmph.

I understand something might be wrong with this logic but could someone help pinpoint that?

the assumption of “to decrease time by 2 hours, speed can be increase by 5km/hr” is wrong. it would be right if you know the initial time and consider from the start but since the journey is already going on, u can’t do that.