**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 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

**Answer: **Option: 1

**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

**Answer: **20

**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

**Answer: **Option: 2

**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

**Answer: **Option: 2

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

**Answer: **Option: 4

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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.