**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 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.

**Answer: **Option: 3

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

**Answer: **Option: 4

**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

**Answer: **Option: 2

**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

**Answer: **75

**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

**Answer: **Option: 2

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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?