# AMCAT Sample Questions Quants Solutions 81- 90

Ques 81 : Choose the correct answer.
The roots of the equation 4x-3*2x+2+32=0 would include-
Option 1 : 2, 3 Option 2 : 1, 2, 3 Option 3 : 1, 2 Option 4 : 4, 8

Given equation is 2^2x - 3.2^x * 2^2 + 32 = 0
2^2x - 12.2^x + 32 = 0
let y = 2^x
y - 12y + 32 = 0
solve y=8 or y=4
2^x = 8
x = 3
and 2^x = 4
x = 2
2 and 3

Ques 82 : Choose the correct answer.
If ax =b, by=c and cz =a, then the value of xyz is:
Option 1 : 0 Option 2 : 1 Option 3 : 2 Option 4 : 3

By substituting values c^z = a (Eq. i) but we know that c = b^y, so suthis value in Eq. 1, we get b^(yz) = a. (Eq. 2) we also know that b = a^x, again sustituting this in eq. 2 we get a^xyz = a. therefore xyz=1.

Ques 83 : Choose the correct answer.
If x = 1+2*1/2 and y=1-2*1/2, then x^2+y^2 is -
Option 1 : 2 Option 2 : 3 Option 3 : 6 Option 4 : 0

Just solve the problem.

Ques 84 : Choose the correct answer.
If 4x+3 = 2x+7, then the value of x is:
Option 1 : 3 Option 2 : 2 Option 3 : 1 Option 4 : None of these

Just solve the problem.

Ques 85 : Choose the correct answer.
2x+y = 2*(2)1/2 and 2x-y = 21/2,the value of x is:
Option 1 : 1 Option 2 : 2 Option 3 : 3 Option 4 : 4 Option 5 : None of these

Just solve the problem.

Ques 86 : Choose the correct answer.
If x = 8, y = 27, the value of (x4/3+y2/3)1/2 is:
Option 1 : 5 Option 2 : 6 Option 3 : 7 Option 4 : 8 Option 5 : None of these

Just solve the problem.

Ques 87 : Choose the correct answer.
If xy = yx and x = 2y, the value of y is:
Option 1 : 1 Option 2 : 2 Option 3 : 3 Option 4 : 4 Option 5 : None of these

Just solve the problem.

Ques 88 : Choose the correct answer.
If 2x * 3y = 18 and 22x * 3y= 36, the value of x is:
Option 1 : 0 Option 2 : 1 Option 3 : 2 Option 4 : 3 Option 5 : None of these

Just solve the problem.

Ques 89 : Choose the correct answer.
What is the value of 50^0 ?
Option 1 : 0 Option 2 : 1 Option 3 : 50 Option 4 : None of these

Value of x^0 is always 1.

Ques 90 : Choose the correct answer.
What is the value of 6^-2 ?
Option 1 : 1/36 Option 2 : 36 Option 3 : -36 Option 4 : None of these