# AMCAT Sample Questions Quants Solutions 51-60

Ques 51 : Choose the correct answer.
If antilog x 5 = 30, what can you infer about x?
Option 1 : x is a number between 1 and 2 Option 2 : x is 305 Option 3 : x is a number between 2 and 3 Option 4 : None of these

Ques 52 : Choose the correct answer.
Every time x is increased by a given constant number, y doubles and z becomes three times. How will log(y) and log(z) behave as x is increased by the same constant number?
Option 1 : Both will grow linearly with different slopes Option 2 : Both will grow linearly with same slopes Option 3 : y will grow linearly, while z will not Option 4 : z will grow linearly, while y will not

Ques 53 : Choose the correct answer.
x triples every second. How will log2x change every second?
Option 1 : It will double every second Option 2 : It will triple every second Option 3 : It increases by a constant amount every second. Option 4 : None of these

Ques 54 : Choose the correct answer.
f(x) grows exponentially with x, how will f(log(x)) grow?
Option 1 : Exponentially Option 2 : Linearly Option 3 : Quadratically Option 4 : None of these

Linearly as it follows mx+c type of equation.

Ques 55 : Choose the correct answer.
What is the value of log512 8?
Option 1 : 3 Option 2 : 1/3 Option 3 : -3 Option 4 : -1/3

log 512 8=n;
512^n=8;
2^9n=2^3;
9n=3;
n=1/3

Ques 56 : Choose the correct answer.
What is the value of log7 (1/49)?
Option 1 : 2 Option 2 : 1/2 Option 3 : -1/2 Option 4 : -2

log7 (1/49)
=log7 (1/7)^2
=log7 (7)^-2
=-2

Ques 57 : Choose the correct answer.
Given that log64 x = 2/6, what is the value of x?
Option 1 : 2 Option 2 : 4 Option 3 : 6 Option 4 : 8

log64 x=2/6 that implies x=(64)^2/6
ans=4=>4

Ques 58 : Choose the correct answer.
If 7x = 85, what is the value of x?
Option 1 : log7 85 Option 2 : log857 Option 3 : log107 Option 4 : log1085

7^x=85
x=log(base 7)85

Ques 59 : Choose the correct answer.
If log10 2 = 0.3010, what is the number of digits in  log2^64
Option 1 : 19 Option 2 : 20 Option 3 : 18 Option 4 : None of these

log2^64=64log2=64 x .3010=19.264
So number of digits in 2^64=19+1=20

Ques 60 : Choose the correct answer.
What is log1 10?
Option 1 : 1 Option 2 : 10 Option 3 : 0 Option 4 : Tends to infinity
Log base 1 and euiq 10 tends to infinity.