# AMCAT Sample Questions Quants Solutions 41- 50

Ques 41 : Choose the correct answer.
If log{(a+b)/3} = 0.5(log a + log b), then the correct relation between a and b is:
Option 1 : a2+b2 = 7ab Option 2 : a2-b2 = 7ab Option 3 : (a+b)2 = 2 Option 4 : (a+b)/3 = (1/2)(a+b) Option 5 : None of these

log((a+b)/3)=0.5log(ab)
a+b/3=(ab)^1/2
(a+b)^2= 9ab
a^2 + b^2 = 7ab

Ques 42 : Choose the correct answer.
If log x = log 3 + 2 log 2- (3/4) log 16. The value of x is:
Option 1 : 1/2 Option 2 : 1 Option 3 : 3/2 Option 4 : 2 Option 5 : None of these

log x= log 3+ 2 log 2 – (3/4)log 16.
log x = log 3 + 2 log 2 – (3/4) log 2^4.
log x = log 3 + 2 log 2 – (3*4)/4 log 2.
log x = log 3 + 2 log 2 – 3 log 2.
log x = log 3 – log 2.
log x = log 3/2.
Therefore, by equating, x = 3/2.

Ques 43 : Choose the correct answer.
If log x =(1/2) log y = (1/5) log z, the value of x4y3z-2 is:
Option 1 : 0 Option 2 : 1 Option 3 : 2 Option 4 : 3 Option 5 : None of these

log(x) = (1/2) log(y) = y = x^2 —(1)
log(x) = (1/5) log(z) => z = x^5 ——(2)
So put y= x^2 & z = x^5 in given Series : x4*y3*z-2
So ( x4*x^6*1/x^10) =x^0 =1
So answer will be 1 only

Ques 44 : Choose the correct answer.
If log10000 x = -1/4, then x is given by:
Option 1 : 1/100 Option 2 : 1/10 Option 3 : 1/20 Option 4 : none of these

log10000 x = -1/4
=> x= 10000^(-1/4)
=> 10

Ques 45 : Choose the correct answer.
The value of 3^(1/2 log3(9)) is:
Option 1 : 3 Option 2 : 1/3 Option 3 : 2/3 Option 4 : none of these

3^{-1/2 log3(3^2)}
3^{-2/2 log3(3)}
3^{-1 log3(3)}
3^(-1)
It means 1/3

Ques 46 : Choose the correct answer.
loge xy – loge |x| equals to:
Option 1 : loge x Option 2 : loge |x| Option 3 : – loge x Option 4 : none of these

if taking x +ve
loge x+loge y-loge x=loge y
if taking x -ve
loge x+loge y+loge x
=2loge x+loge y
=loge x^2y

Ques 47 : Choose the correct answer.
The value of (loga n) / (logab n) is given by:
Option 1 : 1 + loga b Option 2 : 1 + logb a Option 3 : loga b Option 4 : logb a

(loga n) / (logab n)
=(log n/log a)*(log ab/log n)
=log ab/log a
= (log a+log b)/log a
= 1+loga b

Ques 48 : Choose the correct answer.
If (a4 – 2a2b2 + b4)x-1 = (a-b)2x (a+b)-2, then x equals to:
Option 1 : (a – b) / (a + b) Option 2 : log (a2 – b2) Option 3 : log (a + b) / log (a – b) Option 4 : log (a – b) / log (a + b)

Ques 49 : Choose the correct answer.
If a, b, and c are in geometric progression then loga n, logb n and logc n are in:
Option 1 : AP Option 2 : GP Option 3 : HP Option 4 : None of these

Applying base changing law of log,

log(a) to base n = 1/{log(n) to base a}
==> 1/log(a) = log(base a) n ——- (2)
Similarly, 1/log(b) = log(base b) n ———- (3)
and 1/log(c) = log(base c) n ———- (4)

Thus from (1), (2), (3) & (4)

log(base a) n, log(base b) n, log(base c) n