AMCAT Quantitative Aptitude Previous Questions 41 -60

Ques. If log{(a+b)/3} = 0.5(log a + log b), then the correct relation between a and b is:

Op 1: a2+b2 = 7ab

Op 2: a2-b2 = 7ab

Op 3: (a+b)2 = 2

Op 4: (a+b)/3 = (1/2)(a+b)

Op 5: None of these

Correct Op : 1

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

a^2 + b^2 = 7ab

Ques. If log x = log 3 + 2 log 2- (3/4) log 16. The value of x is:

Op 1: 1/2

Op 2: 1

Op 3: 3/2

Op 4: 2

Op 5: None of these

Correct Op : 3

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. If log x =(1/2) log y = (1/5) log z, the value of x4y3z-2 is:

Op 1: 0

Op 2: 1

Op 3: 2

Op 4: 3

Op 5: None of these

Correct Op : 2

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. If log10000 x = -1/4, then x is given by:

Op 1: 1/100

Op 2: 1/10

Op 3: 1/20

Op 4: none of these

Op 5:

Correct Op : 2

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

=> 10

Ques. The value of 3-1/2 log3(9) is:

Op 1: 3

Op 2: 1/3

Op 3: 2/3

Op 4: none of these

Op 5:

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

It means 1/3

Correct Op : 2

Ques. loge xy - loge |x| equals to:

Op 1: loge x

Op 2: loge |x|

Op 3: - loge x

Op 4: none of these

Op 5:

Correct Op : 4

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. The value of (loga n) / (logab n) is given by:

Op 1: 1 + loga b

Op 2: 1 + logb a

Op 3: loga b

Op 4: logb a

Op 5:

Correct Op : 1

(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. If (a4 - 2a2b2 + b4)x-1 = (a-b)2x (a+b)-2, then x equals to:

Op 1: (a - b) / (a + b)

Op 2: log (a2 - b2)

Op 3: log (a + b) / log (a - b)

Op 4: log (a - b) / log (a + b)

Op 5:

Correct Op : 4

Taking log on both sides,
=>(x-1)log(a2-b2)^2=log[(a-b)^2x(a+b)^-2]
=>2(x-1)log(a2-b2)=2xlog(a-b)-2log(a+b)
Cancelling 2 on both sides,and expanding log(a2-b2) into log [(a+b)(a-b)]=>log(a+b)+log(a-b),
=>(x-1)[log(a+b)+log(a-b)]=xlog(a-b)-log(a+b)
=>xlog(a+b)-log(a-b)-log(a+b)+xlog(a-b)=xlog(a-b)-log(a+b)
=>xlog(a+b)=log(a-b)

x=log(a-b)/log(a+b).

Ques. If a, b, and c are in geometric progression then loga n, logb n and logc n are in:

Op 1: AP

Op 2: GP

Op 3: HP

Op 4: None of these

Op 5:

Correct Op : 3

Ques. What is the value of antilog10100?

Op 1: 2

Op 2: 10100

Op 3: 100

Op 4: 10

Op 5:

Correct Op : 2

Ques. If antilog x 5 = 30, what can you infer about x?

Op 1: x is a number between 1 and 2

Op 2: x is 305

Op 3: x is a number between 2 and 3

Op 4: None of these

Op 5:

Correct Op : 1

Ques. 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?

Op 1: Both will grow linearly with different slopes

Op 2: Both will grow linearly with same slopes

Op 3: y will grow linearly, while z will not

Op 4: z will grow linearly, while y will not

Op 5:

Correct Op : 1

Ques. x triples every second. How will log2x change every second?

Op 1: It will double every second

Op 2: It will triple every second

Op 3: It increases by a constant amount every second.

Op 4: None of these

Op 5:

Correct Op : 3

Ques. f(x) grows exponentially with x, how will f(log(x)) grow?

Op 1: Exponentially

Op 2: Linearly

Op 3: Quadratically

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is the value of log512 8?

Op 1: 3

Op 2: 1/3

Op 3: -3

Op 4: -1/3

Op 5:

Correct Op : 2

Ques. What is the value of log7 (1/49)?

Op 1: 2

Op 2: 1/2

Op 3: -1/2

Op 4: -2

Op 5:

Correct Op : 4

Ques. Given that log64 x = 2/6, what is the value of x?

Op 1: 2

Op 2: 4

Op 3: 6

Op 4: 8

Op 5:

Correct Op : 2

Ques. If 7x = 85, what is the value of x?

Op 1: log785

Op 2: log857

Op 3: log107

Op 4: log1085

Op 5:

Correct Op : 1

Ques. If log10 power 2 = 0.3010, what is the number of digits in 2power of 64

Op 1: 19

Op 2: 20

Op 3: 18

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is log110?

Op 1: 1

Op 2: 10

Op 3: 0

Op 4: Tends to infinity

Op 5:

Correct Op : 4

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