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

http://caindiainfo.com/?q=viagra-commercial-youtube 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