AMCAT Sample Questions Quants Solutions 91-100

Ques 91 : Choose the correct answer.
What is the value of 0^-10 ?
Option 1 : 0 Option 2 : 1 Option 3 : -10 Option 4 : None of these

Negative powers dont exist for 0.

Ques 92 : Choose the correct answer.
What is the value of 25^1.5 ?
Option 1 : 325 Option 2 : 32.5 Option 3 : 125 Option 4 : None of these

Break 1.5 as 3/2 thus first 25*25*25 and then divide by 25 two times.

Ques 93 : Choose the correct answer.
What is the value of (0.027)^1/3?
Option 1 : 0.3 Option 2 : 0.03 Option 3 : 0.003 Option 4 : None of these

Ques 94 : Choose the correct answer.
What is the value of (0.016)1/4?
Option 1 : 0.2 Option 2 : 0.02 Option 3 : 0.002 Option 4 : None of these

This is tricky question use calculator you will understand why.

Ques 95 : Choose the correct answer.
Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is:
Option 1 : 1 hour Option 2 : 1 hr 12min Option 3 : 1 hr 15 min Option 4 : 1 hr 20 min

As the distance is same
s*t=6/7s*(t+12)
t=72 min
1 hour 12 min

Ques 96 : Choose the correct answer.
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively ?
Option 1 : 2 : 1 Option 2 : 3 : 2 Option 3 : 8 : 3 Option 4 : Cannot be determined Option 5 : None of these

u-v=x/8.8.....(1)
u+v=x/4.......(22)
calculating both equation,
u=2x/11
v=3x/44
u/v=8/3

Ques 97 : Choose the correct answer.
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Option 1 : 21 m Option 2 : 26 m Option 3 : 28 m Option 4 : 29 m

When A run 100m, B will run 975m.
Distance ratio of A:B= 100:75= 4:3
When B Run 100m, C will run 96m.
Now B:C=100:96= 25/24
now A:C=A:B*B:C
4/3*25/24=25/18
now A:C= 25*4/18*4= 100/72
So when A run 100m, C will run 72 and A will beat C by =(100-72) = 28 m.

Ques 98 : Choose the correct answer.
In a family, the father took 1/5 of the cake and he had 4 times as much as others had, then the family members are:
Option 1 : 16 Option 2 : 17 Option 3 : 18 Option 4 : None of these

If there are 'x' members in a family, father took 1/5 of the cake, so remaining 4/5 cake will be distributed among (x-1) members, so each member will get (4/5)/(x-1)
As 1/5 =4*(4/5)/(x-1)
x=17

Ques 99 : Choose the correct answer.
The price of sugar is increased by 25%. In order not to increase the expenditure a lady must reduce her consumption by:
Option 1 : 25% Option 2 : 20% Option 3 : 30% Option 4 : None of these

Decrease in consumption = [% Price increase/(100 + % Price Increase)]×100
So , If price of onion rises by 25% =>
Decrease in consumption = [25/(100+25)] × 100
= [25/125]×100 = 20
Hence , consumption of onion should be decreased by 20 % so that there is no change in the expenditure.

Ques 100 : Choose the correct answer.
I read 3/8 of a book on one day, and 4/5 of the remainder on another day. If now there were 30 pages unread, the book contains:
Option 1 : 240 pages Option 2 : 230 pages Option 3 : 340 pages Option 4 : 140 pages Option 5 : None of these

Let x be total no. of pages in the book.
You read 3x/8 pages on 1st day and 5x/8*4/5=x/2 pages on another day.
Remaining no of pages=30.
(3x/8)+(x/2)+30=x
Therefore x=240

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