AMCAT Quantitative Ability Previous Papers-13

There are three numbers, these are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. What will be the sum of three numbers :
80
82
85
87
Answer: Option C

Explanation:

As given the questions these numbers are co primes, so there is only 1 as their common factor.
It is also given that two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29;
So first number is : 551/29 = 19
Third number = 1073/29 = 37
So sum of these numbers is = (19 + 29 + 37) = 85

Ques. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

A.    123
B.    127
C.    235
D.    305

Answer: Option B

Explanation:
Required number = H.C.F. of (1657 – 6) and (2037 – 5)
= H.C.F. of 1651 and 2032 = 127.

If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

A.    55/601
B.    601/55
C.    11/120
D.    120/11

Let the numbers be a and b.
Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum =    1/a    +    1/b    =    a + b/ab    =    55/600    =    11/120

Ques  : Choose the correct answer.
What is the value of 4^-2 ?
Option 1 : 1/4
Option 2 : 1/16
Option 3 : -16
Option 4 : None of these

Correct Op: 2

Ques  : Choose the correct answer.
What is the value of (0.081)1/4?
Option 1 : 0.3
Option 2 : 0.03
Option 3 : 0.003
Option 4 : None of these

Correct Op: 1

Ques. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
3 ⅕ min
3 ⅖ min
3 ⅗ min
3 ⅘ min

Do not be confused, Take this question same as that of work done question’s. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:

1 minute work done by both the punctures =
(1/9+1/6)=(5/18)

So both punctures will make the type flat in
(18/5)mins=3 ⅗ mins

Correct Op: 3

Ques. A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work.
27 days
54 days
56 days
68 days

Correct Op: 2

Answer: Option B

Explanation:

As per question, A do twice the work as done by B.
So A:B = 2:1
Also (A+B) one day work = 1/18

To get days in which B will finish the work, lets calculate work done by B in 1 day =
=(1/18∗1/3)=1/54

[Please note we multiplied by 1/3 as per B share and total of ratio is 1/3]

So B will finish the work in 54 days

Ques. To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much time A and C will take
24 days
16 days
12 days
8 days

Answer: Option D

Explanation:

A+B 1 day work = 1/8
B+C 1 day work = 1/12
A+B+C 1 day work = 1/6

We can get A work by (A+B+C)-(B+C)
And C by (A+B+C)-(A+B)

So A 1 day work =
1/6−1/12=1/12

Similarly C 1 day work =
1/6−1/8=(4−3)/24=1/24

So A and C 1 day work =

1/12+1/24=3/24=1/8

So A and C can together do this work in 8 days

Ques. A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
5 days
6 days
7.5 days
8.5 days

Answer: Option C

Explanation:

B’s 5 days work =
1/10∗5=½
Remaining work =1−1/2=½
A can finish work =15∗1/2=7.5days