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GRE Whiz Representative
Joined: 25 May 2022
Posts: 25
Given Kudos: 1
A and B are two positive integers such that their product is 384 and
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15 Oct 2022, 04:36
15 Oct 2022, 04:36
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Question Stats:
39% (02:36) correct
60% (02:39) wrong based on 23 sessions
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A and B are two positive integers such that their product is 384 and their greatest common divisor is 4. Which of the following is(are) possible value(s) of ‘A + B’?
A. 32
B. 44
C. 60
D. 72
E. 84
F. 100
G. 128
A. 32
B. 44
C. 60
D. 72
E. 84
F. 100
G. 128
GRE Whiz Representative
Joined: 25 May 2022
Posts: 25
Given Kudos: 1
A and B are two positive integers such that their product is 384 and
[#permalink]
04 Nov 2022, 22:45
04 Nov 2022, 22:45
1
Expert Reply
SaquibHGREWhiz wrote:
A and B are two positive integers such that their product is 384 and their greatest common divisor is 4. Which of the following is(are) possible value(s) of ‘A + B’?
A. 32
B. 44
C. 60
D. 72
E. 84
F. 100
G. 128
A. 32
B. 44
C. 60
D. 72
E. 84
F. 100
G. 128
Solution:
- We are given positive integers A and B such that \(A\times B=384\)
- GCD of A and B is 4 which means we can assume \(A=4k_1\) and \(B=4k_2\) such that \(k_1\) and \(k_2\) are co-prime i.e., do not have any factor in common apart from 1
- We have \(A\times B=384\)
\(⇒4k_1 \times 4k_2=384\)
\(⇒k_1 \times k_2=\frac{384}{16}\)
\(⇒k_1\times k_2=24\) - Possible values are \(1\times 24=24\) and \(3\times 8=24 \)
- Thus, the value of \(A+B=4k_1+4k_2=4(k_1+k_2)\)
\(=4\times (1+24)\) or \(4\times (3+8)\)
\(= 100\) or \(44\)
Hence the right answers are Options B and F
Re: A and B are two positive integers such that their product is 384 and
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20 May 2024, 15:55
20 May 2024, 15:55
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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