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# If a and b are positive integers, what is the value of a + b

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If a and b are positive integers, what is the value of a + b [#permalink]  16 May 2008, 15:59
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If a and b are positive integers, what is the value of a + b?

(1) $$\frac{a}{b} = \frac{5}{8}$$
(2) The greatest common divisor of a and b is 1.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
[Reveal] Spoiler: OA
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Director
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Kudos [?]: 110 [0], given: 0

Re: If a and b are positive integers, what is the value of a + b [#permalink]  16 May 2008, 16:21
goalsnr wrote:
If a and b are positive integers, what is the value of a + b ?
(1) a/b=5/8
(2) The greatest common divisor of a and b is 1

statement 1 is not suff

statement 2 is not suff, but it says that a & b are not divisible by each other.

C
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Re: If a and b are positive integers, what is the value of a + b [#permalink]  16 May 2008, 16:23
1
KUDOS
1)
let a=5
let b=8

let a=10
let b=16

insufficient

2)
insufficient

1&2)
a and b must maintain the same ratio.

5*x/(8*x). The only value of x that will satisfy 2 is x=1. Therefore, a+b=5+8=13.
sufficient

C
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Re: If a and b are positive integers, what is the value of a + b [#permalink]  16 May 2008, 16:26
1
KUDOS
goalsnr wrote:
If a and b are positive integers, what is the value of a + b ?
(1) a/b=5/8
(2) The greatest common divisor of a and b is 1

C ?

1) a/b =5/8

a=5 ; b=8; a/b =5/8 ; a+b =13
a=10 ;b=16 ;a/b =5/8 ;a+b=26

insuff

2) insuff ...no information about values of a and b .

Together sufficient: if GCD of a and b is 1 , only possible values of a and b are 5 and 8 respectively, so a+b=13
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Re: If a and b are positive integers, what is the value of a + b [#permalink]  30 Apr 2015, 08:04
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Re: If a and b are positive integers, what is the value of a + b [#permalink]  30 Apr 2015, 08:58
Expert's post
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If a and b are positive integers, what is the value of a + b?

(1) $$\frac{a}{b} = \frac{5}{8}$$ --> $$a$$ and $$b$$ could be: (5, 8), (10, 16), (15, 24), ... Not sufficient.

(2) The greatest common divisor of a and b is 1. Clearly insufficient: $$a$$ and $$b$$ could be any co-prime numbers.

(1)+(2) Since from (2) $$a$$ and $$b$$ do not share any common factor but 1, then from (1) $$a=5$$ and $$b=8$$ --> $$a+b=13$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
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Re: If a and b are positive integers, what is the value of a + b   [#permalink] 30 Apr 2015, 08:58
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