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value of A+B? and GCD=1

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value of A+B? and GCD=1 [#permalink] New post 08 Oct 2008, 03:44
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Last edited by blover on 08 Oct 2008, 08:06, edited 1 time in total.
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Re: value of A+B and GCD [#permalink] New post 08 Oct 2008, 04:25
Please, take this with a grain of salt:

1 Not suff. 2 unknows and 1 equation

2 Not suff. a=3, b=5 and a=5, b=3

1+2

Here is my doubt: I'd say both of them are not suff. but maybe I'm missing something...

OA?

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Re: value of A+B? and GCD=1 [#permalink] New post 08 Oct 2008, 08:28
Assuming a/b = 5/8 and GCD of both numbers = 1 then a=5 and b=8 which then gives a+b = 13

So I think both I and II are needed.

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Re: value of A+B? and GCD=1 [#permalink] New post 08 Oct 2008, 11:42
Was going to say E. but smahamkl's answer changed my mind. :-D
Has to be D.
a and b cannot be anything other than 5 and 8 respectively.
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Re: value of A+B? and GCD=1 [#permalink] New post 08 Oct 2008, 11:56
If a and b are positive integers, what is the value of a + b?
(1) a/b = 5/8
(2) GCD(a,b) = 1

(2) GCD(a,b) =1
Obviously insufficient.
However, this tell us that a and b do not have same factors.

(1) 8a = 5b
(\(2^3\))a = 5b
Many possible combinations of a and b. Insufficient.

(1) & (2)
(\(2^3\))a = 5b
Since GCD(a,b) = 1, a must be 5 and b must be \(2^3\)
Sufficient.

The answer is C.
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Re: value of A+B? and GCD=1 [#permalink] New post 09 Oct 2008, 03:19
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A:
a/b = 5/8 so a + b = 13

a/b = 10/16 so a + b = 26

a/b = 15/24 so a + b = 39

so we get multiple values of a+ b , not suffiecient

B: GCD is 1 mean there is no common factor between A and B other than 1 , but this alon is not sufficient as there are thousand such number pair (3,7) , (5,11)...and so on

So B is also not sufficient

---
A + B :
We know ratio is 5/8 and GCD is 1 means they must be 5 and 8 only (if we take 10 and 16 then ratio will remain same but GCD become 2)

So answer will be C:

Thanks
Vishal Shah
Re: value of A+B? and GCD=1   [#permalink] 09 Oct 2008, 03:19
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