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

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Director
Joined: 17 Oct 2005
Posts: 872
If a and b are positive integers, what is the value of a + b?  [#permalink]

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Updated on: 27 Nov 2017, 00:50
1
5
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Difficulty:

35% (medium)

Question Stats:

71% (01:08) correct 29% (01:10) wrong based on 248 sessions

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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: https://gmatclub.com/forum/if-a-and-b-a ... 35199.html

Originally posted by joemama142000 on 30 Nov 2005, 09:51.
Last edited by Bunuel on 27 Nov 2017, 00:50, edited 2 times in total.
Edited the question.
SVP
Joined: 24 Sep 2005
Posts: 1782
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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30 Nov 2005, 10:28
joemama142000 wrote:
If a and b are positive integers, what is the value of a + b?

1) a/b = 5/b

2) the greatest comon divisor of a and b is 1

since a and b are positive integers----> they're not 0
1. ---->a=5 , how about b? -->insuff
2. 3 and 5, 5 and 7, yields different sums ----->insuff

1 and 2. a=5, b can be 3 or 7 or 2, etc.....------>insuff

E
Director
Joined: 17 Oct 2005
Posts: 872
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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30 Nov 2005, 11:15
Here is my explanation:

1) insuff, dont know what a or b are 8a=5b

2)insuff, this is saying that greatest common factor of a and b is 1
ex. 12 and 7 or any prime number pair ( ex. 2 and 5)

together

5/8= a/b : answers have to be multiples of the numberator and denominator. ex. 10 and 16 or 15 and 24. These answers have common factors. Since 5 and 8 are in its most simplified fraction form, it has to be the answer.

If you can explain it better please let us know. thanks
SVP
Joined: 05 Apr 2005
Posts: 1599
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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30 Nov 2005, 17:21
joemama142000 wrote:
If a and b are positive integers, what is the value of a + b?
1) a/b = 5/b
2) the greatest comon divisor of a and b is 1

joemama142000 wrote:
Here is my explanation:
1) insuff, dont know what a or b are 8a=5b
2)insuff, this is saying that greatest common factor of a and b is 1
ex. 12 and 7 or any prime number pair ( ex. 2 and 5)
together
5/8= a/b: answers have to be multiples of the numberator and denominator. ex. 10 and 16 or 15 and 24. These answers have common factors. Since 5 and 8 are in its most simplified fraction form, it has to be the answer.
If you can explain it better please let us know. thanks
Director
Joined: 17 Oct 2005
Posts: 872
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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30 Nov 2005, 17:28
sorry all, my mistake. must have been really tired today. In that case you are correct and the answer is E
Director
Joined: 17 Oct 2005
Posts: 872
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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30 Nov 2005, 17:34
Anyway, here is the original question and explanation. I thought it was tricky.

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.

Here is my explanation:

1) insuff, dont know what a or b are 8a=5b

2)insuff, this is saying that greatest common factor of a and b is 1
ex. 12 and 7 or any prime number pair ( ex. 2 and 5)

together

5/8= a/b : answers have to be multiples of the numberator and denominator. ex. 10 and 16 or 15 and 24. These answers have common factors. Since 5 and 8 are in its most simplified fraction form, it has to be the answer.
Intern
Joined: 29 Jun 2011
Posts: 25
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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19 Jul 2011, 05:46
joemama142000 wrote:
Anyway, here is the original question and explanation. I thought it was tricky.

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.

Here is my explanation:

1) insuff, dont know what a or b are 8a=5b

2)insuff, this is saying that greatest common factor of a and b is 1
ex. 12 and 7 or any prime number pair ( ex. 2 and 5)

together

5/8= a/b : answers have to be multiples of the numberator and denominator. ex. 10 and 16 or 15 and 24. These answers have common factors. Since 5 and 8 are in its most simplified fraction form, it has to be the answer.

SORRY! if i'm asking a silly question...

since a/b = 5/8. why can't we just plug in a = 5 and b = 8? Pls explain. thanks!
Senior Manager
Joined: 11 Apr 2011
Posts: 252
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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19 Jul 2011, 20:22
Damn i thought it was C!
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Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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21 Jul 2011, 06:18
1
at miweekend...

consider
a/b=5/8
if u consider some other number 25/40 and simplifying it would also get 5/8 so the value given might not ration not the original value
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Intern
Joined: 29 Jun 2011
Posts: 25
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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22 Jul 2011, 00:33
miweekend wrote:
joemama142000 wrote:
Anyway, here is the original question and explanation. I thought it was tricky.

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.

Here is my explanation:

1) insuff, dont know what a or b are 8a=5b

2)insuff, this is saying that greatest common factor of a and b is 1
ex. 12 and 7 or any prime number pair ( ex. 2 and 5)

together

5/8= a/b : answers have to be multiples of the numberator and denominator. ex. 10 and 16 or 15 and 24. These answers have common factors. Since 5 and 8 are in its most simplified fraction form, it has to be the answer.

SORRY! if i'm asking a silly question...

since a/b = 5/8. why can't we just plug in a = 5 and b = 8? Pls explain. thanks!

thanks. good explanation indeed. never think of it...
Math Expert
Joined: 02 Sep 2009
Posts: 52902
Re: If a and b are positive integers, what is the value of a + b?  [#permalink]

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27 Nov 2017, 00:50
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: https://gmatclub.com/forum/if-a-and-b-a ... 35199.html
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Re: If a and b are positive integers, what is the value of a + b?   [#permalink] 27 Nov 2017, 00:50
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