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# Is a+b divisible by 7? a and b are both +ve integers. 1) a

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Intern
Joined: 16 Jan 2007
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Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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04 Aug 2010, 11:29
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Difficulty:

35% (medium)

Question Stats:

87% (00:23) correct 13% (00:29) wrong based on 15 sessions

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Is a+b divisible by 7? a and b are both +ve integers.

1) a is not divisible by 7
2) b is not divisible by 7

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-sum-of-integers-a-and-b-divisible-by-85639.html

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Intern
Joined: 03 Aug 2010
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Schools: Sloan '14 (M\$)
GRE 1: Q168 V169
WE: Engineering (Energy and Utilities)
Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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04 Aug 2010, 11:35
1) let a = 1, then if b = 1 we have a+b not divisible by 7. on the other hand if b =6, a+b is divisible by seven. Not Sufficient
2) Use the same argument as in 1), Not Sufficient
1 & 2) Use the same argument as in 1). Not Sufficient

Hence E
Intern
Joined: 16 Jan 2007
Posts: 17
Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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04 Aug 2010, 11:41
Also we can think it this way:

1) Non Multiple (of 7) + Multiple (of 7) = always non multiple (of 7)
where as
2) Non Multiple + Non Multiple = either multiple or non Multiple
3) Multiple + Multiple = always multiple

Senior Manager
Joined: 18 Sep 2009
Posts: 258
Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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17 Aug 2010, 15:33

By combining 2 statements

For ex = a+b= 8+15/7 =23/7= not divisible
a+b= 15+6/7=21/7 = divisible
Senior Manager
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Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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27 Jun 2011, 10:08
Is the sum of integers a & b divisible by 7?

1) a is not divisible by 7
2) a-b is divisible by 7.

I can solve this by number picking, but not mathematically i.e. with concept. So can anyone please help in trying to explain the concept? My understanding is:

a) Statement 1 is not sufficient as it doesn't say anything about b. Is my understanding correct?

b) If I pick numbers I can tell that this is insufficient. But what does it means mathematically? Does it not mean that a-b is a multiple of 7 and both a & b should be a multiple of 7. But then if we pick 20 and 13 its not but a-b is still divisible by 7. Anyhow this is insufficient.I can tell, but its a guess work and not my concept based answer.

Combining the two statement

a is not a multiple of 7, so a can be anything i.e. 8, 11, 13

a-b is divisible by 7. So if a is 8, then b has to be 1 to make a-b divisible by 7. But if a is 11 then b has to be either 4 to make it divisible.So in either case a+b is not divisible by 7. Is my conceptual understanding correct?

PS: I am focusing myself in understanding concepts now first as I have already taken GMAT 3 times and I think I never scored high because of the weaker concepts. Do you guys think I am doing it right way this time?
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Manager
Joined: 05 Jul 2010
Posts: 132
Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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27 Jun 2011, 10:37
1
i think sometimes concept is nothing but picking numbers. So i would say you are right on track. I too will do by numbers.

But on the other hand, with a concept will be,
a-b = 7x But since 7 is a prime number any two number difference should be multiple of 7. Which tells either both a and b is divisible of 7 or both are not. like 8,1 or 9,2 or 10,3 etc. where as 14,7 or 21, 14 or 35,7 etc all will give the desired result. So if one of the two is divisible of 7 that means both has to be divisible of 7, and so is true for adding two numbers.
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Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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27 Jun 2011, 11:27
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Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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27 Jun 2011, 13:46
Thanks brandy96 and fluke. You guys are awesome
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Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a  [#permalink]

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14 Aug 2017, 05:06
paam0101 wrote:
Is a+b divisible by 7? a and b are both +ve integers.

1) a is not divisible by 7
2) b is not divisible by 7

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-sum-of-integers-a-and-b-divisible-by-85639.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Is a+b divisible by 7? a and b are both +ve integers. 1) a   [#permalink] 14 Aug 2017, 05:06
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