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

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

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New post 04 Aug 2010, 11:29
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A
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C
D
E

Difficulty:

  35% (medium)

Question Stats:

86% (00:25) correct 14% (00:29) wrong based on 14 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: https://gmatclub.com/forum/is-the-sum-o ... 85639.html
[Reveal] Spoiler: OA

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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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New post 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

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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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New post 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

Hence the answer E.

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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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New post 17 Aug 2010, 15:33
Answer should be E

By combining 2 statements

For ex = a+b= 8+15/7 =23/7= not divisible
a+b= 15+6/7=21/7 = divisible

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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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New post 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.

Correct answer C.

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

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New post 27 Jun 2011, 10:37
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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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New post 27 Jun 2011, 11:27
Please follow here: divisibility-primes-115907.html#p937876
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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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New post 27 Jun 2011, 13:46
Thanks brandy96 and fluke. You guys are awesome :-)
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MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

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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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New post 14 Aug 2017, 05:06

Kudos [?]: 124217 [0], given: 12076

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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