Data Sufficiency Problem : DS Archive
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# Data Sufficiency Problem

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27 Aug 2009, 04:48
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Question Stats:

33% (05:40) correct 67% (00:57) wrong based on 5 sessions

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Pls. help with the explanation for the Data Sufficiency problem from Manhattan GMAT:

Is the sum of integers a and b divisible by 7?

1) a is not divisible by 7
2) a-b is divisible by 7
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27 Aug 2009, 05:09
mirzohidjon wrote:
Pls. help with the explanation for the Data Sufficiency problem from Manhattan GMAT:

Is the sum of integers a and b divisible by 7?

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

C

1. if a is not divisible by 7:
b =1..7 a = 1..6. From that the sum could be anything and it might be divisible by 7 but not always so INSUFF

2. if a-b is divisible by 7:
a=9. b=2. a=10 b=3 a=14 b=7 ... they sometimes add up being divisible by 7 (when both are divisible by 7)

both:
a not divisible by 7 but subtract by b results in divisible by 7:
a = 8,9,10,11,12,13
b= 1, 2,3,4,5,6
sum=9,11,13,15,17,19
As you can see for A+B divisible by 7 they BOTH need to be divisible by 7. Since from 1 A CANT be divisible by 7 then we can never have scenarios like a=14, b=7 etc. so C is sufficient.
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27 Aug 2009, 05:12
1) Insuff, we do not know what a and b is.
2)Insuff
say a = x mod 7
b = y mod 7
b-a=x-y mod 7
x-y=0 mod 7
this means x=y
it means a = b = x = y mod 7
So a+b=2x=2y mod 7
if x=y=0 than a+b can be divisible by 7. But in any other case a+b can not be divisible by 7.

Together
We know x is not 0 in mod 7 . So a+b is not divisible by 7
C
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27 Aug 2009, 07:11
yep, another false positive question.
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27 Aug 2009, 11:38
maliyeci wrote:
flyingbunny wrote:
yep, another false positive question.
What does it mean?

I think flyingbunny means that this is yet another question where we get an answer NO by combining two stmts...i.e. YES we can find the answer by C and the answer is NO
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27 Aug 2009, 12:14
Combining 1 and 2 we get,
a = k + 7n
b = k
So, a + b = 2k + 7n
2k + 7n is not divisible by 7 as k is not divisible by 7.
Re: Data Sufficiency Problem   [#permalink] 27 Aug 2009, 12:14
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