Data Sufficiency Problem

Question

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

shaselai · Answer

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.

maliyeci · Answer

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

flyingbunny · Answer

yep, another false positive question.

Economist · Answer

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

Aleehsgonji · Answer

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. 
So answer is C

Data Sufficiency Problem

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