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Bunuel
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Statement 1, a-b-c = 6*m, where m is any integer.
a+b+c= 6*m+2*(b+c). We don't know if 2*(b+c) is divisible by 6. Not sufficient.

Statement 2, (a+b)*c = 6n, where n is any integer.
This doesn't provide any definite answer to the question.
Say a=2, b=3, c=6; (a+b)*c = 30 but a+b+c = 11. And if a=3, b=3, c=6; (a+b)*c = 36 but a+b+c = 12
Not sufficient.

Combined, still not sufficient.

E
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nks2611
no the answer should be A, as whatever values we take in statement 1. like 12-3-3/6 or 12-4-2/6 in all cases we get a+b+c divisible by 6 so suff. and in statement 2 take values like (0+1)6/6=integer but a+b+c/6 not an integer so insuff.

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You have taken special cases where b+c is divisible by 6. (b,c)={(3,3), (4,2)}
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i am confused well let's other explain, but still my answer is A ?
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nks2611
i am confused well let's other explain, but still my answer is A ?


Hi nks2611

please check my above post where a= -4 , b= -2 && c= 4

as per (1) a-b-c = -4 -( -2) -4 =-8+2 = -6 divisible by 6
but their sum a+b+c= -4 + ( -2) + 4= -6+4 = -2....not divisible by 6

Hence A is not suff
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Ya i got your mean then the OA could be wrong

Sent from my HM 1SW using GMAT Club Forum mobile app
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Bunuel
If a, b and c are integers, is their sum divisible by 6?

(1) a – b – c is divisible by 6.
(2) (a + b)c is divisible by 6.

For such problem, I think trying to get a value that contradicts the statements is the easiest way. For example, 1) if we take a = 12, b= -6, c =-6, then statement 1 will be true but their sum will be 0 and that will not go with our desired value. again, a=12, b=3, c=3 will match both statements. so not sufficient.

2) as long as c is divisible by 6, the values of a and b doesn't matter. so not sufficient.

together, when, a=12, b= -6, c= 6, all statements comply but for a= 10, b=4, c=-6, both statements match but their sum is not divisible by 6.
E is the answer
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