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03 Nov 2016, 02:26
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If a, b, and c are integers, is abc divisible by 8?
(1) a and b are even integers.
(2) a, b, and c are consecutive multiples of 2
(1) a and b are even integers.
(2) a, b, and c are consecutive multiples of 2
Vinayak Shenoy
Joined: 06 Jun 2016
Last visit: 27 Jun 2017
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Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
03 Nov 2016, 02:36
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Bunuel
If a, b, and c are integers, is abc divisible by 8?
(1) a and b are even integers.
(2) a, b, and c are consecutive multiples of 2
(1) a and b are even integers.
(2) a, b, and c are consecutive multiples of 2
IMO B
From statement 1
we only know about a and b are even
if a, b and c are even Yes abc is divisible by 8
if c is odd No abc is not divisible by 8
Nature of integer c is not known hence Insufficient
From statement 2
all the integers are even.
hence abc is divisible by 8
Hence B
03 Nov 2016, 05:25
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Bunuel
If a, b, and c are integers, is abc divisible by 8?
(1) a and b are even integers.
(2) a, b, and c are consecutive multiples of 2
(1) a and b are even integers.
(2) a, b, and c are consecutive multiples of 2
First, the prime factorization of 8 is 2^3. Thus, for a number to be divisible by 8, this number shall at least contain 3 '2s'.
Statement1: ' a and be are even numbers' tells us nothing about 'c', and in addition, a and b can both be equal to 2. So we can never know if abc is divisible by 8.
Statement2: when a,b and c are consecutive multiples of 2, thus these 3 numbers contain at least 3 '2s' which is exactly what we need. Thus, B alone is sufficient.
So answer is B.
