If a, b, and c are integers, is abc divisible by 8?

Question

(1) a and b are even integers.
(2) a, b, and c are consecutive multiples of 2

Vinayak Shenoy · Answer

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

georgekaterji · Answer

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.

mvictor · Answer

to be divisible by 8, the number must have 3 factors of 2.

1. a and b are even
since we don't know whether a and b are different integers, we can assume that both of them are 2.
c might be odd integer.
in this case, abc is not divisible by 8.
but, if a =2, b=4, and regardless of what c is, we know for sure that it's divisible by 8.
A and D are out.

2. a,b,c are consecutive multiples of 2.
suppose a=2, b=4, c=6 - abc divisible by 8
what if one of the numbers is negative or one of the numbers is zero?
if a=-2, then b=0, and c=2. abc=0, which is divisible by 8...
in any case, statement 2 alone is sufficient.

answer is B.

GMATinsight · Answer

Question : Is abc divisible by 8?

Statement 1: : a and b are even integers 
Case 1: a = 2 and b = 6 and c=3 and abc is NOT divisible by 8
Case 2: a = 2 and b = 4 and c=3 and abc is divisible by 8, Hence
NOT SUFFICIENT

Statement 2: : a, b, and c are consecutive multiples of 2 
  IMPORTANT : Any Two consecutive multiples of 2 contain one multiple of 2 and other multiple of 4 at least 
i.e. product of two consecutive multiples of 2 is always divisible by 2*=8
i.e. 2*4=8
and 4*6=24
and 6*8=48 etc, Hence
SUFFICIENT

Answer: Option B

stonecold · Answer

Nice Question.
Here is what i did on this one =>
We need to see if a*b*c is divisible by 8 or not.
Statement 1->
a=even
b=even
a=2
b=2
c=1
=> NO
a=2
b=2
c=2
YES
Hence not sufficient.

Statement 2=>
As they are some multiples of 2 => All are even => a*b*c must be a multiple of 8.
Hehe sufficient.
Hone B.

If a, b, and c are integers, is abc divisible by 8?

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