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If a, b, and c are positive distinct integers, is (a/b)/c an integer? c = 2 a = b + c

Hi,

the equation can be rewritten as (ac/b).

Stat. 1 is not sufficient let's take a=1, b=3 and c=2 the result is not an integer. And if we take b=4 the result is an integer.

Stat. 2 gives us [(b+c)c]/b = b + (c²/b).
if c=2 and b=3, the result is not an integer.
if c=2 and b=4 the result is an integer => thus stat. 2 not sufficient

Combining 1 & 2 we have both cases (integer and non integer)

If a, b, and c are positive distinct integers, is (a/b)/c an integer? c = 2 a = b + c

Hi,

the equation can be rewritten as (ac/b).

Stat. 1 is not sufficient let's take a=1, b=3 and c=2 the result is not an integer. And if we take b=4 the result is an integer.

Stat. 2 gives us [(b+c)c]/b = b + (c²/b). if c=2 and b=3, the result is not an integer. if c=2 and b=4 the result is an integer => thus stat. 2 not sufficient

Combining 1 & 2 we have both cases (integer and non integer)

A: Insuff. Given a, b are distinct integers, a/b must be an even integer. a=4, b=1 - true. a=9, b=3 - false. Both, true & false possible. Hence, inconclusive. B: On simplifying, given b, c are distinct integers, (1/b + 1/c) must be an integer. For any b,c where b <> c, this is false. Hence, conclusive.

Thus, B.

gmatclubot

Re: DS_divisibility m05 #36
[#permalink]
26 Jun 2014, 22:18