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# If positive integers a, b and c are such that a < b < c, is the produc

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If positive integers a, b and c are such that a < b < c, is the produc  [#permalink]

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24 Sep 2018, 06:12
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Difficulty:

65% (hard)

Question Stats:

55% (02:07) correct 45% (01:56) wrong based on 42 sessions

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If positive integers a, b and c are such that a < b < c, is the product of a, b, & c even?

(1) c − b = b − a
(2) c − 16 = a

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Re: If positive integers a, b and c are such that a < b < c, is the produc  [#permalink]

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24 Sep 2018, 07:39
Bunuel wrote:
If positive integers a, b and c are such that a < b < c, is the product of a, b, & c even?

(1) c − b = b − a
(2) c − 16 = a

Question: is the product of a, b, & c even?
We already know that all a b and c are integers i.e. we only need to know if anyone of them is even or not

Statement 1: c − b = b − a
i.e. a+c=2b
Case 1: a = 1, c = 3, b = 2 YES
Case 2: a = 1, c = 5, b = 3 NO
NOT SUFFICIENT

Statement 2: c − 16 = a
Case 1: a = 2, c = 18, b = 10 YES
Case 2: a = 1, c = 17, b = 9 NO
NOT SUFFICIENT

Combining the two statements
Case 1: a = 2, c = 18, b = 10 YES
Case 2: a = 1, c = 17, b = 9 NO
NOT SUFFICIENT

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Re: If positive integers a, b and c are such that a < b < c, is the produc  [#permalink]

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11 Sep 2019, 05:30
A) b =(a+c)/2 since b is an integer
a= 3 c=7 then b=5 (abc= odd)
a= 2 c= 8 then b=5 (abc= even)
B) c= 16+a NS
A+B
c-b= 8 many possible combinations NS
so E
Re: If positive integers a, b and c are such that a < b < c, is the produc   [#permalink] 11 Sep 2019, 05:30
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