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# If a, b, and c are integers, is abc divisible by 4?

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Manager
Joined: 08 Sep 2017
Posts: 77
Location: Colombia
GMAT 1: 710 Q49 V39
If a, b, and c are integers, is abc divisible by 4?  [#permalink]

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06 Oct 2018, 12:34
00:00

Difficulty:

65% (hard)

Question Stats:

65% (01:48) correct 35% (01:25) wrong based on 20 sessions

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If a, b, and c are integers, is abc divisible by 4?

(1) a + b + 2c is even
(2) a + 2b + c is odd

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Intern
Joined: 15 Jan 2014
Posts: 33
Location: India
Concentration: Technology, Strategy
Schools: Haas '19
GMAT 1: 650 Q49 V30
GPA: 2.5
WE: Information Technology (Consulting)
If a, b, and c are integers, is abc divisible by 4?  [#permalink]

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06 Oct 2018, 13:00
To check if $$abc/4$$=0.

We need to find if $$abc$$ can produce two 2's

St1 :
$$a + b + 2c$$ is even

We know:$$E+E = E$$ and $$O+O = E$$

Here 2c is Even so $$a+b$$ has to be even to give final output as Even .

If a and b are even then $$abc/4$$ is divisible but If a and b are odd then $$abc/4$$ depends on c,which we don't know is even or odd . So no clear answer (Insufficient) .

St2 : Same approach as above (Insufficient)

$$St1 + St2$$ == > add both equations :

$$ODD+EVEN = ODD$$

$$2a+3(b+c)$$= ODD ==>$$b+c$$ will be ODD so either b or c is odd but not both . So we get one 2 from either b or c but we don't know about a Since it is multiplied by 2 .

So still Insufficient.

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Math Expert
Joined: 02 Sep 2009
Posts: 56244
Re: If a, b, and c are integers, is abc divisible by 4?  [#permalink]

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07 Oct 2018, 03:14
dimmak wrote:
If a, b, and c are integers, is abc divisible by 4?

(1) a + b + 2c is even
(2) a + 2b + c is odd

Discussed here: https://gmatclub.com/forum/if-a-b-and-c ... 60759.html

TOPIC IS LOCKED AND ARCHIVED.
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Re: If a, b, and c are integers, is abc divisible by 4?   [#permalink] 07 Oct 2018, 03:14
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