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

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Manager
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If a, b, and c are integers, is abc divisible by 4?  [#permalink]

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New post 06 Oct 2018, 12:34
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A
B
C
D
E

Difficulty:

  55% (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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If a, b, and c are integers, is abc divisible by 4?  [#permalink]

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New post 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.
Answer E

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Re: If a, b, and c are integers, is abc divisible by 4?  [#permalink]

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New post 07 Oct 2018, 03:14
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Re: If a, b, and c are integers, is abc divisible by 4? &nbs [#permalink] 07 Oct 2018, 03:14
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If a, b, and c are integers, is abc divisible by 4?

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