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# If a and b are 1-digit positive integers, is 100a+10b+2 divisible by 4

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6826
GMAT 1: 760 Q51 V42
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If a and b are 1-digit positive integers, is 100a+10b+2 divisible by 4  [#permalink]

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19 May 2017, 00:51
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25% (medium)

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76% (00:53) correct 24% (00:57) wrong based on 37 sessions

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If a and b are 1-digit positive integers, is 100a+10b+2 divisible by 4?

1) a=2.
2) b=3.

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Re: If a and b are 1-digit positive integers, is 100a+10b+2 divisible by 4  [#permalink]

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19 May 2017, 01:15
Lets look at this expression: 100a + 10b + 2.
Here 100a will be always be divisible by 4 whether 'a' be any digit (because 100 is divisible by 4).
We just need to know whether 10b + 2 is divisible by 4 or not. For this we need to know something about 'b'.

Statement 1. Doesn't help, nothing about 'b'. Insufficient.

Statement 2. b=3, 10b + 2 = 32, which is divisible by 4. Sufficient.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: If a and b are 1-digit positive integers, is 100a+10b+2 divisible by 4  [#permalink]

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21 May 2017, 16:59
==> If you modify the original condition and the question, the remainder when an integer n is divided by 4 is equal to the remainder when only the units digit and the tens digit are divided by 4, and so you only need to find b. Thus, for con 2), you get b=3, which becomes 10(3)+2=32, and so it is always divisible by 4, hence yes, it is sufficient.

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Re: If a and b are 1-digit positive integers, is 100a+10b+2 divisible by 4 &nbs [#permalink] 21 May 2017, 16:59
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