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# If m is a positive integer, is m + 4 even?

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
If m is a positive integer, is m + 4 even?  [#permalink]

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26 Jul 2018, 00:37
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Difficulty:

25% (medium)

Question Stats:

73% (01:07) correct 27% (01:28) wrong based on 51 sessions

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If m is a positive integer, is m + 4 even?

(1) 2m + 1 is odd.
(2) 2m + 4 is a multiple of 4.

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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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If m is a positive integer, is m + 4 even?  [#permalink]

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Updated on: 26 Jul 2018, 01:03
Bunuel wrote:
If m is a positive integer, is m + 4 even?

(1) 2m + 1 is odd.
(2) 2m + 4 is a multiple of 4.

we are asked to find out whether m +4 = even .

In this case m has to be even.****

Statement 1: 2m +1 = odd. Clearly NOT sufficient. m could be even or odd.

Statement 2: 2m +4 = multiple of 4

In this case m has to be even. Sufficient .

Originally posted by selim on 26 Jul 2018, 00:43.
Last edited by selim on 26 Jul 2018, 01:03, edited 1 time in total.
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Re: If m is a positive integer, is m + 4 even?  [#permalink]

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26 Jul 2018, 00:58
Bunuel wrote:
If m is a positive integer, is m + 4 even?

Is m + 4 even ?
Since 4 is even , question asks is m even ?

(1) 2m + 1 is odd.
m could be either even or odd
Insufficient

(2) 2m + 4 is a multiple of 4.
For 2m + 4 to be multiple of 4, 2m must be multiple of 4
In which case m must always be even
Sufficient

Hence, B.
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Re: If m is a positive integer, is m + 4 even?  [#permalink]

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26 Jul 2018, 02:59
1
Bunuel wrote:
If m is a positive integer, is m + 4 even?

(1) 2m + 1 is odd.
(2) 2m + 4 is a multiple of 4.

1) 2m+1 is odd
2m is always even & even + odd(1) is always odd
nothing can be determined about m. insufficient.
2) 2m+4 = 4k
2(m+2) = 4k
m+2 = 2k
m = 2(k-1)
=> m is a multiple of 2 (even). so m+4 is always even. sufficient.

B.
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Re: If m is a positive integer, is m + 4 even? &nbs [#permalink] 26 Jul 2018, 02:59
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# If m is a positive integer, is m + 4 even?

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