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# If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer?

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If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2016, 02:48
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If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer?

(1) p is an even number.
(2) p is a multiple of 3.
[Reveal] Spoiler: OA

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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2016, 02:58
The answer should be D, the equation will be an integer if p^2 +p is even

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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2016, 04:10
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Bunuel wrote:
If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer?

(1) p is an even number.
(2) p is a multiple of 3.

Question : Is $$\frac{(p^2+p)}{2p}$$ = integer ?

Is $$\frac{p(p+1)}{2p}$$ = integer ?

Is $$\frac{p+1}{2}$$ = integer ?

St -1 : p is an even integer.

say p=2, then $$\frac{(2+1)}{2}\neq{integer}$$

When p is even then the answer is always no. Sufficient

We can try with other even values.

St-2 : p is a multiple of 3 .

say p is 3, then $$\frac{(3+1)}{2}$$= integer

if p = 6, then $$(6+1)/2\neq{integer}$$

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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2016, 06:41
Bunuel wrote:
If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer?

(1) p is an even number.
(2) p is a multiple of 3.

Answer will be A as from statement 1
we can definitely say P will not be an integer
because and Even number+1 will always be odd and and Odd Number divided by 2 will never be integer hence it is sufficient

and from 2nd statement if P is an multiple of 3 this means it can either be even or either be odd
in that case the expression can be or can not be integer hence this statement alone is not sufficient.

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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2016, 09:27
abhi1484 wrote:
The answer should be D, the equation will be an integer if p^2 +p is even

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Try solving it again. You have missed a couple of things in this question.
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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2016, 10:16
abhimahna wrote:
abhi1484 wrote:
The answer should be D, the equation will be an integer if p^2 +p is even

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Try solving it again. You have missed a couple of things in this question.

buddy
it says (P^2+P)/2P
lets take value of P=2
4+2=6
6/2*2=6/4=1.5

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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2016, 10:25
shubham2312 wrote:
abhimahna wrote:
abhi1484 wrote:
The answer should be D, the equation will be an integer if p^2 +p is even

Sent from my MI 3W using GMAT Club Forum mobile app

Try solving it again. You have missed a couple of things in this question.

buddy
it says (P^2+P)/2P
lets take value of P=2
4+2=6
6/2*2=6/4=1.5

In this case, simplifying the equation prior to testing numbers is essential.

(P^2+P) / 2P = (P+1)/2.

If P+1=even, P+1/2 is an integer.

The question thus lands in whether P is even or odd.

P is even. Look at that, just what we wanted. P+1 won't be even and thus (P+1)/2 won't be an integer. Sufficient.

(2)
P is a multiple of 3. Any even multiple of 3 will be even and any odd multiple of 3 will be odd. As such, we can't determine whether p+1 is even or odd and in extension whether the equation gives an integer answer.
Insufficient.
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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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22 Aug 2017, 10:31
1
KUDOS
Bunuel wrote:
If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer?

(1) p is an even number.
(2) p is a multiple of 3.

What does this symbol '' mean? Is it typo or actually has any meaning?
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Hasan Mahmud

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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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22 Aug 2017, 10:33
Mahmud6 wrote:
Bunuel wrote:
If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer?

(1) p is an even number.
(2) p is a multiple of 3.

What does this symbol '' mean? Is it typo or actually has any meaning?

It's formatting bug. Edited. Thank you.
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Kudos [?]: 124488 [0], given: 12079

Senior Manager
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Re: If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2017, 01:45
If p is a positive integer, is it necessary to mention p≠0?
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If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer? [#permalink]

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23 Aug 2017, 01:48
Mahmud6 wrote:
If p is a positive integer, is it necessary to mention p≠0?

Hi Mahmud6 ,

You are right. Positive integer means greater than zero. Hence, it is not required to be mentioned explicitly.
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If p is a positive integer, and p ≠ 0, is (p^2 + p)/(2p) an integer?   [#permalink] 23 Aug 2017, 01:48
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