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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.

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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 $$(6+1)/2\neq{integer}$$

So, answer is A.
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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.

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

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