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

Question

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

abhi1484 · Answer

The answer should be D, the equation will be an integer if p^2 +p is even

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AkshdeepS · Answer

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}
eq{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
eq{integer}

So, answer is A.

shubham2312 · Answer

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

abhimahna · Answer

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

shubham2312 · Answer

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

MarkusKarl · Answer

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.

Let's start with (1)
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.

Mahmud6 · Answer

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

Bunuel · Answer

It's formatting bug. Edited. Thank you.

Mahmud6 · Answer

If p is a positive integer, is it necessary to mention p≠0?

abhimahna · Answer

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?

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GMAT Data Sufficiency (DS) Questions

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

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