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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.
(1) p is an even number.
(2) p is a multiple of 3.
23 Aug 2016, 04:10
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Bunuel
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.
(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.
