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# If p,q and r are integers, is pq+r even? 1) p+r is even

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Senior Manager
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If p,q and r are integers, is pq+r even? 1) p+r is even [#permalink]

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10 Mar 2011, 13:18
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35% (medium)

Question Stats:

66% (02:36) correct 34% (00:30) wrong based on 32 sessions

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1) If p,q and r are integers, is pq+r even?

1) p+r is even

M getting D

OA is different. Pls confirm if answer is not D
[Reveal] Spoiler: OA

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10 Mar 2011, 13:52
GMATD11 wrote:
1) If p,q and r are integers, is pq+r even?

1) p+r is even

M getting D

OA is different. Pls confirm if answer is not D

We want to know if pq+r is even

Statement 1) says p+r is even implying that p and r are either both odd or both even. When they are both even, then irrespective of q being even or odd, pq+r will be even. When they are both odd, depending on q, pq+r can be odd or even. So, insufficient

Statement 2) says q+r is odd, implying at least one of q or r is odd and the other one is even. When r is odd and q is even, pq+r is odd. When q is odd and r is even, pq+r is even or odd depending on value of p, so insufficient.

Combining the two, when p and r are even and hence q is odd, pq+r is even

when p and r are odd and hence q is even, pq+r is odd, so again insufficient

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10 Mar 2011, 20:15
1) Insufficient
p + r = even
p = even r = even. The answer is YES
p = odd r = odd q = even. The answer is NO

2) Insufficient
q + r = odd
q = odd r = even p = even. The answer is YES
q = odd r = even p = odd. The answer is NO

combine 1) and 2) Insufficient
p + r = even
q + r = odd
let r = even, p = even, q=odd. The answer is YES
let r = odd, p = odd, q= even. The answer is NO

Hence E.

GMATD11 wrote:
1) If p,q and r are integers, is pq+r even?

1) p+r is even

M getting D

OA is different. Pls confirm if answer is not D
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10 Mar 2011, 20:22
For pq+r to be even, pq = even and r = even OR pq = odd and r = odd.

From (1)
p + r is even so p is even and r is even or p is odd and r is odd

but no info about q, if q is even and p and r are odd, then pq+r is odd, otherwise even

From (2) , q + r is odd, so q is even and r is odd OR q is odd and r is even

So if p is even, then pq -> even + r (odd) = odd or even + r (even) = even

Not sufficient

Combining both (1) and (2), if p and r ar even, pq + r is even

if p and r are odd then, pq + r is odd (as q is even then)

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Re: Is pq+r even?   [#permalink] 10 Mar 2011, 20:22
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