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# If p is a negative even integer and q is a positive odd integer, which

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Re: If p is a negative even integer and q is a positive odd integer, which [#permalink]
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Bunuel wrote:
If p is a negative even integer and q is a positive odd integer, which of the following must be true?

A. pq is a negative odd integer.
B. p/q is a negative odd integer.
C. p − q is a positive odd integer.
D. p + q is a positive odd integer.
E. q − p is a positive odd integer.

p = - Even
q = Odd

A. pq is a negative odd integer.

pq = (-Even)*Odd = - Even
Not correct

B. p/q is a negative odd integer.

p/q = -Even/Odd = -Even
Not correct

C. p − q is a positive odd integer.

p - q = - Even - Odd = - Odd
Not correct

D. p + q is a positive odd integer.

p + q = -Even + Odd => Whether it is positive or negative depends on which of p and q has a higher absolute value and which has lower.
-2 + 1 = -1
-2 + 5 = 3
Not correct

E. q − p is a positive odd integer.
q - p = Odd - (-Even) = Odd + Even = Odd
Correct

Answer (E)
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Re: If p is a negative even integer and q is a positive odd integer, which [#permalink]
Expert Reply
Bunuel wrote:
If p is a negative even integer and q is a positive odd integer, which of the following must be true?

A. pq is a negative odd integer.
B. p/q is a negative odd integer.
C. p − q is a positive odd integer.
D. p + q is a positive odd integer.
E. q − p is a positive odd integer.

Since p is even and q is odd, p - q, p + q and q - p are all odd. However, since q is positive and p is negative, only q - p must be positive (whereas p - q must be negative and p + q could be either positive or negative). So the only correct answer is E.

Answer: E
Re: If p is a negative even integer and q is a positive odd integer, which [#permalink]
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