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

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Joined: 02 Sep 2009
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If p is a negative even integer and q is a positive odd integer, which  [#permalink]

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31 Oct 2018, 23:53
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Difficulty:

25% (medium)

Question Stats:

84% (01:08) correct 16% (00:48) wrong based on 58 sessions

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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.

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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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01 Nov 2018, 03:26
A: pq has to be negative and even, So INCORRECT
B: Take p = -2, q = 3, p/q is not even an integer, So INCORRECT
C: p-q has to be negative since negative-positive = negative, so, INCORRECT
D: If p = -2, q = 3, then p+q = 1, which is positive odd, but if p = -4 and q = 3, p+q = -1, which is negative odd, So, INCORRECT
E: q-p = positive - negative = positive - (-1*positive) = positive, also odd - even = odd, hence CORRECT!

Option E
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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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01 Nov 2018, 04:12

Solution

Given:
• p is a negative even integer
• q is a positive odd integer

To find:
• Which of the given answer choices is always true?

Approach and Working:
Option A: pq = -even * odd = -even – FALSE
Option B: $$\frac{p}{q}$$ = -even/odd = may not be an integer – MAY NOT BE TRUE
Option C: p - q = -even - odd = -odd – FALSE
Option D: p + q = -even + odd = +/- odd – MAY NOT BE TRUE (depends on the absolute value of p and q)
o If |p| > |q|, then p + q = -odd
o If |p| < |q|, then p + q = odd

Option E: q - p = odd + even = odd – TRUE

Hence, the correct answer is Option E

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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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01 Nov 2018, 10:46
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

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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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04 Nov 2018, 17:02
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.

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Re: If p is a negative even integer and q is a positive odd integer, which &nbs [#permalink] 04 Nov 2018, 17:02
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