GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 15:08

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58445
If p is a negative even integer and q is a positive odd integer, which  [#permalink]

### Show Tags

01 Nov 2018, 00:53
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:18) correct 12% (00:46) wrong based on 67 sessions

### HideShow timer Statistics

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.

_________________
Manager
Joined: 09 Jun 2018
Posts: 187
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: If p is a negative even integer and q is a positive odd integer, which  [#permalink]

### Show Tags

01 Nov 2018, 04:26
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
_________________
If you found this relevant and useful, please Smash that Kudos button!
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: If p is a negative even integer and q is a positive odd integer, which  [#permalink]

### Show Tags

01 Nov 2018, 05:12

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

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If p is a negative even integer and q is a positive odd integer, which  [#permalink]

### Show Tags

01 Nov 2018, 11:46
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

_________________
Karishma
Veritas Prep GMAT Instructor

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If p is a negative even integer and q is a positive odd integer, which  [#permalink]

### Show Tags

04 Nov 2018, 18:02
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If p is a negative even integer and q is a positive odd integer, which   [#permalink] 04 Nov 2018, 18:02
Display posts from previous: Sort by