If p is an even integer and q is an odd integer, which of the followin

Question

If p is an even integer and q is an odd integer, which of the following must be an odd integer?

A. p/q 
B. pq 
C. 2p+q 
D. 2(p+q) 
E. 3p/q

BrentGMATPrepNow · Accepted Answer

Another approach is to take each answer choice and plug in an even number for p and an odd number for q, and see which answer choices yield an ODD value. 
The easiest numbers to test are p =  0  (which is EVEN) and q =  1  (which is ODD)

We get: 
A. p/q =  0 / 1  = 0, which is EVEN. ELIMINATE A
B. pq = ( 0 )( 1 ) = 0, which is EVEN. ELIMINATE B
C. 2p+q = 2( 0 ) +  1  = 1, which is ODD.   KEEP C  
D. 2(p+q) = 2( 0  +  1 ) = 2, which is EVEN. ELIMINATE D
E. 3p/q = (3)( 0 )/ 1  = 0, which is EVEN. ELIMINATE E

Answer: C

Cheers,
Brent

camlan1990 · Answer

A. p/q 
p = 6, q = 3 => p/q is odd integer
p = 4, q=3 =>p/q is not integer
B. pq 
Must be even
C. 2p+q 
2p must be even, q is odd=> 2p+q must be ODD: CORRECT 
D. 2(p+q)
must be even
E. 3p/q
Same A

Ans: C

mvictor · Answer

this is a must question:

A. p/q 
can be a non-integer

B. pq 
always even

C. 2p+q 
2p = even -> even+odd = odd

D. 2(p+q) 
always even - p+q = odd *2 -> even

E. 3p/q
might be a non integer.

C

RR88 · Answer

Option C

p = Even, q = Odd. Odd: O, Even: E & Fraction: F

A. p/q = E/O = E or F
B. pq = E*O = E
C. 2p+q = 2E + O = O
D. 2(p+q) = 2(E+O) = E
E. 3p/q = 3(E/O) = 3E or 3F

EMPOWERgmatRichC · Answer

Hi All,

If you know the Number Properties involved in this question, then you can get to the correct answer relatively easily. You can also TEST VALUES to get to the answer.

We're told that P is an EVEN integer and Q is an ODD integer. We're asked which of the following must be an ODD integer...

IF....
P = 2 AND Q = 1, then...

Answer A: 2/1 = 2 NOT an odd
Answer B: 2(1) = 2 NOT an odd
Answer C: 2(2) + 1 = 5 This IS an odd
Answer D: 2(2+1) = 6 NOT an odd
Answer E: 3(2)/1 = 6 NOT an odd

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

There are three ways to get an odd integer: odd x odd = odd OR odd/odd = odd OR even + odd = odd. Let’s examine our answer choices to determine which must produce an odd integer.

A) p/q

Since p is even and q is odd, p/q will never be an odd integer.

B) pq

Again, since p is even and q is odd, p/q will never be an odd integer.

C) 2p+q

Since 2p is even and q is odd, 2p + q WILL BE an odd integer.

Answer: C

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If p is an even integer and q is an odd integer, which of the followin

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If p is an even integer and q is an odd integer, which of the followin

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards