If m and n are positive integers, and m + n and m/n are both even numb

Question

If m and n are positive integers, and m + n and m/n are both even numbers, which of the following cannot be an even integer ?

A. (m + n)/2

B. m/2

C. (n + 2)/2

D. (m + 4)/2

E. (m + 6)/2

SaquibHGMATWhiz · Accepted Answer

Solution:

We are given  m+n=even 
  This means m and n are either  both even or both odd    
 It is also given that  \frac{m}{n}=even  
 Combining both the info, we can infer that  m and n are both even and m is even multiple of n  
 Let us assume  n=2p  and  m=2q*2p=4pq  where p and q are positive integers

Option A: (m + n)/2
   \frac{2p+4pq}{2}=p+2pq=   may be even

Option B: m/2
   \frac{4pq}{2}=2pq=   even

Option C: (n + 2)/2
   \frac{2p+2}{2}=p+1=   may be even

Option D: (m + 4)/2
   \frac{4pq+4}{2}=2pq+2=   even

Option E: (m + 6)/2
   \frac{4pq+6}{2}=2pq+3=   definitely not even

Hence the right answer is    Option E

Bunuel · Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=bEm8yjQEU0Q

stne · Answer

Picking numbers worked best for me. Please note : Once we have tested an option we need not test that option again.

M =4  and n =2

B, C and D can be eliminated as all of these give even.

M =8  and n =4

We can eliminate A

Ans E

Hope it helps.

Kinshook · Answer

Asked:  If m and n are positive integers, and m + n and m/n are both even numbers, which of the following cannot be an even integer ?

m + n is an even number; 
m & n both are even
or
m & n both are odd

m/n is an even number
m is an even number and is a multiple of 4.
n is an even number

A. (m + n)/2: even number

B. m/2 : even number

C. (n + 2)/2 = n/2 + 1: May be even or odd

D. (m + 4)/2 = m/2 + 2: even number

E. (m + 6)/2 = m/2 + 3: odd number

IMO E

If m and n are positive integers, and m + n and m/n are both even numb

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GMAT Problem Solving (PS) Questions

If m and n are positive integers, and m + n and m/n are both even numb

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