Problem Solving (PS) | Re: m and n are positive integers. If m/n and m+n both are even, which of

Solution:

• m and n are positiveintegers
• It is given that\(m+n=even\) which means either\(m\) and\(n\) are both even or bothodd
• It is also given that\(\frac{m}{n}\) is even which means couple ofthings
  
  • \(m\) and\(n\) are botheven (because odd/odd is noteven)
  • \(m\) is even multiple of\(n\)

• Let us assume\(n=2k\) and\(m=2qn=4kq\) where k and q are positive integers
• Let us analyze each statement one byone

• (m+n)/2
  
  \(⇒\frac{4kq+2k}{2}=2kq+k=\) may or may not beodd

• (m+2)/2
  
  \(⇒\frac{4kq+2}{2}=2kq+1=even+1=\) alwaysodd

• (n+2)/2
  
  \(⇒\frac{2k+2}{2}=k+1=\) may or may not beodd

Hence the right answer is OptionB
...

Statistics : Posted by SaquibHGMATWhiz • on 02 Feb 2023, 08:50 • Replies 2 • Views 150

---