Question

Let $m$ and $n$ be positive integers such that one-third of $m$ is $n$ less than one-half of $m$. Mark the possible value of $m$.

• A. $15$
• B. $21$
• C. $24$
• D. $26$
• E. $28$

Answer 1

Answer: (C)

$24$

As given $m$ and $n$ be positive integers such that one-third of $m$ is $n$ less than one-half of $m$.
It can be re-written as; $\frac{m}{3}=\frac{m}{2}-n$
Multiplying both sides by $6$,

$\Rightarrow \frac{6m}{3}=\frac{6m}{2}-6n$

$2m=3m-6n$
$\Rightarrow m=6n$
So, the possible value of $m$ must be a positive multiple of $6$.
As we can see, the options mentioned above is not a multiple of $6$ except option C.
Hence, option C is correct.