Number System
Aptitude

 Back to Questions
Q.

The positive integers $m$ and $n$ leave remainders of 2 and 3, respectively, when divided by 6. $m > n$.

What is the remainder when $m – n$ is divided by 6?

 A.

2

 B.

3

 C.

5

 D.

6

 Hide Ans

Solution:
Option(C) is correct

We are given that the numbers $m$ and $n$, when divided by 6, leave remainders of 2 and 3, respectively.

Hence, we can represent the numbers $m$ and $n$ as $6p + 2$ and $6q + 3$, respectively, where $p$ and $q$ are suitable integers.

Now,
$\begin{align*}
m - n &= (6p + 2) - (6q + 3)\\
&= 6p - 6q - 1 \\
&= 6(p - q) - 1
\end{align*}$

A remainder must be positive, so let’s add 6 to this expression and compensate by subtracting 6:
$\begin{align*}
6(p - q) - 1 &= 6(p - q) - 6 + 6 - 1\\
& =6(p - q) - 6 + 5\\
& = 6(p - q - 1) + 5
\end{align*}$

Thus, the remainder is 5


(1) Comment(s)


Shobia
 ()

take any value which is multiple of 6 and add 2 with that no., from my guess i choose 26., 26/6 will give the remainder 2 and take any value which is multiple of 6 and add 3 with that no., from my guess i choose 15.,15/6 will give the remainder 3,

$26-15=11$

$\dfrac{11}{6}$ will give remainder 5

ans:5