Aptitude Discussion

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 |

**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**

**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