# Easy Number System Solved QuestionAptitude Discussion

 Q. The remainder when the positive integer $m$ is divided by $7$ is $x$. The remainder when $m$ is divided by 14 is $x + 7$. Which one of the following could $m$ equal?
 ✖ A. 45 ✔ B. 53 ✖ C. 72 ✖ D. 85

Solution:
Option(B) is correct

Choice (A):
$\dfrac{45}{7} = 6 + \dfrac{3}{7}$, so $x = 3$.
Now,$\dfrac{45}{14} = 3 + \dfrac{3}{14}.$
The remainder is 3, not $x + 7 (= 10)$. Reject.

Choice (B):
$\dfrac{53}{7} = 7 + \dfrac{4}{7}$, so $x = 4$.
Now, $\dfrac{53}{14} = 3 + \dfrac{11}{14}$.
The remainder is 11, and equals $x + 7 (= 11)$. Correct.

Choice (C):
$\dfrac{72}{7} = 10 + \dfrac{2}{7}$, so $x = 2$.
Now, $\dfrac{72}{14} = 5 + \dfrac{2}{14}$.
The remainder is 2, not $x + 7 (= 9)$. Reject.

Choice (D):
$\dfrac{85}{7} = 12 + \dfrac{1}{7}$, so $x = 1$.
Now,$\dfrac{85}{14} = 6 + \dfrac{1}{14}$.
The remainder is 1, not $x + 7 (= 8)$. Reject.