Number System
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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

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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.

The answer is (B).


(2) Comment(s)


Shreyash Okhade
 ()

why option b is correct



Merf Lady
 ()

I smell like cheese Crying