Aptitude 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.**

The answer is **(B)**.

**Shreyash Okhade**

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**Merf Lady**

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I smell like cheese

why option b is correct