Aptitude Discussion

Q. |
The two positive integers '$p$' and '$q$' satisfy: $dfrac{(p+q)}{t} = text{HCF}(p,q)$. Which of the following two numbers sum up to '$t$'? |

✖ A. |
13 and 52 |

✖ B. |
132 and 96 |

✖ C. |
18 and 126 |

✔ D. |
56 and 45 |

**Solution:**

Option(**D**) is correct

Let $\text{HCF(p, q)} = H$

For two numbers $A$ and $B$, which are co-primes to each other.

We can represent $p$ and $q$ as

$p = H×A \text{ and } q= H×B$

So that $\dfrac{(p+q)}{t} =\text{ HCF(p, q)} = H$

⇒ $t = (A+B)$

Hence $t$ cab be represented as the sum of any two numbers which are co prime to each other.

Hence **option(D)** is correct choice.

**Ravi**

*()
*

Where and how did we get that $t=a+b$?