a) 404 and 808

b) 202 and 1010

c) 303 and 909

d) 505 and 707

correct answer is: d) 505 and 707

#### Explanation

According to the question,

The sum of two numbers are 1212.

And, their HCF is 101.

We know that the HCF of two numbers is the largest number that divides both of them. Also, the sum of the numbers is 1212. So, we need to find two numbers that are multiples of 101 and whose sum is 1212.

Since the HCF is 101, let’s try to find multiples of 101:

101\times1=101

101\times2=202

101\times3=303

101\times4=404

101\times5=505

101\times6=606

101\times7=707

101\times8=808

101\times9=909

101\times10=1010

101\times11=1111

Now,

We see that 505 and 707 are two multiples of 101 that add up to 1212 and their HCF is 101.

On the other side, we see that 1111 and 101 are another two multiples of 101 that add up to 1212 their HCF is also 101.

So that,

The two numbers, which have a sum of 1212 and a HCF of 101, are either 101 and 1111 or 505 and 707. **Ans:** The two numbers are either 101 and 1111 or 505 and 707.

###### Alternative phrasings for this particular math query are:

**Find two numbers whose sum is 1212 and highest common factor (HCF) is 101.****If the sum of two numbers is 1212 and their HCF is 101, what are the numbers?****Two numbers have a sum of 1212 and a highest common factor (HCF) of 101. Find the values of the numbers.**