Question

The sum of two numbers is 28 and their difference is 2. Then which of the following statement is/are true about the two numbers?

• A. Both are primes.
• B. Both are odd numbers.
• C. One is an odd multiple of 3 and the other one is a prime.
• D. Both are multiples of 3.

Answer 1

Answer: (B), (C)

The correct options are
B

Both are odd numbers.

C

One is an odd multiple of 3 and the other one is a prime.

Let the two numbers be $x$ and $y$.

Let us assume that $x$ is greater than $y$.

Given, the sum of these two numbers is 28.
i.e., $x+y=28$

Also, given that, the difference of these two numbers is 2.
i.e., $x-y=2$

We know that $(x+y)+(x-y)=2x$

Then, $28+2=2x$

$⟹2x=30$

$⟹x=15$

Then $x+y=28$ implies that $y=13$ [$x-y=2$ may be considered too]

Hence, the two required numbers are 15 and 13.

Therefore option (b) and (c) are correct.