The sum of the three prime numbers is 100. If one of them exceeds another number by 24, then one of the other numbers is

Question

Question

This question was previously asked in

UPPSC Civil Service 2019 Official Paper 2

Answer 1

Let three prime numbers be X, X + 24 and Y.

According to the question,

X + X + 24 +Y = 100

⇒ 2X + Y = 76 ...i)

We can observe that 2X is an even number,

⇒ Y is also an even number

⇒ Y = 2 ...[∵ 2 is only even prime number]

Now, 2X + 2 = 76

⇒ 2X = 74

⇒ X = 37

∴ The three prime numbers are 2, 37, (37 + 24) = 61