UKMT - Intermediate Mathematical Challenge - 2024 - 2 | Exact Science

2

What is the difference between the smallest two-digit prime and the largest two-digit prime?

A. 86 B. 84 C. 82 D. 80 E. 78

Answer

A. 86

SOLUTIOn

99 and 98 are not primes, but 97 is a prime.

Therefore the largest two-digit prime is 97.

10 is not prime but 11 is a prime.

Therefore the smallest two-digit prime is 11.

The difference between these is 97 − 11 which is equal to 86.

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