Question

Choose the prime number from 175, 161, 129, 101

• A. 161
• B. 101
• C. 175
• D. 129

Hint:

Familiarizing yourself with prime numbers up to \(200\) can save crucial time.
Common tricky composites to watch out for in exams are \(119\) (\(7 \times 17\)), \(133\) (\(7 \times 19\)), and \(161\) (\(7 \times 23\)).
Always test the prime divisibility rule up to \(\sqrt{N}\) to be absolutely sure.

Answer 1

The Correct Option is B

Step 1: Check divisibility of each option.
175 = 5 x 35 (not prime). 161 = 7 x 23 (not prime). 129 = 3 x 43 (not prime).
Step 2: Test 101 for primality.
Since sqrt(101) is less than 11, we only need to check divisibility by primes 2, 3, 5, and 7. 101 is not divisible by any of them.
Step 3: Confirm the answer.
101 has no factors other than 1 and itself, confirming it is a prime number. \[ \boxed{101} \]