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In the set {61, 62...100}, the sum of the second greatest and the second smallest prime numbers is:
164
150
158
156
156
List primes in the range (61, 67, 71, 73, 79, 83, 89, 97). Identify the 2nd and 7th terms quickly by scanning from both ends of the set.
We are given the set {61, 62,..., 100}. We need to find the sum of the second smallest and second greatest prime numbers within this range.
Sum=Ps2+Pg2
List primes in the range (61, 67, 71, 73, 79, 83, 89, 97). Identify the 2nd and 7th terms quickly by scanning from both ends of the set.
Students often include 61 as the smallest prime, but the question asks for the second smallest. Also, 91 is a common trap (it is 7×13, not prime).
Identify primes in the set {61,..., 100}
The prime numbers between 61 and 100 (inclusive) are 61, 67, 71, 73, 79, 83, 89, 97.
Primes={61,67,71,73,79,83,89,97}
Find the second smallest and second greatest primes
The smallest prime is 61, so the second smallest (Ps2) is 67. The greatest prime is 97, so the second greatest (Pg2) is 89.
Ps2=67,Pg2=89
Calculate the sum
Adding the identified primes: 67+89=156.
67+89=156
D is correct because the second smallest prime in the set is 67 and the second greatest prime is 89, which sum to 156.
Always verify primality for numbers ending in 1, 3, 7, and 9 near the upper bounds, as numbers like 91 (7×13) or 87 (3×29) are often mistaken for primes.
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