Question

The sum of prime numbers that are greater than 60, but less than 70 is:

• A. 128
• B. 191
• C. 197
• D. 260

Hint:

Only 61 and 67 are prime between 60 and 70; add them together.

Answer 1

The Correct Option is A

This can also be solved with a quick sieve (elimination) approach instead of testing each number one by one.
Since $\sqrt{69} < 9$, it is enough to check divisibility by 2, 3, 5 and 7 only to confirm primality for numbers up to 69.
First remove all even numbers from 61 to 69: that eliminates 62, 64, 66 and 68.
Next remove multiples of 3 from what remains (61, 63, 65, 67, 69): that eliminates 63 and 69.
Next remove multiples of 5 from what remains (61, 65, 67): that eliminates 65.
What remains is 61 and 67. Checking multiples of 7 near this range ($7 \times 9 = 63$, $7 \times 10 = 70$) confirms neither 61 nor 67 is a multiple of 7.
So the only primes in the range are 61 and 67, and their sum is $61 + 67 = 128$.\[\boxed{128}\]