Official Guide Explanation:
Problem Solving #7




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Solution and Metadata

Question: 7
Page: 153
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Properties of Integers > Primes

Explanation: The GMAT doesn't expect you to memorize every prime number up to 70, but it does expect that you know how to determine which numbers (out of a small group such as 60 to 70) are prime. Even numbers aren't prime, so the only possibilities are 61, 63, 65, 67, and 69. 63 and 69 are multiples of 3 (if the digits of the number add up to a multiple of 3, the number itself is a multiple of 3), and 65 is a multiple of 5. That leaves only 61 and 67. The only possible answer choices for us at this point are 67 and 128, so the question comes down to: is 61 prime? It isn't divisible by 2, 3, or 5, and it isn't divisible by 7. (If you know that 63 is divisible by 7, or even that 70 is divisible by 7, you can figure out that 61 isn't.) If a number is not prime, it must have at least one factor that is equal or less than its square root, and 61's square root is less than 8 (8 squared is 64), so we know that 61 is prime. Thus the answer is (B), 128, the sum of 61 and 67.

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