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If n is a positive integer, are n and 1 the only positive divisors of n? (1) n is less than 14. (2) If n is doubled, the result is less than 27
Target question:Are n and 1 the only positive divisors of n? This is a good candidate for rephrasing the target question.
If n and 1 the only positive divisors of n, what does this tell us about n? It tells us that n is prime (since prime numbers are the only numbers with exactly 2 divisors) So the original target question is really just asking us to determine whether n is prime...
REPHRASED target question:Is n prime?
Aside: the video below has tips on rephrasing the target question
Statement 1: n is less than 14 There are several values of n that satisfy statement 1. Here are two: Case a: n = 2. In this case, the answer to the REPHRASED target question is YES, n is prime Case b: n = 6. In this case, the answer to the REPHRASED target question is NO, n is not prime Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: If n is doubled, the result is less than 27 This information feels just as vague as the information provided him statement 1. So, perhaps I'll test some numbers here. IMPORTANT: If you're going to test some values, you can sometimes save time by first checking to see whether we can re-use the values you used when analyzing statement 1. In this case, both values (n = 2 and n = 6) also satisfy statements 2. That is: Case a: n = 2. In this case, the answer to the REPHRASED target question is YES, n is prime Case b: n = 6. In this case, the answer to the REPHRASED target question is NO, n is not prime Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Since I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED. In other words, Case a: n = 2. In this case, the answer to the REPHRASED target question is YES, n is prime Case b: n = 6. In this case, the answer to the REPHRASED target question is NO, n is not prime Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers, Brent RELATED VIDEO FROM MY COURSE
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