GMATBusters
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 14There 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 primeCase b: n = 6. In this case, the answer to the REPHRASED target question is
NO, n is not primeSince 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 27This 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 primeCase b: n = 6. In this case, the answer to the REPHRASED target question is
NO, n is not primeSince 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 primeCase b: n = 6. In this case, the answer to the REPHRASED target question is
NO, n is not primeSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
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