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If n is a positive integer, are n and 1 the only positive divisors of
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06 Dec 2018, 06:36
06 Dec 2018, 06:36
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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
(1) n is less than 14.
(2) If n is doubled, the result is less than 27
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Re: If n is a positive integer, are n and 1 the only positive divisors of
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06 Dec 2018, 20:02
06 Dec 2018, 20:02
Question : Whether n and 1 are the only positive divisors of n?
Question is asking whether n is prime or not.
From statement 1:
n < 14
If n is 2, then 2 and 1 are the only divisors of 2.
If n is 4, then 1,2 and 4 are the divisors of 4.
Hence, Insufficient.
From statement 2:
If n = 2n, then 2n < 27.
Still Insufficient.
Combining both:
Again n can be a prime or a non-prime number.
Insufficient.
E is the answer.
Question is asking whether n is prime or not.
From statement 1:
n < 14
If n is 2, then 2 and 1 are the only divisors of 2.
If n is 4, then 1,2 and 4 are the divisors of 4.
Hence, Insufficient.
From statement 2:
If n = 2n, then 2n < 27.
Still Insufficient.
Combining both:
Again n can be a prime or a non-prime number.
Insufficient.
E is the answer.
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If n is a positive integer, are n and 1 the only positive divisors of
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Updated on: 18 Apr 2024, 01:40
Updated on: 18 Apr 2024, 01:40
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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?(1) n is less than 14.
(2) If n is doubled, the result is less than 27
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
Originally posted by BrentGMATPrepNow on 25 Mar 2020, 06:45.
Last edited by Bunuel on 18 Apr 2024, 01:40, edited 2 times in total.
Last edited by Bunuel on 18 Apr 2024, 01:40, edited 2 times in total.
