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If n is a positive integer, are n and 1 the only positive divisors of
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Author:  GMATBusters [ 06 Dec 2018, 05:36 ]
Post subject:  If n is a positive integer, are n and 1 the only positive divisors of

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

Author:  Chethan92 [ 06 Dec 2018, 19:02 ]
Post subject:  Re: If n is a positive integer, are n and 1 the only positive divisors of

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.

Author:  BrentGMATPrepNow [ 25 Mar 2020, 05:45 ]
Post subject:  Re: If n is a positive integer, are n and 1 the only positive divisors of

GMATBusters wrote:

Project DS Butler: Day 31: Data Sufficiency (DS61)


For DS butler Questions Click Here


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

Author:  dadie [ 27 Jul 2020, 13:35 ]
Post subject:  Re: If n is a positive integer, are n and 1 the only positive divisors of

Is n a prime number ?

1- prime umber less than 14 9 they are moe than one (2, 3, 5, 7 etc...) Not Sufficient
2- 2n< 27, a lot of number are in this case

3- both 2*2, 3*2 and 7*2 are less than 27 so the answer is E

Author:  bumpbot [ 23 Nov 2021, 17:41 ]
Post subject:  Re: If n is a positive integer, are n and 1 the only positive divisors of

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