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Median of Set

Expert replies
by neeti2711 » Mon Dec 26, 2016 10:53 pm
What is the median of set A {-8, 15, -9, 4, N}?

(1) Number N is prime, and N^6 is even.

(2) 2N + 14 < 20

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
(B) Statement (2) ALONE is sufficient, but statement (1) alone is notsufficient to answer the question asked
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient to answer the question asked
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

The OA is[spoiler] (A)[/spoiler]

However I think that the answer should be [spoiler](E)[/spoiler] because if we consider statement 1, there are two possible values of N -> +2 and -2. So statement 1 alone is not sufficient to answer the question
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Source: — Data Sufficiency |

by Jay@ManhattanReview » Tue Dec 27, 2016 5:33 am
neeti2711 wrote:What is the median of set A {-8, 15, -9, 4, N}?

(1) Number N is prime, and N^6 is even.

(2) 2N + 14 < 20


The OA is[spoiler] (A)[/spoiler]

However I think that the answer should be [spoiler](E)[/spoiler] because if we consider statement 1, there are two possible values of N -> +2 and -2. So statement 1 alone is not sufficient to answer the question
Hi Neeti,

By the usual definition of prime for integers, negative integers cannot be prime. Thus, statement 1 itself is sufficient.

Hope this helps!

-Jay

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by [email protected] » Tue Dec 27, 2016 9:36 am
Hi neeti2711,

We're asked for the MEDIAN of the set {-9, -8, 4, 15 and N} -- note that N could be ANY value; I've placed it at the "end" of the list for convenience.

1) N is prime and N^6 is even.

By definition, the only PRIME number that results in N^6 being EVEN is 2. Thus, we know the median of the set (it's 2).
Fact 1 is SUFFICIENT.

2) 2N + 14 < 20

We can simplify this inequality...
2N < 6
N < 3

IF...
N = 2, then the median is 2
N = 1, then the median is 1
Fact 2 is INSUFFICIENT

Final Answer: A

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Rich
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