What is the median of set A {-8, 15, -9, 4, N}? (1) N is a p

[Anaira Mitch]

What is the median of set A {-8, 15, -9, 4, N}?
(1) N is a prime and N^6 is even
(2) 2N + 14 < 20

I am stuck with above problem OA says A but I think both statements are sufficient. Please guide.

[ceilidh.erickson]

DS questions about MEDIANS are relatively common. The best strategy is often to test cases.

What is the median of set A {-8, 15, -9, 4, N}?

First, put the known terms in order: [-9, -8, 4, 15]. There are several possibilities for what the median could be:

- if N</= -8, then -8 will be the median: [N, -9, -8, 4, 15]

- if N >/= 4, then 4 will be the median: [-9, -8, 4, N, 15]

- if N is between -8 and 4, N itself will be the median: [-9, -8, N, 4, 15]

In the first 2 cases, knowing either the value of N or simply the range of N would be sufficient to tell us the value of the median. In the 3rd case, we would have to know the value of N itself.

(1) N is a prime and N^6 is even
If some power of N is even, then N itself must be even. If it is also prime, then N = 2 (the only even prime). This is sufficient: the median must be 2.

(2) 2N + 14 < 20
Simplify:
2N < 6
N < 3

If N < 3, it might also be less than -8, making -8 the median. Or it might be the -8 < N < 3, in which case N is the median (of unknown value). This is insufficient to tell us the value of the median.

The answer is A.

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Hi Anaira Mitch,

When reviewing questions, or if you're stuck on a question, it helps to define the 'work' that you've done so far. You think that Face 2 is sufficient, but you haven't stated WHY you think that.

We have a set of 5 values: -9, -8, 4, 15 and N (but we don't know what N is... it could be really big, really small, a duplicate of one of the numbers that's already there, some other number, etc.). We're asked for the MEDIAN of that group.

2) 2N + 14 < 20

We can simplify this Fact...

2N < 6
N < 3

IF....
N = 2, then the group is -9, -8, 2, 4 and 15 and the median = 2

IF....
N = -8, then the group is -9, -8, -8, 4 and 15 and the median = -8
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

[Jay@ManhattanReview]

What is the median of set A {-8, 15, -9, 4, N}?
(1) N is a prime and N^6 is even
(2) 2N + 14 < 20

I am stuck with above problem OA says A but I think both statements are sufficient. Please guide.

Hi Anaira,

S2 is not sufficient.

We know that 2N + 14 < 20 => N < 3. N can be any number 2, 1, 0, 1/2, -10, etc. The question does not state that N in an integer. Though S1 implies that N is an integer, we must forget S1 and focus only on S2.

Let us arrange the four known terms in ascending order: {-9, -8, 4, 15}

N can be in the following three places, rendering no unique value of median; {-9, -8, N, 4, 15}, {-9, N, -8, 4, 15}, and {N, -9, -8, 4, 15}. Insufficient.

-Jay

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