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

Question

(1) N is a prime and N^6 is even 
(2) 2N + 14 < 20

thefibonacci · Answer

A.

1) N is prime and N^6 is even implies N is 2 (as all other primes are odd and odd^6 = odd) 
hence A is sufficient.

2) 2N + 14 < 20
N < 3 
clearly insufficient.

Thoughtosphere · Answer

This is really tricky question, which is based on the the concept that negative numbers can not be prime.

1. Smallest prime is 2 and it also happens to be an even number, and 2^6 is even. Thus N = 2.
2. 2N + 14 < 20 => N < 6 Thus N can have infinite values.

Thus A

premjr85@gmail.com · Answer

Hi, I have a silly question.

Why is n<3 insufficient. Does it not point towards the fact the N=2?

Shouldnt the answer be D?

Bunuel · Answer

N < 3 means that N can be ANY number less than 3, not necessarily 2. It can be say, -1000 or -1000000 or 0 or 1 or 1.2.

rohit8865 · Answer

1) N^6 is even ,it means N is even number 
Further any even number which is prime also is only 2.
So we have N=2 ,thus we can calculate median of set.....sufficient
2)2N + 14 < 20
2N < 20- 14
N<3
so N can have as many values <3
so we cannot calculate median of given set.........insufff..

Ans A

Nunuboy1994 · Answer

We don't necessarily need to know the exact value of N to find the median of the set (middle number)- but we possibly need to know a range.

Statement 1

Any odd number to any power will always result in an odd number- the only prime number that satisfies the condition in statement 1 is the number 2- sufficient

Statement 2

This reduces to

2n <6
 n < 3

There are infinite possibilities for "N" (-∞, 2) - insufficient

Hence 
"A"

Nunuboy1994 · Answer

Primes, indeed, can only be positive. I think this is a bit beyond a 500 level question.

St 1

Only 2 can satisfy this value

insuff
St 2

n could be -500 or -2 or 0 which would alter the median

insuff

A

AliciaSierra · Answer

In order to find out median, we need to know value of N.

As per Option(1), N is a prime and  N^6  is even. 
The only way a product of integers is odd is if each thing in the product is odd. So in order for  N^6  to be even N has to be even. 2 is only prime number which is even so  N  is 2

Option 2 doesn't give us exact value of N. From option 2, N can be anything less than 3 i.e. -9,0,1,2 etc.

Option 1 is sufficient to get an answer.

saurabhlatad · Answer

Statement 1 : n is prime and the 6th power of N is even. This means that N is clearly 2 since it is the only prime number that will result in a even number. We can now calculate the median.  Sufficient  
 Statement 2:  2N + 14 < 20 i.e. 
2N < 6 ---> N<3, N can be any below less than 3 and this will keep changing the median.  Not Sufficient

apurvag95 · Answer

From this can we say N can be 2 or -2, how can we be sure that N is positive?

Bunuel · Answer

A prime numbers are positive only, 2 being the smallest one.

RexLenny · Answer

Write the set in order
Set A = { −9, −8, 4, 15, N }.
 To find the  median , we’ll need the numbers  in increasing order .
 
From (1): “N is a prime and N6 is even.”
If N6 is even, then N must be even (because any even number raised to any power stays even, odd → odd).
 The only even prime =  2 .
 → So N = 2.
Now set A = { −9, −8, 2, 4, 15 }
 This is already in order.
 → Median = the 3rd number =  2 .

* Statement (1) alone is  sufficient .
 
From (2): “2N + 14 < 20.”
Simplify → 2N < 6 → N < 3.
 So N can be any number less than 3 (e.g., 2, 0, −1, −8 etc.).
If N = 2, set = { −9, −8, 2, 4, 15 } → median = 2.
 If N = 0, set = { −9, −8, 0, 4, 15 } → median = 0.
 Different medians possible.

* Statement (2) alone is  not sufficient .
 
Final Answer:
 Statement (1) alone is sufficient; statement (2) alone is not. 
 →  Answer (A) .

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

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GMAT Data Sufficiency (DS) Questions

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

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