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Median

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Source: — Data Sufficiency |
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by goalevan » Sun Jul 17, 2011 7:47 am
We are given 4 of the 5 numbers in the set {-9, -8, 4, 15, N} with N as an unknown value.

If -8 <= N <= 4, then N is the median, since there are an odd number of integers in the set.
If N < -8 or N > 4, then (-8 + 4)/2 = -2 is the median.

In other words, if we know that -8 <= N <= 4, we must know its value to know the median. If we know that N < -8 or N > 4, we need no other information to know that the median of the set is -2.

1) If N^6 is even, then N is even since any number multiplied by an even number is even, and N^6 consists only of factors N.

Thus this statement tells you that N is even AND a prime number. The only even prime number is 2.

If we know that N = 2, the median of the set can be calculated. Sufficient.

Statement 2) 2N + 14 < 20
2N < 6
N < 3

From above, we know that if -8 <= N < 3, then N is the median. But if N < -8, then -2 is the median. Even if we did know that -8 <= N, we don't know N's value, so this statement is insufficient.

A
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by beatthegmat.garry » Sun Jul 17, 2011 7:50 am
IMO the choice is A

Statement (1):
N is prime and N^6 is even hence N is even as well. So N will be 2 (as 2 is the only even prime number)
Hence (1) is sufficient.

Note: Prime numbers can only be positive.

Statement (2):
2N+14<20 and hence N<3. But we cant guess the exact value of N.
Hence (2) is not sufficiet.

Hope this helps :)

Thanks !
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by MI3 » Sun Jul 17, 2011 7:51 am
goalevan wrote:We are given 4 of the 5 numbers in the set {-9, -8, 4, 15, N} with N as an unknown value.

If -8 <= N <= 4, then N is the median, since there are an odd number of integers in the set.
If N < -8 or N > 4, then (-8 + 4)/2 = -2 is the median.

In other words, if we know that -8 <= N <= 4, we must know its value to know the median. If we know that N < -8 or N > 4, we need no other information to know that the median of the set is -2.

1) If N^6 is even, then N is even since any number multiplied by an even number is even, and N^6 consists only of factors N.

Thus this statement tells you that N is even AND a prime number. The only even prime number is 2.

If we know that N = 2, the median of the set can be calculated. Sufficient.

Statement 2) 2N + 14 < 20
2N < 6
N < 3

From above, we know that if -8 <= N < 3, then N is the median. But if N < -8, then -2 is the median. Even if we did know that -8 <= N, we don't know N's value, so this statement is insufficient.

A
Hello Goalevan,

Thank you for the detailed explanation, but I still have a doubt (and the reason why I chose E instead of A), would "-2" not get classified as a prime number and (-2)^6 and even number?
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by MI3 » Sun Jul 17, 2011 7:56 am
beatthegmat.garry wrote:IMO the choice is A

Statement (1):
N is prime and N^6 is even hence N is even as well. So N will be 2 (as 2 is the only even prime number)
Hence (1) is sufficient.

Note: Prime numbers can only be positive.

Statement (2):
2N+14<20 and hence N<3. But we cant guess the exact value of N.
Hence (2) is not sufficiet.

Hope this helps :)

Thanks !
Hello Garry,

I think our posts crossed, my understanding was that negative numbers are also prime numbers? Is that not the case? Sorry, I know this is a fundamental question, but I thought I read somewhere that negative numbers are also included as prime numbers (unless on the GMAT we don't treat them as prime?).

Thanks.
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by beatthegmat.garry » Sun Jul 17, 2011 8:20 am
I think negative numbers are not prime:

https://www.beatthegmat.com/negative-pri ... t1374.html
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by Frankenstein » Sun Jul 17, 2011 8:25 am
Hi,
Negative numbers are never considered prime. Just stick to the basic definition. Any number which is divisible by 1 and itself is a prime. And the prime number has only two factors. So, if you consider -2, it is divisible by1,-1,2,-2.. So, never think about negative numbers.
Hello Garry,

I think our posts crossed, my understanding was that negative numbers are also prime numbers? Is that not the case? Sorry, I know this is a fundamental question, but I thought I read somewhere that negative numbers are also included as prime numbers (unless on the GMAT we don't treat them as prime?).

Thanks.
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by Ian Stewart » Sun Jul 17, 2011 3:03 pm
Negative numbers are never considered prime. The smallest prime number is 2. If a number is both even and prime, that number must be equal to 2, which makes Statement 1 sufficient.
goalevan wrote: In other words, if we know that -8 <= N <= 4, we must know its value to know the median. If we know that N < -8 or N > 4, we need no other information to know that the median of the set is -2.
While the reasoning in your solution is correct, you've made one mistake (a few times). If N < -8, the median of the set is not equal to -2. If N is the smallest element in the set, for example, then the set is, in increasing order:

N, -9, -8, 4, 15

and the median is -8, not -2. I imagine you were averaging -8 and 4 to get a median of -2, but you would only average two elements to find a median if you had an even number of elements in a set, and here we have an odd number of elements: the median *must* be in the set. The only way the median can be -2 here is if N = -2.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by ArpanaAmishi » Mon Jul 18, 2011 12:28 am
Ian Stewart wrote:Negative numbers are never considered prime. The smallest prime number is 2. If a number is both even and prime, that number must be equal to 2, which makes Statement 1 sufficient.
Need a clarification... point 1 said N is prime and N^6 is even , this is not said 'N' itself is even prime, so I think N could be anyother prime number too (though I couldn't check all combinations)
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by Frankenstein » Mon Jul 18, 2011 5:09 am
ArpanaAmishi wrote: Need a clarification... point 1 said N is prime and N^6 is even , this is not said 'N' itself is even prime, so I think N could be anyother prime number too (though I couldn't check all combinations)
Hi,
An odd number raised to power 6(in fact raised to any positive integer power) is always odd.
Similarly, an even number number raised to any positive integer power can only be even.
So, N has to be even in this case and every prime number other than 2 is odd.
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by ArpanaAmishi » Mon Jul 18, 2011 9:52 pm
got it thanks :-)
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by amit2k9 » Mon Jul 18, 2011 11:23 pm
a.N^6 = even meaning N = 2.sufficient.

b N < 3 meaning N can be both positive and negative numbers. not sufficient.

A it is.
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