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S is a set containing 9 different positive odd primes

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S is a set containing 9 different positive odd primes [#permalink] New post 13 Jan 2012, 08:10
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41% (02:24) correct 59% (01:20) wrong based on 86 sessions
S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

(A) The median of S is prime.
(B) The median of T is prime
(C) The median of S is equal to the median of T.
(D) The sum of the terms in S is prime.
(E) The sum of the terms in T is prime.


If E were not a choice, how to eliminate the other choices in less than two minutes? Specially, choice D.
[Reveal] Spoiler: OA

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Re: Sets of primes [#permalink] New post 13 Jan 2012, 16:44
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Hi, there! I'm happy to help with this. :)

What is the source of this question? This is a very challenging question. It seems to me considerably harder than what the GMAT would ask. It is certainly not something you should worry about figuring out completely in under two minutes!

Here is my explanation. The question states: "S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?"

(A) The median of S is prime.
This must be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.

(B) The median of T is prime.
This may or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numbers could be even (average of 71 and 73 is 72), and hence not prime, or it could be odd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.

(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89 & 113, which happens to be 101. It's an exceptional case, but it could be true.

(D) The sum of the terms in S is prime.
This may or may not be true. The sum of 9 odd number must be an odd number. That odd number could be prime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.

(E) The sum of the terms in T is prime.
This must be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.

Again, I realize that's not an incredibly fast approach, but this is a difficult question. Here's another practice question about prime numbers.

http://gmat.magoosh.com/questions/850

The question at that link should be followed by a video solution.

I hope my response was helpful to some extent. Please let me know if you have any questions on what I've said.

Mike :)
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Re: Sets of primes [#permalink] New post 14 Jan 2012, 01:55
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metallicafan wrote:
S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

(A) The median of S is prime.
(B) The median of T is prime
(C) The median of S is equal to the median of T.
(D) The sum of the terms in S is prime.
(E) The sum of the terms in T is prime.


If E were not a choice, how to eliminate the other choices in less than two minutes? Specially, choice D.


In my opinion, the concept the question maker wanted to test is pretty simple - the sum of even number of odd numbers is even i.e. the sum of 8 odd numbers will be even. It is a GMAT relevant question which can be solved in under a minute because of this reason. If option (E) were not given, it would take quite a bit of time and the question wouldn't be GMAT relevant anymore.

This is an example of how GMAT makes high level questions which still test you on basic concepts by making the question look convoluted.
When you read the question, you should note that S has 9 different odd prime numbers and T has 8 different odd prime numbers. Do not start analyzing the options before reading all of them once. A single read is enough to tell you that sum of all numbers of T must be even and hence will not be prime.

Mike above has shown you exactly how all other options can be discarded so I will not repeat the explanation but mind you, it will take some time to go through them if you miss out on the simple concept of option (E).
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Re: Sets of primes [#permalink] New post 14 Jan 2012, 13:10
Just to add to what Karishma said above, there is one useful takeaway from this question: if a question ever asks "which of the following...", then start with the simplest answer choice. Even if it isn't right, it should take you very little time to analyze. Note that you never need to bother working with the hardest answer choice; if the four simplest ones are all incorrect, by process of elimination you know the hardest one must be correct.

The question in the post above can be solved quite quickly if you focus on the easiest statements to analyze first. If you start by looking at the hardest choice (which is D), you can spend a long time on it.
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Re: S is a set containing 9 different positive odd primes [#permalink] New post 02 Dec 2013, 10:02
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Re: S is a set containing 9 different positive odd primes   [#permalink] 02 Dec 2013, 10:02
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