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# S is a set containing 8 different positive odd numbers

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Manager
Joined: 11 Aug 2012
Posts: 110
Schools: HBS '16, Stanford '16
S is a set containing 8 different positive odd numbers  [#permalink]

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25 Oct 2012, 14:40
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Difficulty:

45% (medium)

Question Stats:

69% (01:49) correct 31% (01:48) wrong based on 203 sessions

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S is a set containing 8 different positive odd numbers. T is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

(A) The range of T is even.
(B) The mean of S is even.
(C) The mean of T is even.
(D) The range of S is equal to the range of T.
(E) The median of T is equal to the mean of T.
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Re: S is a set containing 8 different positive odd numbers  [#permalink]

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25 Oct 2012, 18:58
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danzig wrote:
S is a set containing 8 different positive odd numbers. T is a set containing 7 di¤erent numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The range of T is even.
(B) The mean of S is even.
(C) The mean of T is even.
(D) The range of S is equal to the range of T.
(E) The median of T is equal to the mean of T.

Option C.

Given: S is a set containing 8 different positive odd numbers
Easily inferred: T is a set containing 7 different odd numbers

(A) The range of T is even. - Always even, since it is a difference of two odd numbers
(B) The mean of S is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of T is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of S is equal to the range of T.
(E) The median of T is equal to the mean of T
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Re: S is a set containing 8 different positive odd numbers  [#permalink]

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26 Oct 2012, 04:09
danzig wrote:
S is a set containing 8 different positive odd numbers. T is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

(A) The range of T is even.
(B) The mean of S is even.
(C) The mean of T is even.
(D) The range of S is equal to the range of T.
(E) The median of T is equal to the mean of T.

Similar question to practice: s-is-a-set-containing-9-different-positive-odd-primes-126042.html

Hope it helps.
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Joined: 27 Jul 2017
Posts: 47
Re: S is a set containing 8 different positive odd numbers  [#permalink]

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24 Feb 2018, 08:18
danzig wrote:
S is a set containing 8 different positive odd numbers. T is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

(A) The range of T is even.
(B) The mean of S is even.
(C) The mean of T is even.
(D) The range of S is equal to the range of T.
(E) The median of T is equal to the mean of T.

Question statement - "T is a set containing 7 different numbers, all of which are members of S" means T is a subset of S and its all 7 numbers in the set are odd. By integer addition rule, we know odd+odd = even but if we pay special attention then will notice there are total 3 pairs of odd numbers and 1 still is left out.

Hence the answer should be (C) as its mean can never be even.
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Re: S is a set containing 8 different positive odd numbers   [#permalink] 24 Feb 2018, 08:18
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