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M18-11

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M18-11  [#permalink]

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New post 16 Sep 2014, 01:03
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (00:48) correct 36% (00:45) wrong based on 36 sessions

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Re M18-11  [#permalink]

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New post 16 Sep 2014, 01:03
Official Solution:


Statement (1) by itself is insufficient. S1 allows \(x\) to be either -1 or 9 (the range is either \(7 - (-1) = 8\) or \(9 - 1 = 8\)).

Statement (2) by itself is insufficient. S2 allows \(x\) to be any number smaller than 2.

Statements (1) and (2) combined are sufficient. S1 and S2 exclude \(x = 9\) as a solution and we are left with \(x = -1\).


Answer: C
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Re: M18-11  [#permalink]

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New post 18 Jun 2015, 07:52
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient. S1 allows \(x\) to be either -1 or 9 (the range is either \(7 - (-1) = 8\) or \(9 - 1 = 8\)).

Statement (2) by itself is insufficient. S2 allows \(x\) to be any number smaller than 2.

Statements (1) and (2) combined are sufficient. S1 and S2 exclude \(x = 9\) as a solution and we are left with \(x = -1\).


Answer: C


Hi!

Does the second condition mean that x is smaller than 2 but also equal?

If not, Why Not ?

Thanks in advance.

ALe
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Re: M18-11  [#permalink]

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New post 18 Jun 2015, 07:57
BCCLSN wrote:
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient. S1 allows \(x\) to be either -1 or 9 (the range is either \(7 - (-1) = 8\) or \(9 - 1 = 8\)).

Statement (2) by itself is insufficient. S2 allows \(x\) to be any number smaller than 2.

Statements (1) and (2) combined are sufficient. S1 and S2 exclude \(x = 9\) as a solution and we are left with \(x = -1\).


Answer: C


Hi!

Does the second condition mean that x is smaller than 2 but also equal?

If not, Why Not ?

Thanks in advance.

ALe


Yes, from the second statement, x can be 2 too.
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Re: M18-11  [#permalink]

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New post 18 Jun 2015, 08:01
perfect ! thank you
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M18-11  [#permalink]

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New post 04 Jan 2018, 20:26
JourneyToTheTop wrote:
The question must make clear that x is an integer, not any real number.


Hope the solution below explains why is that not necessary.

If set \(S =\{2, 5, 1, x, 7\}\), what is \(x\) ?

(1) The range of set \(S\) is 8. If we consider the range of \(S =\{2, 5, 1, x, 7\}\), without x, then it's largest - smallest = 7 - 1 = 6. Since, the range of S is 8, then x must be either the largest or the smallest element. If x is the largest, then x - 1 = 8 --> x = 9 and if x is the smallest, then 7 - x = 8 --> x = -1. Not sufficient.

(2) The median of set \(S\) is 2. The median of a set with odd number of elements is the middle term, when arranged in ascending/descending order. Since 2 is the median, then it's the middle term: S = {x, 1, 2, 5, 7}. So, x must be less than or equal to 2. Not sufficient.

(1)+(2) From (1) x = 9 or x = -1 and from (2) x <=2, hence x = -1. Sufficient.

Answer: C.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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M18-11 &nbs [#permalink] 04 Jan 2018, 20:26
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