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# If X is a set of four numbers, a, b, c, and d, is the range of the num

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Math Expert
Joined: 02 Sep 2009
Posts: 46166
If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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12 Jan 2015, 11:07
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25% (medium)

Question Stats:

63% (00:39) correct 37% (00:34) wrong based on 115 sessions

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If X is a set of four numbers, a, b, c, and d, is the range of the numbers in X greater than 4?

(1) a is the greatest number in X
(2) a – d > 4

Kudos for a correct solution.

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Manager
Joined: 27 Oct 2013
Posts: 238
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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12 Jan 2015, 23:20
here we go.

St1: a is the greatest number in X

Clearly Insufficient

St2: a – d > 4

No information is given about b and c
Clearly Insufficient

Combining -

a is the greatest number in X, and a – d > 4 ---> a > d+4

If d is the minimum value in X, avg has to be greater than 4 (already given)

And If b or c has the minimum value (a being the greatest), b/c will be less than d (in that case) -> and that will automatically give Range greater than 4.

According to me Option C is the correct answer
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Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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12 Jan 2015, 23:31
1
Statement 1: In deed clearly insufficient as we are given no information about the difference off the numbers.

Statement 2: Sufficient. Even if a is not the largest number our be is not the smallest, there difference is larger than 4, so the range of the entire set cannot be smaller than 4. If the other two numbers are further apart, that only increases the range.

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Intern
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Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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13 Jan 2015, 12:16
1

If we have the difference of any two numbers in the set X greater than 4, the range will be at least equal to that difference, so it will be as well greater than 4
Manager
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Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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13 Jan 2015, 12:35
1
My 2 Cents on B !!!! Clearly A-B>4....sufficient enough to tell range atleast 4
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Joined: 23 Oct 2014
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Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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13 Jan 2015, 12:52
Bunuel wrote:
If X is a set of four numbers, a, b, c, and d, is the range of the numbers in X greater than 4?

(1) a is the greatest number in X
(2) a – d > 4

Kudos for a correct solution.

I want to pick C.

1. a is the greatest number in X. This info is insufficient as it tells us nothing about the value of a or what the other variables are.

2. a-d>4
This info is also insufficient as we still don't know what the other variables are.

Together:
Since we know that a is the greatest number in the set, a-d>4 tells us that
(The greatest value) - d > 4.
Even if d is not the smallest number to give us the range of set X we know that the range has to be greater than a-d, which is much greater than 4.
If d is the smallest value of the set then the range surely has to be be greater than 4.

So together we can only assume that the range must be greater than 4.
Manager
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Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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13 Jan 2015, 13:32
It still should be B. Even if a is not the greatest number of all, still the range is at least 5. If b or c are even greater than a, the range will be greater accordingly.
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Math Expert
Joined: 02 Sep 2009
Posts: 46166
Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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19 Jan 2015, 03:53
Bunuel wrote:
If X is a set of four numbers, a, b, c, and d, is the range of the numbers in X greater than 4?

(1) a is the greatest number in X
(2) a – d > 4

Kudos for a correct solution.

OFFICIAL SOLUTION:

To solve this problem, you have to be able to say with certainty that the range is greater than 4.
range = largest value – smallest value

Statement (1) tells you nothing to help you determine the range. It tells you which variable is largest, but you don’t know its value or the value of the lowest variable. Statement (1) isn’t sufficient, so the answer isn’t A or D.

Statement (2) tells you that the difference between two of the values, d and a, is more than 4. This is helpful because if any of the two numbers in the set have a difference of more than 4, the range, at the very least, has to be greater than 4. Statement (2) is sufficient, and you can eliminate C and E. Choose B.
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Math Expert
Joined: 02 Sep 2009
Posts: 46166
Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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19 Jan 2015, 03:53
Bunuel wrote:
Bunuel wrote:
If X is a set of four numbers, a, b, c, and d, is the range of the numbers in X greater than 4?

(1) a is the greatest number in X
(2) a – d > 4

Kudos for a correct solution.

OFFICIAL SOLUTION:

To solve this problem, you have to be able to say with certainty that the range is greater than 4.
range = largest value – smallest value

Statement (1) tells you nothing to help you determine the range. It tells you which variable is largest, but you don’t know its value or the value of the lowest variable. Statement (1) isn’t sufficient, so the answer isn’t A or D.

Statement (2) tells you that the difference between two of the values, d and a, is more than 4. This is helpful because if any of the two numbers in the set have a difference of more than 4, the range, at the very least, has to be greater than 4. Statement (2) is sufficient, and you can eliminate C and E. Choose B.

Similar question to practice: if-s-is-a-set-of-four-numbers-w-x-y-and-z-is-the-range-o-166184.html
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Re: If X is a set of four numbers, a, b, c, and d, is the range of the num [#permalink]

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11 Sep 2017, 04:56
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Re: If X is a set of four numbers, a, b, c, and d, is the range of the num   [#permalink] 11 Sep 2017, 04:56
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