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Manager  Joined: 06 Feb 2010
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Schools: University of Dhaka - Class of 2010
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If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?

(A) 0
(B) 2
(C) 12
(D) 13
(E) 15
Math Expert V
Joined: 02 Sep 2009
Posts: 59727
Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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6
monirjewel wrote:
If the range of the six numbers 4, 3, 14, 7, 10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15

The range of a set is the difference between the largest and smallest elements of a set.

Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.

The the difference between the greatest possible value of x and least possible value of x is 15-2=13.

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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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X must either be 15 or 2 to produce a range of 12.

D. +1
Senior Manager  Joined: 08 Nov 2010
Posts: 268
Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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nice question. As in international student, the word "range" didnt say anything to me before that.

Thanks.

+1 from me.
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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3
monirjewel wrote:
If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15

Range= Greatest value- least value

Range= 12

For the greatest value of x= 15, range will be 15-3= 12

For the least value of x= 2, the range will be 14-2= 12

so the difference between greatest and least value= 15-2= 13

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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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1
monirjewel wrote:
If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15

The Range of the numbers without x is 14-3 = 11......
Now x changes the range to 12....

so x can be 1 greater than largest value or 1 lesser than eth smallest value....
so Range = 11+1+1 = 13
D
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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4
monirjewel wrote:
If the range of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15

We are given that the range of the six numbers 4,3,14,7,10, and x is 12.

If x is the largest value in the list, then 3 would be the smallest number in the list. Since the range is 12, the largest number that x could be is 3 + 12 = 15.

If x is the smallest value in the list, then 14 would be the largest number in the list. Since the range is 12, the smallest number that x could be is 14 - 12 = 2.

Thus, the difference between the largest and smallest possible values of x is 15 - 2 = 13.

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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1
Hi All,

The general category of 'statistics' will show up on the GMAT at least a couple of times on Test Day, so it's important to know the 'math definition' of each of the statistical words - "mean", "median", "mode", "range" and "standard deviation." Sometimes you'll be asked to calculate one (or more) of those terms; sometimes you'll use information given about one of those terms to figure out something else.

Here, we're told that the RANGE of six numbers is 12. Since range is 'the difference between the largest and smallest terms', it helps to list out the numbers...

Notice how one of the numbers is a VARIABLE though; I'm going to put that at the end of the list for convenience.

3, 4, 7, 10, 14...... X

The range of the first 5 numbers is 11, so we have to make the X some number that will make the range = 12.

We COULD make X = 15... since 15 - 3 = 12

We COULD make X = 2... since 14 - 2 = 12

Now we know the greatest and least possible values of X, so the answer to the question is 15 - 2 = 13

GMAT assassins aren't born, they're made,
Rich
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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Bunuel wrote:
monirjewel wrote:
If the range of the six numbers 4, 3, 14, 7, 10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15

The range of a set is the difference between the largest and smallest elements of a set.

Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.

The the difference between the greatest possible value of x and least possible value of x is 15-2=13.

Hello Brunel, I got confused because I thought there was a hidden constraint indicating that x cannot be greater than 14 (based on the set given). In addition, if X is given as 12, I am not sure how to know when to use that information to then decipher that X can be either 15 or 13. I never put that together. Why is it OK in this situation to take givens (such as x=12) and then further solve for X? May you please help clarify? Thank you!
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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1
Hi IKR9,

In this question, we are NOT told that X is 12, we are told that the RANGE of six numbers is 12. Since range is 'the difference between the largest and smallest terms', it helps to list out the numbers...

Notice how one of the numbers is a VARIABLE though; I'm going to put that at the end of the list for convenience.

3, 4, 7, 10, 14...... X

The range of the first 5 numbers is 11, but we're told the range is 12, so we have to make the X some number that will increase the range to 12.

We COULD make X = 15... since 15 - 3 = 12

We COULD make X = 2... since 14 - 2 = 12

Now we know the greatest and least possible values of X, so the answer to the question is 15 - 2 = 13

GMAT assassins aren't born, they're made,
Rich
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Joined: 02 Sep 2009
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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IKR9 wrote:
Bunuel wrote:
monirjewel wrote:
If the range of the six numbers 4, 3, 14, 7, 10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 0
(B) 2
(C) 12
(D) 13
(E) 15

The range of a set is the difference between the largest and smallest elements of a set.

Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.

The the difference between the greatest possible value of x and least possible value of x is 15-2=13.

Hello Brunel, I got confused because I thought there was a hidden constraint indicating that x cannot be greater than 14 (based on the set given). In addition, if X is given as 12, I am not sure how to know when to use that information to then decipher that X can be either 15 or 13. I never put that together. Why is it OK in this situation to take givens (such as x=12) and then further solve for X? May you please help clarify? Thank you!

It is not given that x = 12. The stem says that the range of the six numbers {4, 3, 14, 7, 10, x} is 12.
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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Hello Brunel, I got confused because I thought there was a hidden constraint indicating that x cannot be greater than 14 (based on the set given). In addition, if X is given as 12, I am not sure how to know when to use that information to then decipher that X can be either 15 or 13. I never put that together. Why is it OK in this situation to take givens (such as x=12) and then further solve for X? May you please help clarify? Thank you![/quote]

It is not given that x = 12. The stem says that the range of the six numbers {4, 3, 14, 7, 10, x} is 12.[/quote]

Thank you for the confirmation. That's odd because I am using the wiley efficient program that has the computer version of all GMAT questions, it appears its a bit different on that vs. the text book on this question.

Thanks!
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Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the  [#permalink]

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_________________ Re: If the range of the six numbers 4,3,14,7,10 and x is 12, what is the   [#permalink] 11 Jun 2019, 19:10
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