If the range of the six numbers 4, 3, 14, 7, 10 and x is 12, what is

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.

Answer: D.
_________________

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

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

D. +1

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

Thanks.

+1 from me.

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

D is the answer
_________________

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
_________________

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.

Answer: D
_________________

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

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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!

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

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.
_________________

Answer: D.[/quote]

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!

If we examine the KNOWN values in ascending order, we have {3, 4, 7, 10, 14}
These numbers have a range of 11 (since 14 - 3 = 11)

In order the set to have a range of 12, there are two possible values for x:

case a: x = 2, in which case the set is {2, 3, 4, 7, 10, 14}
case b: x = 15, in which case the set is {3, 4, 7, 10, 14, 15}

So, the difference in x-values = 15 - 2 = 13

Answer: D

Answer: Option D

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

Answer: Option D

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

why the smallest is not 3-x = 12, then x = -9

Hi Tanchat,

The prompt tells us that the range of the SIX numbers is 12, meaning that the difference between the largest and the smallest of those six numbers must equal 12. If X = -9, then the group of six numbers is: -9, 3, 4, 7, 10, 14.... but this group has a range of 14 - (-9) = 23, which does not match-up with the information in the prompt. There are two numbers for the value of X that will make the overall range of the six numbers equal 12...

X = 15... since 15 - 3 = 12

and

X = 2... since 14 - 2 = 12

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

Thank you, I missed "the range" Thank you for your help ! EMPOWERgmatRichC

X is random variable and I dont know where to place but I saw in question it has mentioned something highest or lowest so here is my approach

1.) Lets say x comes at lowest place in series
X,3,4,7,10,14
Range => 14-x=12
X=2 (lowest value)

2.) Now put x at the highest place
3,4,7,10,14,x
Range=> x-3=12
X=15 (highest value)

Difference of highest and lowest value of x is 15-2=13
HENCE 13 is the answer.

Posted from my mobile device