OG-17 Problem solving

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Joy Shaha: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu May 05, 2016 4:20 am; Thanked: 3 times

by Joy Shaha » Mon Jan 23, 2017 11:06 am

Q. 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 the least possible
value of x?
A) 0 B) 2 C) 12 D) 13 E) 15

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Source: Beat The GMAT — Problem Solving | Mon Jan 23, 2017 11:06 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jan 23, 2017 11:21 am

Joy Shaha wrote:Q. 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 the least possible
value of x?
A) 0 B) 2 C) 12 D) 13 E) 15

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

RELATED VIDEO
- Range and Standard Deviation: https://www.gmatprepnow.com/module/gmat ... /video/806

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Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Jan 24, 2017 6:12 am

Joy Shaha wrote:Q. 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 the least possible
value of x?

A) 0
B) 2
C) 12
D) 13
E) 15

Hi Joy,

For a better reference, I suggest that you mention question number also in the subject. There are at least three posts with the subject 'OG -17 Problem-solving.'

Let us discuss the problem now.

Let us arrange the given numbers in an ascending order: 3, 4, 7, 10, 14.

We know that the range = 12.

To get the least value of X, we must make 14 the greatest. Thus Range = 12 = 14 - Smallest number

=> Smallest number = 14 - 12 = 2 = X

To get the greatest value of X, we must make X the greatest. Thus Range = 12 = X - 3

=> Greatest number = X = 12 + 3 = 15.

So, the difference in the values of X = 15 - 2 = 13.

Answer: D

-Jay
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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Jan 24, 2017 6:21 am

Another approach to this question could be...

Presently the range of 3, 4, 7, 10, and 14 is 14 - 3 = 11.

We want to increase the range by '1' (12 - 11).

This can be done in two ways:

1. Decrease '3' by '1', thus, X = 3 - 1 = 2 (Least value)

2. Increase '14' by '1', thus, X = 14 + 1 = 15 (Greatest value)

Difference in values of X = 15 - 2 = 13.

Answer: D

-Jay
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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Fri Jan 27, 2017 10:08 am

Joy Shaha wrote:Q. 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 the 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.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Jan 27, 2017 5:44 pm

Hi Joy Shaha,

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: D

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

Contact Rich at [email protected]

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