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## OG-17 Problem solving

tagged by: Brent@GMATPrepNow

This topic has 5 expert replies and 0 member replies
Joy Shaha Senior | Next Rank: 100 Posts
Joined
05 May 2016
Posted:
59 messages
3

#### OG-17 Problem solving

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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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
Joined
09 Apr 2015
Posted:
506 messages
Followed by:
6 members
39
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.

_________________
Jeffrey Miller Head of GMAT Instruction

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
8946 messages
Followed by:
468 members
2867
GMAT Score:
800
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

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

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
Joined
09 Apr 2015
Posted:
506 messages
Followed by:
6 members
39
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.

_________________
Jeffrey Miller Head of GMAT Instruction

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
8946 messages
Followed by:
468 members
2867
GMAT Score:
800
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

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

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
902 messages
Followed by:
18 members
470
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.

-Jay
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Manhattan Review GMAT Prep

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