X, 81, 73, 71, 98, 73, 64 What is the value of X in the

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Dec 11, 2019 7:25 am

X, 81, 73, 71, 98, 73, 64

What is the value of X in the above list of 7 numbers?

(1) The average (arithmetic mean) of these 7 numbers is 80.
(2) The range of these 7 numbers is 36.

OA A

Source: Official Guide

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Source: Beat The GMAT — Data Sufficiency | Wed Dec 11, 2019 7:25 am

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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 » Thu Dec 12, 2019 11:04 pm

BTGmoderatorDC wrote:X, 81, 73, 71, 98, 73, 64

What is the value of X in the above list of 7 numbers?

(1) The average (arithmetic mean) of these 7 numbers is 80.
(2) The range of these 7 numbers is 36.

OA A

Source: Official Guide

Let's take each statement one by one.

(1) The average (arithmetic mean) of these 7 numbers is 80.

=> Sum of these 7 numbers = 80*7 = 560. Thus, X = 560 - 81 - 73 - 71 - 98 - 73 - 64 = A unique value. Sufficient.

(2) The range of these 7 numbers is 36.

Case 1: Say 98 is the largest number, thus the smallest = 98 - 36 = 62. X can be 62.
Case 2: Say X is the largest number, thus the smallest = 64 = X - 36 => X = 100. X can be 100.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

edited:

by deloitte247 » Thu Dec 19, 2019 10:23 pm

We want to find the value of X in the list of 7 numbers mentioned in this question.
Statement 1: The average (arithmetic mean) of the 7 numbers is 80.
$$\frac{Summation\ FX}{Summation\ f}=80\ where\ f=7\ and\ fx=X+81+73+71+98+73+64\ =\ x+460$$
$$\frac{X+460}{7}=80$$
$$X+460=560$$
$$X=560-460=100$$
Statement 1 is SUFFICIENT.

Statement 2: The range of these 7 numbers is 36.
To find the range, the 7 numbers must be arranged in ascending order, and with this;
Range = highest number - lowest number
The position of X include;
- X can be the highest number i.e, 64, 71, 73, 73, 81, 98, X.
- X can be the lowest number i.e, X, 64, 71, 73, 73, 81, 98.
- X can neither be the highest nor lowest i.e 64, 71, X, 73, 73, 81, 98.
If X is neither the highest nor lowest, then we cannot use the range to find the value of X.
However, if X is the highest number, then,
Range = X - 64
36 = X - 64
X = 36 + 64 = 100

Also, if X is the lowest number,
Range = 98 - X
36 = 98 - X
X = 98 - 36 = 62
These are the two different and possible values of X in this statement, hence, statement 2 is NOT SUFFICIENT.

Since statement 1 alone is SUFFICIENT, the correct answer is option A. $$$$

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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

Re: X, 81, 73, 71, 98, 73, 64 What is the value of X in the

by Brent@GMATPrepNow » Wed Apr 08, 2020 8:57 am

BTGmoderatorDC wrote: ↑
Wed Dec 11, 2019 7:25 am
X, 81, 73, 71, 98, 73, 64

What is the value of X in the above list of 7 numbers?

(1) The average (arithmetic mean) of these 7 numbers is 80.
(2) The range of these 7 numbers is 36.

OA A

Source: Official Guide

Target question: What is the value of X?

Statement 1: The average (arithmetic mean) of these 7 numbers is 80.

We can write: [m][fraction]X + 81+73+71+98+73+64/7[/fraction]=80[/m]

Multiplyvboth sides of the equation by [m]7[/m] to get: [m]X + 81+73+71+98+73+64 = 560[/m]

At this point, we can see that we COULD solve this equation for X, which means we could answer the target question (but we would never waste time doing so on test day)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The range of these 7 numbers is 36.
Let's arrange the 6 KNOWN values in ascending order: 64, 71, 73, 73, 81, 98
98 - 64 = 34
So the range of the 6 KNOWN values is 34.
To get a range of 36, X can be one of two different values. Consider these two cases:

Case a: x = 62, which means we get: 62, 64, 71, 73, 73, 81, 98. Range = 98 - 62 = 36 (Perfect!) In this case, the answer to the target question is x = 62
Case b: x = 100, which means we get: 64, 71, 73, 73, 81, 98, 100. Range = 100 - 64 = 36 (Perfect!) In this case, the answer to the target question is x = 100
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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