BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is the average (arithmetic mean) of x, y, and z equal to the

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Is the average (arithmetic mean) of x, y, and z equal to the

by Max@Math Revolution » Wed Mar 06, 2019 11:57 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

Is the average (arithmetic mean) of x, y, and z equal to their median?

1) y is the average (arithmetic mean) of x, y, and z
2) z = 2y - x
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

evenly spaced x, y and z

by GMATGuruNY » Thu Mar 07, 2019 4:06 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Max@Math Revolution wrote:[GMAT math practice question]

Is the average (arithmetic mean) of x, y, and z equal to their median?

1) y is the average (arithmetic mean) of x, y, and z
2) z = 2y - x
Statement 1:
In other words, y is HALFWAY BETWEEN x and z, implying that x, y and z are EVENLY SPACED.
For any evenly spaced set, the average = the median.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
x+z = 2y
(x+z)/2 = y
Implication:
y is the average of x and z -- the same information as that given in Statement 1.
Since Statement 1 is sufficient, so is Statement 2.
SUFFICIENT.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Sun Mar 10, 2019 5:02 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

If data are symmetric, then the average and the median of the data are the same.

Condition 1):
If y is the mean of x, y and z, then x, y, z are symmetric. To see this note that ( x + y + z ) / 3 = y implies that y = ( x + z ) / 2. So, 2y = x + z and y - x = z - y, which means that x, y, z are symmetric.
Condition 1) is sufficient.

Condition 2):
z = 2y - x is equivalent to y - x = z - y, which is equivalent to condition 1).
Condition 2) is sufficient.

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, D is the answer.
Answer: D
Top
Post new topic Post Reply
• Page 1 of 1