• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If x and y are unknown positive integers, is the mean of the

This topic has 2 expert replies and 0 member replies

If x and y are unknown positive integers, is the mean of the

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Manhattan Prep

If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set?

1) x + y = 7.
2) x - y = 3.

OA A.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
AAPL wrote:
Manhattan Prep

If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set?

1) x + y = 7.
2) x - y = 3.
Known values, in ascending order:
1, 5, 6, 7

Statement 1: x+y = 7
Mean = sum/quantity = (1+5+6+7+x+y)/6 = (1+5+6+7+7)/6 = 26/6 = 13/3 = 4.33.
Text EXTREMES.

Case 1: x and y are far from each other
If x=1 and y=6, we get:
1, 1. 5, 6, 6, 7
Median = (5+6)/2 = 11/2 = 5.5

Case 2: x and y are near each other
If x=3 and y=4, we get:
1, 3, 4, 5, 6, 7
Median = (4+5)/2 = 9/2 = 4.5

In both cases, the mean is LESS than the median, so the answer to the question stem is NO.
SUFFICIENT.

Statement 2: x-y = 3
Again, test EXTREMES.

Case 1: x and y are as small as possible.
If x=4 and y=1, we get:
1, 1, 4, 5, 6, 7
Mean = (1+1+4+5+6+7)/6 = 24/6 = 4
Median = (4+5)/2 = 9/2 = 4.5.
In this case, the mean is LESS than the median, so the answer to the question stem is NO.

Case 2: x and y are large
If x=100 and y=97, we get:
1, 5, 6, 7, 97, 100
Mean = (1+5+6+7+97+100)/6 = 216/6 = 108/3 = 36.
Median = (6+7)/2 = 13/2 = 6.5.
In this case, the mean is GREATER than the median, so the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

The correct answer is A.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Post
AAPL wrote:
Manhattan Prep

If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set?

1) x + y = 7.
2) x - y = 3.

OA A.
Let's take each statement one by one.

1) x + y = 7.

Mean = (1 + 5 + 6 + 7 + x + y)/6 = (19 + x + y)/6 = (19 + 7)/6 = 4.33

To find out median, we must first arrange terms in an ascending order.

The terms, excluding x and y are: 1, 5, 6, 7.

Median, excluding x and y: 5.5

If one of the terms (x and y) is less than equal to 5 and the other term is greater than or equal 6, i.e. one is added to the left of 5.5 and the other is added to its right, the median would not change.

Given x + y = 7, the pairs of x and y are: (1, 6); (2, 5); and (3, 4)

Needless to state that if the pair (1, 6) is added, the median would not change. Or, Median = 5.5 . Mean = 4.33. The answer is No.

It will be interesting to see how would median change when we add (2, 5) and (3, 4).

Since for both the pairs, the maximum values (5 and 4) are less than the median value (5.5), the new median would be less than 5.5. But will the median be greater than 4.33? Let's see.

Again, since for the pair (2, 5), the maximum value (5) is greater than mean (4.33), the new median, would though be less than 5.33, it would be greater than mean 4.33. The answer is No.

So, we are left with the last pair (3, 4).

The set would be 1, 3, 4, 5, 6, 7 and its median would be (4 + 5)/2 = 4.5 > Mean 4.33. The answer is still No.

Unique answer. Sufficient.

2) x - y = 3.

If x and y both are very big, then both of them added to the right of median, 5.5,

Mean = Mean = (19 + x + y)/6 = a very big number

The set would be 1, 5, 6, 7, x, y and its median would be (6 + 7)/2 = 6.5 < Very big Mean. The answer is Yes.

However, given x - y = 3, we can have x and y as: (4, 1); (5, 2); etc.

Let's see the pair (4, 1).

Mean = Mean = (19 + x + y)/6 = (19 + 4 + 1)/6 = 4

The set would be 1, 1, 4, 5, 6, 7 and its median would be (4 + 5)/2 = 4.5 > Mean 4. The answer is No.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Himayatnagar | Hyderabad GMAT Prep | Bangalore GMAT Courses | Kukatpally GRE Prep | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Top First Responders*

1 Brent@GMATPrepNow 67 first replies
2 fskilnik@GMATH 53 first replies
3 Jay@ManhattanReview 39 first replies
4 GMATGuruNY 34 first replies
5 Rich.C@EMPOWERgma... 31 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

128 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 image description Max@Math Revolution

Math Revolution

88 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

78 posts
5 image description Jay@ManhattanReview

Manhattan Review

75 posts
See More Top Beat The GMAT Experts