GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jan 2019, 20:58

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# x, y, and z are integers and x<y<z. C is the set of all integers from

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52164
x, y, and z are integers and x<y<z. C is the set of all integers from  [#permalink]

### Show Tags

17 May 2017, 23:25
2
13
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:34) correct 43% (02:27) wrong based on 117 sessions

### HideShow timer Statistics

x, y, and z are integers and x<y<z. C is the set of all integers from x to y, inclusive, and D is the set of all integers from y to z, inclusive. The median of set C is $$\frac{5}{8}y$$ and the median of set D is $$\frac{3}{4}z$$. If E is the set of all integers from x to z, inclusive, then the median of set E is what fraction of z?

A. 1/2
B. 9/16
C. 5/8
D. 11/16
E. 3/4

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2722
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: x, y, and z are integers and x<y<z. C is the set of all integers from  [#permalink]

### Show Tags

18 May 2017, 05:41
5
1
Bunuel wrote:
x, y, and z are integers and x<y<z. C is the set of all integers from x to y, inclusive, and D is the set of all integers from y to z, inclusive. The median of set C is $$\frac{5}{8}y$$ and the median of set D is $$\frac{3}{4}z$$. If E is the set of all integers from x to z, inclusive, then the median of set E is what fraction of z?

A. 1/2
B. 9/16
C. 5/8
D. 11/16
E. 3/4

C is the set of all integers from x to y

CONCEPT: For terms in Arithmatic progression (in which adjacent terms are equidistant) the MEAN = MEDIAN = Average of First and Last Term

i.e. Median of C = (x+y)/2 = (5/8)y (Given)
i.e. 4x + 4y = 5y
i.e. y = 4x

D is the set of all integers from y to z
i.e. Median of D = (y+z)/2 = (3/4)z (Given)
i.e. 2y + 2z = 3z
i.e. z = 2y

Median of Set E = (x+z)/2 = [(y/4)+2y]/2 = 9y/8 = (9/8)*(z/2) = (9/16)z

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

##### General Discussion
Intern
Joined: 29 Jan 2017
Posts: 47
Re: x, y, and z are integers and x<y<z. C is the set of all integers from  [#permalink]

### Show Tags

21 May 2017, 18:56
1
Set C: make y= 8 then the median is 5 and x=2
Set Z: make z=4 then the median is 3 and y=2

x<y<z
C: 2<8
Z: 2<4 (x4)
E: 2<8<16 median is 9

9/16
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1428
Location: India
Re: x, y, and z are integers and x<y<z. C is the set of all integers from  [#permalink]

### Show Tags

21 May 2017, 21:44
2
Lets take y=8, so take median of C = 5/8 * 8 = 5.
So set C is a set of consecutive integers which goes upto 8 and its median is 5.
This means C must be: C = {2, 3, 4, 5, 6, 7, 8}

Now set D should start from 8 and go upto z such that median = 3z/4
lets try for z=16, so median becomes 3*16/4 = 12
So set D goes from 8 to 16 and median is 12 (which fits in properly, no mistake)
D = {8, 9, 10, 11, 12, 13, 14, 15, 16}

now Set E = {2, 3, 4, ....., 16}
15 terms, median will be the middle term, which is (15+1)/2 = 8th term
8th term of set E is 9.

We have to say 9 is what fraction of z.
9/16
Intern
Joined: 12 Sep 2017
Posts: 28
Re: x, y, and z are integers and x<y<z. C is the set of all integers from  [#permalink]

### Show Tags

08 Oct 2017, 08:08
How do we know that the numbers are consecutive?
Math Expert
Joined: 02 Sep 2009
Posts: 52164
Re: x, y, and z are integers and x<y<z. C is the set of all integers from  [#permalink]

### Show Tags

08 Oct 2017, 08:10
@s wrote:
How do we know that the numbers are consecutive?

We are told that C is the set of all integers from x to y, inclusive.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9423
Re: x, y, and z are integers and x<y<z. C is the set of all integers from  [#permalink]

### Show Tags

25 Dec 2018, 19:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: x, y, and z are integers and x<y<z. C is the set of all integers from &nbs [#permalink] 25 Dec 2018, 19:56
Display posts from previous: Sort by