Given the ascending set of positive integers {a, b, c, d, e, : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 07:19

### 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 June
Open Detailed Calendar

# Given the ascending set of positive integers {a, b, c, d, e,

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 29 Jan 2011
Posts: 367
Followers: 0

Kudos [?]: 201 [0], given: 87

Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

19 Jun 2011, 13:36
6
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:23) correct 31% (01:51) wrong based on 430 sessions

### HideShow timer Statistics

Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

(1) a + e = (3/4)(c + d)

(2) b + f = (4/3)(c + d)
[Reveal] Spoiler: OA

Last edited by siddhans on 20 Jun 2011, 21:32, edited 1 time in total.
Senior Manager
Joined: 29 Jan 2011
Posts: 367
Followers: 0

Kudos [?]: 201 [0], given: 87

### Show Tags

19 Jun 2011, 14:03
bong1993 wrote:
C it is

Please give detailed steps...Dont just give A,B, c...I already know its C
Manager
Joined: 02 Nov 2009
Posts: 138
Followers: 3

Kudos [?]: 165 [0], given: 97

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

04 Aug 2012, 14:59
Anyone can provide the logic behind this please..
Manager
Joined: 02 Nov 2009
Posts: 138
Followers: 3

Kudos [?]: 165 [0], given: 97

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

04 Aug 2012, 15:00
Bunuel If you can provide your inputs pls that vvill help
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93079 [5] , given: 10542

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

04 Aug 2012, 15:32
5
KUDOS
Expert's post
6
This post was
BOOKMARKED
Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

The median of a set with even number of elements is the average of two middle elements when arranged in ascending/descending order. Thus, the median of {a, b, c, d, e, f} is $$\frac{c+d}{2}$$.

So, the question asks: is $$\frac{c+d}{2}>\frac{a+b+c+d+e+f}{6}$$? --> is $$3c+3d>a+b+c+d+e+f$$? --> is $$2(c+d)>a+b+e+f$$?

(1) a + e = (3/4)(c + d) --> the question becomes: is $$2(c+d)>b+f+\frac{3}{4}(c + d)$$? --> is $$\frac{5}{4}(c + d)>b+f$$? Not sufficient.

(2) b + f = (4/3)(c + d). The same way as above you can derive that this statement is not sufficient.

(1)+(2) The question in (1) became: is $$\frac{5}{4}(c + d)>b+f$$? Since (2) says that $$b + f = \frac{4}{3}(c + d)$$, then the question becomes: is $$\frac{5}{4}(c + d)>\frac{4}{3}(c + d)$$? --> is $$\frac{1}{12}(c+d)<0$$? --> is $$c+d<0$$? As given that $$c$$ and $$d$$ are positive numbers, then the answer to this question is definite NO. Sufficient.

Not a good question.
_________________
Manager
Joined: 02 Nov 2009
Posts: 138
Followers: 3

Kudos [?]: 165 [0], given: 97

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

04 Aug 2012, 17:37
Bunuel Is this not a GMAT type question ?

Bunuel wrote:
Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

The median of a set with even number of elements is the average of two middle elements when arranged in ascending/descending order. Thus, the median of {a, b, c, d, e, f} is $$\frac{c+d}{2}$$.

So, the question asks: is $$\frac{c+d}{2}>\frac{a+b+c+d+e+f}{6}$$? --> is $$3c+3d>a+b+c+d+e+f$$? --> is $$2(c+d)>a+b+e+f$$?

(1) a + e = (3/4)(c + d) --> the question becomes: is $$2(c+d)>b+f+\frac{3}{4}(c + d)$$? --> is $$\frac{5}{4}(c + d)>b+f$$? Not sufficient.

(2) b + f = (4/3)(c + d). The same way as above you can derive that this statement is not sufficient.

(1)+(2) The question in (1) became: is $$\frac{5}{4}(c + d)>b+f$$? Since (2) says that $$b + f = \frac{4}{3}(c + d)$$, then the question becomes: is $$\frac{5}{4}(c + d)>\frac{4}{3}(c + d)$$? --> is $$\frac{1}{12}(c+d)<0$$? --> is $$c+d<0$$? As given that $$c$$ and $$d$$ are positive numbers, then the answer to this question is definite NO. Sufficient.

Not a good question.
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93079 [0], given: 10542

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

04 Aug 2012, 17:40
venmic wrote:
Bunuel Is this not a GMAT type question ?

It's a GMAT type question, but from my point of view not a very good one.
_________________
Intern
Joined: 06 Apr 2011
Posts: 13
Followers: 0

Kudos [?]: 2 [1] , given: 292

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

12 Feb 2013, 13:29
1
KUDOS
if all of the integers are positive, then how come c+d<o ?
question system contradicts with the solution...
You are right Bunuel.. not an air tight question.
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93079 [0], given: 10542

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

13 Feb 2013, 00:17
mbhussain wrote:
if all of the integers are positive, then how come c+d<o ?
question system contradicts with the solution...
You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Hope it's clear.
_________________
Manager
Joined: 23 May 2013
Posts: 167
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5
Followers: 2

Kudos [?]: 70 [0], given: 39

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

07 Mar 2014, 10:00
Bunuel wrote:
mbhussain wrote:
if all of the integers are positive, then how come c+d<o ?
question system contradicts with the solution...
You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Hope it's clear.

Bunuel, you have an algebra mistake in your solution, as the statements 1) and 2) combined boil down to:

$$1/2 (c+d) > 37/72 (c+d)$$.

This seems like a perfectly reasonable GMAT question.
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93079 [0], given: 10542

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

08 Mar 2014, 06:36
speedilly wrote:
Bunuel wrote:
mbhussain wrote:
if all of the integers are positive, then how come c+d<o ?
question system contradicts with the solution...
You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Hope it's clear.

Bunuel, you have an algebra mistake in your solution, as the statements 1) and 2) combined boil down to:

1/2 (c+d) > 37/72 (c+d)

This seems like a perfectly reasonable GMAT question.

What mistake are you talking about?
_________________
Joined: 25 Feb 2014
Posts: 233
GMAT 1: 720 Q50 V38
Followers: 7

Kudos [?]: 37 [1] , given: 145

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

09 Mar 2014, 19:55
1
KUDOS
We don't have to do any calculations here. For mean, we have to have the sum of the all the numbers in the set while for for the median c and d are sufficient. Since both the options together can give us the mean in terms of c+d, we can compare that against the mean which is also in terms of c+d. So C should be the right choice.
_________________

Consider KUDOS if my post helped

I got the eye of the tiger, a fighter, dancing through the fire
'Cause I am a champion and you're gonna hear me roar

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13436
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

11 May 2015, 15:40
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13436
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

09 Aug 2016, 12:08
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.
_________________
Manager
Joined: 26 Oct 2016
Posts: 117
Location: United States
Schools: HBS '19
GPA: 4
WE: Education (Education)
Followers: 5

Kudos [?]: 13 [0], given: 513

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]

### Show Tags

10 Dec 2016, 15:44
Below is the best reply that I have found on another forum. It's quite understandable.

Median = (c+d)/2
Average = (a+b+c+d+e+f)/6

Median > Average
(c+d)/2 > (a+b+c+d+e+f)/6
3c + 3d > a+b+c+d+e+f
2c + 2d > a+b+e+f
2(c+d) > a+b+e+f

Thus, the question can be rephrased:

Is 2(c+d) > a+b+e+f?

Statement 1: a + e = (3/4)(c + d)
Insufficient.

Statement 2: b + f = (4/3)(c + d)
Insufficient.

Statement 1 and 2 together:
a+b+e+f = (3/4)(c+d) + (4/3)(c+d)
a+b+e+f = (3/4 + 4/3)(c+d)
a+b+e+f = (25/12)(c+d)
Sufficient.

_________________

Thanks & Regards,
Anaira Mitch

Re: Given the ascending set of positive integers {a, b, c, d, e,   [#permalink] 10 Dec 2016, 15:44
Similar topics Replies Last post
Similar
Topics:
a, b, c, d, and e are integers. Is the median of the integers greater 1 06 Dec 2016, 00:53
1 If a, b, c, d, and e are integers and cde = 0, is d = 0 ? 5 01 Oct 2016, 11:53
a, b, c, d, and e are five different positive integers. Which of the 3 14 Sep 2016, 04:57
9 If a, b, c, d, and e are positive integers such that 6 19 Jun 2015, 01:07
5 Set X has 5 integers: a, b, c, d, and e. If m is the mean 7 14 Jan 2012, 21:40
Display posts from previous: Sort by