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

It is currently 21 Aug 2018, 23:02

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

For which of the above lists is the average of the numbers less than t

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6047
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
For which of the above lists is the average of the numbers less than t  [#permalink]

Show Tags

New post 14 Nov 2017, 01:16
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:07) correct 37% (01:46) wrong based on 63 sessions

HideShow timer Statistics

[GMAT math practice question]

I. \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}\)
II. \(\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}\)
III. \(\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}\)
For which of the above lists is the average of the numbers less than the median of numbers?

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1208
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
For which of the above lists is the average of the numbers less than t  [#permalink]

Show Tags

New post 14 Nov 2017, 03:48
1
MathRevolution wrote:
[GMAT math practice question]

I. \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}\)
II. \(\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}\)
III. \(\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}\)
For which of the above lists is the average of the numbers less than the median of numbers?

A. I only
B. II only
C. III only
D. II and III
E. I, II and III


LCM of 2, 3, 4, 5, 6 = 60

So multiply numerator and denominator of each fraction by 60

I. becomes => 30, 40, 45, 48, 50

Average of above numbers = 42.6 and Median=45. clearly this satisfies the required condition

II. becomes => 30, 20, 15, 12, 10

Average of above numbers = 17.4 and Median = 15. Does not satisfy our condition.

We can Stop here and eliminate all option. so our answer is A

for the sake of testing -

III becomes => 10, 20, 30, 40, 50

Average of above numbers = median of above set = 30. Hence does not satisfy given condition.

Option A
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6564
For which of the above lists is the average of the numbers less than t  [#permalink]

Show Tags

New post 14 Nov 2017, 07:34
MathRevolution wrote:
[GMAT math practice question]

I. \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}\)
II. \(\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}\)
III. \(\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}\)
For which of the above lists is the average of the numbers less than the median of numbers?

A. I only
B. II only
C. III only
D. II and III
E. I, II and III



Hi...
If you don't want to get into lengthy calculations as it would surely eat into your time, some observations...

here is a method...
III. \(\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}\)
this is clearly an AP with difference \(\frac{1}{6}\), so MEDIAN = MEAN
so III is out

ONLY A and B are without III
which means either I is correct or II, but only one
here you have been able to get down to TWO choices out of 5, so 50% chance to answer correctly

But lets see II
II. \(\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}\)
median is 1/4 and highest value is 1/2, which is1/4 away from the median 1/4, so lowest should be 0 to reach median
mean = median at 0,1/4,1/2 but it is 1/6,1/4,1/2
BUT the lowest value is >0, so HIGHER values are MORE farther from the MEDIAN, so MEAN will be above median
so mean>median.... so NO

ans is I or the choice A


but lets see why I is correct..
I. \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}\)
these can be written as
I. \(1-\frac{1}{2},1-\frac{1}{3},1-\frac{1}{4},1-\frac{1}{5},1-\frac{1}{6}\)
MEAN will be 1-(average of 1/2,1/3,1/4,1/5,1/6)
this is OPPOSITE of B, here we are subtracting higher values from 1 in 1/2 and 2/3 as compared to 1/5 and 1/6
so m
MEAN<median
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6047
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: For which of the above lists is the average of the numbers less than t  [#permalink]

Show Tags

New post 16 Nov 2017, 01:41
1
1
=>
I. The differences between the consecutive terms are \(\frac{1}{6} (= \frac{2}{3} – \frac{1}{2} )\), \(\frac{1}{12} (= \frac{3}{4} – \frac{2}{3} )\), \(\frac{1}{20} (= \frac{4}{5} – \frac{3}{4} )\), and \(\frac{1}{30} (= \frac{5}{6} – \frac{4}{5})\). As these are decreasing, the average is smaller than the median.

II. The differences between consecutive terms are - \(\frac{1}{6}(= \frac{1}{3} – \frac{1}{2})\),\(-\frac{1}{12}(= \frac{1}{4} – \frac{1}{3} )\), - \(\frac{1}{20}(= \frac{1}{5} – \frac{1}{4})\), and \(-\frac{1}{30}(= \frac{1}{6} – \frac{1}{5})\). As these are increasing, the average is larger than the median.

III. As the data are symmetric, the average and the median are equal.

Therefore, the answer is A

Answer: A
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: For which of the above lists is the average of the numbers less than t &nbs [#permalink] 16 Nov 2017, 01:41
Display posts from previous: Sort by

For which of the above lists is the average of the numbers less than t

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.