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

 It is currently 23 Oct 2019, 21:30 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If the mean of set S is 20, what is the median of set S ?

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

Hide Tags

Manager  S
Joined: 17 Aug 2015
Posts: 100
GMAT 1: 650 Q49 V29 If the mean of set S is 20, what is the median of set S ?  [#permalink]

Show Tags

16 00:00

Difficulty:   95% (hard)

Question Stats: 37% (01:59) correct 63% (01:46) wrong based on 113 sessions

HideShow timer Statistics

If the mean of set S is 20, what is the median of set S ?

1. In set S there are as many numbers larger than 20 as there are numbers smaller than 20.
2. All numbers in set S are even integers.
Manhattan Prep Instructor G
Joined: 04 Dec 2015
Posts: 832
GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: If the mean of set S is 20, what is the median of set S ?  [#permalink]

Show Tags

9
3
Well, they don't tell us how many numbers there are in set S, so let's keep it as simple as possible. It's easier to find the median with an odd number of numbers, so we'll start with sets that have 3 elements (although we might have to try even-numbered sets, too, if we can't find good cases.)

(1)

Let's say the set is (10, 20, 30). The mean is 20. The median is also 20.
Next, try (19, 20, 21). The mean is 20. The median is also 20.

It seems like whenever we have one element larger than 20, and one element smaller than 20, the median is 20. That makes sense, because the third number in the set would have to be equal to 20. That number would be in the middle, so it would be the median.

What if we try some sets of four numbers, then? There could be two numbers smaller than 20, and two numbers bigger than 20.

(0, 0, 40, 40) - the mean is 20, and the median is 20 again (average of 0 and 20, the two middle numbers).

BUT, how about (0, 19, 30, 31)? The mean is 20 (I figured this out by making sure the sum was 80) but the median definitely isn't 20.

Insufficient.

(2) This is definitely insufficient on its own, since we could test almost any set.

(1+2) It's pretty easy to find a case where the median is equal to 20, and that fits both statements: (10,20,30) would work. What we need, then, is to find a case where the median isn't equal to 20. That is, we want a case similar to the one that worked for statement (1), above, except where all of the numbers are even.

Let's use the same idea - a set that sums to 80 and has 4 elements, but that isn't 'evenly spaced'. One set that works here is (0, 18, 30, 32), which has a mean of 20 but a median of 24.

Insufficient.

The correct answer is E.
_________________ Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!
General Discussion
Manager  S
Joined: 17 Aug 2015
Posts: 100
GMAT 1: 650 Q49 V29 If the mean of set S is 20, what is the median of set S ?  [#permalink]

Show Tags

1
1
the trick of this question is not to assume that 20 is one of the numbers in the set

( 0, 19, 30, 31), average of 04 numbers is 20 and median is now 20 now

( 0,19, 20, 30, 31) average is 20 and median is 20

choice 1

0, 18, 30,32 , average is 20 and median is 24

0, 18, 20, 30, 32 average of 05 numbers is 20 and median is now 20

choice 2
all even, above all numbers are even

combined both we don't get the definite answer

so choice E is the correct answer
Intern  B
Joined: 04 Aug 2017
Posts: 11
Re: If the mean of set S is 20, what is the median of set S ?  [#permalink]

Show Tags

If the mean of set S is 20, what is the median of set S ?

1. In set S there are as many numbers larger than 20 as there are numbers smaller than 20.
2. All numbers in set S are even integers.

Option 1
Consider set1 - 16, 18, 20, 22,24 - Mean=20, Median=20
Set2 - 0,21,23,36 - mean=20, Median=22 - INSUFF

Option 2
Consider set1 - 16, 18, 20, 22,24 - Mean=20, Median=20
Set2 - 2,4,6,68 = Mean=20, Median=5 - INSUFF

Both -(the key here is 0 is an even no, and not necessarily 20 be there in the list)
Consider set1 - 16, 18, 20, 22,24 - Mean=20, Median=20
Set2 - 0,2,20,58 - mean=20, Median=11 - INSUFF
Non-Human User Joined: 09 Sep 2013
Posts: 13418
Re: If the mean of set S is 20, what is the median of set S ?  [#permalink]

Show Tags

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: If the mean of set S is 20, what is the median of set S ?   [#permalink] 17 Apr 2019, 06:51
Display posts from previous: Sort by

If the mean of set S is 20, what is the median of set S ?

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

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