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

 It is currently 17 Oct 2019, 13:51 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.  Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number

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

Hide Tags

Manager  Joined: 16 Feb 2011
Posts: 179
Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number  [#permalink]

Show Tags

1
8 00:00

Difficulty:   85% (hard)

Question Stats: 53% (02:41) correct 47% (02:39) wrong based on 75 sessions

HideShow timer Statistics

Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the numbers greater than 35 are greater than 40. Which of the following could be the median number?

I. 34
II. 35
III. 36

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

I get till this part...200*0.165=x*0.333 =>x=99

Can someone help me with next steps??
Manager  Joined: 14 Mar 2011
Posts: 184
Re: Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number  [#permalink]

Show Tags

DeeptiM wrote:
Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the numbers greater than 35 are greater than 40. Which of the following could be the median number?
I. 34
II. 35
III. 36
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

I get till this part...200*0.165=x*0.333 =>x=99

Can someone help me with next steps??

yes I think you have deducted correctly till now. If 99 numbers are > 35 , it means rest 101 numbers are equal to or less than 35.

median in the list of a set of 200 members will be the average of 100th and 101st member of the set when we arrange the members of the set in ascending order. From deduction we know that 102nd member to 200th member of the set are greater than 35 , and 1st member to 101st member are less than or equal to 35. 100th and 101st member could be 34 or 35 . so 34 and 35 could be the median.
Intern  Joined: 17 May 2009
Posts: 27
Location: United States
GMAT 1: 770 Q51 V44 GPA: 3.62
WE: Corporate Finance (Manufacturing)
Re: Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number  [#permalink]

Show Tags

The median occurs at term$$\frac{(n + 1)}{2}=\frac{201}{2}=100.5$$, and for a set with an even count (200 in this case), it will be the average of terms $$100$$ and $$101$$.

With $$200*16.5% = \frac{1}{3}x$$, you have established that the $$x = 200*16.5%*3=99$$ highest observations are each greater than 35 and that the $$200*16.5%=33$$ highest observations are each greater than 40. All other terms must be less than or equal to 35.

The average of the 101st and 100th terms is the median. The 99th term in descending order is the $$200-99+1=102$$nd term in ascending order. The average of the 101st term and the 100th term, which are each less than or equal to 35, can only be 34 or 35.
Manager  G
Joined: 30 Mar 2017
Posts: 127
GMAT 1: 200 Q1 V1 Re: Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number  [#permalink]

Show Tags

1
In my opinion, the fact that there are 200 numbers is irrelevant. We can deduce the median just by working with the percentages.

We're given that:
- 16.5% of the 200 numbers are greater than 40
- 33.3% of the numbers greater than 35 are greater than 40

Combining the 2 statements:
- 33.3% of the numbers greater than 35 are 16.5% of the 200 numbers

So, 100% of the numbers greater than 35 are 49.5% of the 200 numbers

Since the median is at the 50% mark when the numbers are arranged in order, and since 49.5% are greater than 35, then the median must be less than or equal to 35.

Non-Human User Joined: 09 Sep 2013
Posts: 13244
Re: Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number  [#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: Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number   [#permalink] 29 May 2019, 01:29
Display posts from previous: Sort by

Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number

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

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