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

 It is currently 22 Jul 2018, 16:57

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

On Monday, 9 students each took a test with 100 questions. The average

Author Message
TAGS:

Hide Tags

Intern
Joined: 14 Sep 2017
Posts: 35
Location: Italy
On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

Show Tags

01 Mar 2018, 10:18
3
00:00

Difficulty:

35% (medium)

Question Stats:

45% (01:10) correct 55% (00:24) wrong based on 20 sessions

HideShow timer Statistics

On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?

II. At least one student had more than 40 and less than 50 correct answers.

A) I only
B) II only
C) III only
D) I and III
E) II and III
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2961
Location: India
GPA: 3.12
Re: On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

Show Tags

01 Mar 2018, 12:29
Fedemaravilla wrote:
On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?

II. At least one student had more than 40 and less than 50 correct answers.

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

Imagine the score that the 9 students took in a test to be values of a set

Here, 40 is the median of the set and the mean(average) is 50.
The 5th element(middle element) is 40 - the median.
Therefore, the other 4 elements before the median take a minimum value of 40.

To offset this difference of 10(from the 5 elements of the set), at least one of the elements
in the set will have to greater than 60, in order to attain the average of 50!

Illustrating with the help of an example

40 40 40 40 40 60 60 60 x is one possibility for the set.

$$\frac{40*5 + 60*3 + x}{9} = 50$$ -> $$200 + 180 + x = 450$$ -> $$x = 450 - 380 = 70$$

Here, the minimum value that x will take is 70, making Option A(I only) correct.
This example also proves that case II and III are wrong!
_________________

You've got what it takes, but it will take everything you've got

Intern
Joined: 18 Jun 2017
Posts: 13
On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

Show Tags

02 Mar 2018, 23:10
let us take one option at a time. Let none of the scores are more than 60. Then the maximum score that can be obtained will be 40+40+40+40+40+59+59+59+59 = 436. This is clearly not possible since the average is 50 (the sum must be 450). So, the option I is correct. This automatically eliminates option II but not option III. How about having 39+39+39+39+40+62+62+62+68? Option III does not cap the number of correct answers on the upper side. Am I missing something here?

pushpitkc wrote:
Fedemaravilla wrote:
On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?

II. At least one student had more than 40 and less than 50 correct answers.

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

Imagine the score that the 9 students took in a test to be values of a set

Here, 40 is the median of the set and the mean(average) is 50.
The 5th element(middle element) is 40 - the median.
Therefore, the other 4 elements before the median take a minimum value of 40.

To offset this difference of 10(from the 5 elements of the set), at least one of the elements
in the set will have to greater than 60, in order to attain the average of 50!

Illustrating with the help of an example

40 40 40 40 40 60 60 60 x is one possibility for the set.

$$\frac{40*5 + 60*3 + x}{9} = 50$$ -> $$200 + 180 + x = 450$$ -> $$x = 450 - 380 = 70$$

Here, the minimum value that x will take is 70, making Option A(I only) correct.
This example also proves that case II and III are wrong!
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2961
Location: India
GPA: 3.12
Re: On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

Show Tags

03 Mar 2018, 00:29
sandeepkonda wrote:
let us take one option at a time. Let none of the scores are more than 60. Then the maximum score that can be obtained will be 40+40+40+40+40+59+59+59+59 = 436. This is clearly not possible since the average is 50 (the sum must be 450). So, the option I is correct. This automatically eliminates option II but not option III. How about having 39+39+39+39+40+62+62+62+68? Option III does not cap the number of correct answers on the upper side. Am I missing something here?

pushpitkc wrote:
Fedemaravilla wrote:
On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?

II. At least one student had more than 40 and less than 50 correct answers.

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

Imagine the score that the 9 students took in a test to be values of a set

Here, 40 is the median of the set and the mean(average) is 50.
The 5th element(middle element) is 40 - the median.
Therefore, the other 4 elements before the median take a minimum value of 40.

To offset this difference of 10(from the 5 elements of the set), at least one of the elements
in the set will have to greater than 60, in order to attain the average of 50!

Illustrating with the help of an example

40 40 40 40 40 60 60 60 x is one possibility for the set.

$$\frac{40*5 + 60*3 + x}{9} = 50$$ -> $$200 + 180 + x = 450$$ -> $$x = 450 - 380 = 70$$

Here, the minimum value that x will take is 70, making Option A(I only) correct.
This example also proves that case II and III are wrong!

Hey sandeepkonda

If you read the question which reads "With of the following statements must be true"

As already written in the previously mentioned case, it is not always necessary that the statement III is always right
If we have 40 40 40 40 40 60 60 60 60 70, the average is 50 and the median is 40, but none of the students

Hope this helps you!
_________________

You've got what it takes, but it will take everything you've got

Intern
Joined: 18 Jun 2017
Posts: 13
Re: On Monday, 9 students each took a test with 100 questions. The average  [#permalink]

Show Tags

03 Mar 2018, 00:41
Thanks!!! I missed the "must be true" part of the question.

Sent from my ONEPLUS A5010 using GMAT Club Forum mobile app
Re: On Monday, 9 students each took a test with 100 questions. The average &nbs [#permalink] 03 Mar 2018, 00:41
Display posts from previous: Sort by

Events & Promotions

 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®.