It is currently 18 Nov 2018, 14:25
My Tests

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.

QOTD # 15 The greatest of the 21 positive integers in a cert

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 4914
Followers: 74

Kudos [?]: 977 [1] , given: 4499

CAT Tests
QOTD # 15 The greatest of the 21 positive integers in a cert [#permalink] New post 10 Sep 2016, 02:04
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

90% (02:09) correct 10% (02:18) wrong based on 10 sessions
The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers?

    A) 4
    B) 5
    C) 6
    D) 7
    E) 8

Practice Questions
Question: 15
Page: 180
[Reveal] Spoiler: OA

_________________

Get the 2 FREE GREPrepclub Tests

2 KUDOS received
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 4914
Followers: 74

Kudos [?]: 977 [2] , given: 4499

CAT Tests
Re: QOTD # 15 The greatest of the 21 positive integers in a cert [#permalink] New post 10 Sep 2016, 02:06
2
This post received
KUDOS
Expert's post
Explanation


You are given that the median of the 21 positive integers is 10 and the greatest of the 21 integers is 16. This means that when the 21 integers are listed in order from least to greatest,

• the 1st through 10th integers are between 1 and 10, inclusive;
• the 11th integer is 10;
• the 12th through 20th integers are between 10 and 16, inclusive; and
• the 21st integer is 16.

The least possible average of the 21 integers would be achieved by using the least possible value of each integer as described above in the reordered list:

• the 1st through 10th integers would each be 1;
• the 11th integer would be 10;
• the 12th through 20th integers would each be 10; and
• the 21st integer would be 16.

For the least possible integers, the sum is (10)(1) + 10 + (9)(10) + 16, or 126. Therefore the least possible average is \(\frac{126}{21}\) or 6.

The correct answer is Choice C.
_________________

Get the 2 FREE GREPrepclub Tests

1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1177
Followers: 44

Kudos [?]: 1054 [1] , given: 6

CAT Tests
Re: QOTD # 15 The greatest of the 21 positive integers in a cert [#permalink] New post 19 Sep 2016, 17:00
1
This post received
KUDOS
Expert's post
Carcass wrote:
The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers?

    A) 4
    B) 5
    C) 6
    D) 7
    E) 8


Let the following spaces represent the 21 integers listed in ASCENDING ORDER, with a red space indicating the median:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _


The greatest of the 21 positive integers in a certain list is 16
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 16


The median of the 21 integers is 10
_ _ _ _ _ _ _ _ _ _ 10 _ _ _ _ _ _ _ _ _ 16


What is the least possible average (arithmetic mean) of the 21 integers?
We must MINIMIZE the 19 remaining integers.
So, the first 10 integers must be 1, since 1 is the smallest positive integer.
1 1 1 1 1 1 1 1 1 1 10 _ _ _ _ _ _ _ _ _ 16

The remaining integers must be greater than or equal to 10 and less than or equal to 16
Since, we're trying to MINIMIZE the remaining integers, we'll let each number be 10 to get:
1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 16

Average = (1+1+1+1+1+1+1+1+1+1+10+10+10+10+10+10+10+10+10+10+16)/21
= 126/21
= 6

Answer:
[Reveal] Spoiler:
C


RELATED VIDEO

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

1 KUDOS received
Target Test Prep Representative
User avatar
Status: Head GRE Instructor
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 114 [1] , given: 0

Re: QOTD # 15 The greatest of the 21 positive integers in a cert [#permalink] New post 04 May 2018, 09:21
1
This post received
KUDOS
Expert's post
Carcass wrote:
The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers?

    A) 4
    B) 5
    C) 6
    D) 7
    E) 8


There are 21 numbers in the list, and, if we list the numbers in ascending order, the median is the 11th number.

Thus, we can let each of the first 10 numbers = 1, each of the next 10 numbers = 10, and the last number = 16.

Thus, the average is (10 x 1 + 10 x 10 + 16)/21 = 126/21 = 6.

Answer: C
_________________

Jeffery Miller
Head of GRE Instruction

GRE Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: QOTD # 15 The greatest of the 21 positive integers in a cert   [#permalink] 04 May 2018, 09:21
Display posts from previous: Sort by

QOTD # 15 The greatest of the 21 positive integers in a cert

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.