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

It is currently 25 Sep 2018, 16:08

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

Which of the following statements must be true about the average (arit

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49496
Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 20 Jun 2018, 00:23
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (00:42) correct 12% (00:43) wrong based on 267 sessions

HideShow timer Statistics

Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.


A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III


NEW question from GMAT® Official Guide 2019


(PS00984)

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2014
Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 20 Jun 2018, 02:21
3

Solution



Given:
    • We are given 5 consecutive integers.

To find:
    • We need to find the average and median of 5 consecutive integers.

Approach and Working:

Let us assume that 5 consecutive numbers are: a-2, a-1, a, a+1, a+2.
    • Thus, the average of the 5 integers = \(\frac{(a-2)+ (a-1) + (a) + (a+1) + (a+2)}{5}\)= \(\frac{5a}{5}\)= a
    • And their median= a.

Thus, average and median both are the same and are one of the integers among 5 consecutive integers.

Hence, option E is the correct answer.

Answer: E
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
avatar
G
Joined: 01 Aug 2017
Posts: 192
Location: India
Concentration: General Management, Leadership
Schools: ISB '20 (S), IIMA (S)
GMAT 1: 500 Q47 V15
GPA: 3.4
WE: Information Technology (Computer Software)
Premium Member Reviews Badge CAT Tests
Re: Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 20 Jun 2018, 02:29
1
Bunuel wrote:
Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.


A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III


NEW question from GMAT® Official Guide 2019


(PS00984)


Ans is E.

It is the property of consecutive number :
For every n consecutive integer, when n is an odd integer
a) The average & median is always an integer.
b) The median always equals the average.

Thanks !!
_________________

If it helps you please press Kudos!

Thank You
Sudhanshu

Manager
Manager
User avatar
B
Joined: 13 Feb 2018
Posts: 131
CAT Tests
Re: Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 20 Jun 2018, 03:29
Let 5 Consecutive integers be: 1, 2, 3, 4, 5

Mean=(1+2+3+4+5)/5=3
Median= 3
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2906
Location: Canada
Re: Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 27 Jun 2018, 06:07
Top Contributor
Bunuel wrote:
Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.


A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III


There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

Since consecutive integers are equally spaced, the average (mean) of this set of 5 integers will equals its median.
So, statement III is true
Check the answer choices.....ELIMINATE A, B and D

Also, since the set has an ODD number of values, the median will be the middle value (when the numbers are arranged in ascending order).
Since the set consists of INTEGERS only, and since the median equals the middle value, the median must be an integer
So, statement II is true
Check the answer choices.....ELIMINATE C

By the process of elimination, the correct answer must be E

RELATED VIDEO FROM OUR COURSE

_________________

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

Intern
Intern
avatar
B
Joined: 08 Oct 2017
Posts: 24
GMAT ToolKit User CAT Tests
Re: Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 27 Jun 2018, 06:17
5 consecutive integer - a, a+1, a+2, a+3, a+4
Avg = (5a+10)/5 = a+2
Median = a+2
Median = avg
Manager
Manager
User avatar
B
Joined: 07 Feb 2017
Posts: 180
Re: Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 27 Jun 2018, 11:58
x-2,x-1,x,x+1,x+2

average=x
median=x

Answer E.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: Which of the following statements must be true about the average (arit  [#permalink]

Show Tags

New post 02 Jul 2018, 10:02
Bunuel wrote:
Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.


A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III


For a set of 5 consecutive integers, the median = average. Furthermore, both the mean and the median are one of the given integers.

For example:

1, 2, 3, 4, 5

Average = 15/5 = 3 = median.

Answer: E
_________________

Jeffery Miller
Head of GMAT Instruction

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

GMAT Club Bot
Re: Which of the following statements must be true about the average (arit &nbs [#permalink] 02 Jul 2018, 10:02
Display posts from previous: Sort by

Which of the following statements must be true about the average (arit

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

Events & Promotions

PREV
NEXT


Copyright

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®.