It is currently 24 Nov 2017, 06:23

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

When there are consecutive integers and if their range is equal to the

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

Hide Tags

Expert Post
1 KUDOS received
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4362

Kudos [?]: 3066 [1], given: 0

GPA: 3.82
Premium Member CAT Tests
When there are consecutive integers and if their range is equal to the [#permalink]

Show Tags

New post 29 Feb 2016, 20:39
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

57% (01:35) correct 43% (01:45) wrong based on 108 sessions

HideShow timer Statistics

When there are consecutive integers and if their range is equal to their median, what is the number of them?

1) The smallest number of them is 5
2) The largest number of them is 15


* A solution will be posted in two days.
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3066 [1], given: 0

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4362

Kudos [?]: 3066 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: When there are consecutive integers and if their range is equal to the [#permalink]

Show Tags

New post 02 Mar 2016, 22:51
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

When consecutive integers are there and if their range is equal to their median, what is the number of them?

1) The smallest number of them is 5
2) The largest number of them is 15


In the original condition, there are 2 variables(you need to figure out the starting number and the number of them) and 1 equation(range=median), which should match with the number of equations. So you need 1 variable. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), only 5,6,7,8,9,10,11,12,13,14,15 are possible and so as 2).
Therefore, the answer is D.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3066 [0], given: 0

1 KUDOS received
Manager
Manager
avatar
Joined: 07 Jul 2016
Posts: 80

Kudos [?]: 25 [1], given: 51

GPA: 4
Re: When there are consecutive integers and if their range is equal to the [#permalink]

Show Tags

New post 04 Aug 2016, 14:17
1
This post received
KUDOS
1
This post was
BOOKMARKED
MathRevolution wrote:
When there are consecutive integers and if their range is equal to their median, what is the number of them?


Let \(a\) be the first element of the set, \(b\) be the final element of the set, and \(n\) be the range.

The median of a set of consecutive numbers is the same as the mean: \(\frac{\text{first term} + \text{last term}}{2}\)

1) The smallest number of them is 5

\(a = 5\\
b = 5 + n\\
\text{median} = \frac{a + b}{2} = \frac{10 + n}{2} = n\\
2n = 10 + n\\
n = 10\\\)

Sufficient

2) The largest number of them is 15

\(b = 15\\
a = 15 - n\\
\text{median} = \frac{a + b}{2} =\frac{15 + 15 - n}{2} = n\\
30 - n = 2n\\
30 = 3n\\
n = 10\)

Sufficient

Knowing \(n\) and a start point, there are 11 elements from 5 to 15.

[Reveal] Spoiler:
(D) each statement alone is sufficient

_________________

Please press +1 Kudos if this post helps.

Kudos [?]: 25 [1], given: 51

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15499

Kudos [?]: 283 [0], given: 0

Premium Member
Re: When there are consecutive integers and if their range is equal to the [#permalink]

Show Tags

New post 17 Sep 2017, 13:14
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Intern
Intern
avatar
B
Joined: 29 May 2017
Posts: 5

Kudos [?]: 0 [0], given: 112

Re: When there are consecutive integers and if their range is equal to the [#permalink]

Show Tags

New post 25 Sep 2017, 21:02
This seems to be easier if we apply the basic logic for consecutive integers.

We know that for a set of consecutive integers, mean=median.
Consider the first term as 'a' and last term as 'b'.

Range= b-a
Median=Mean= (a+b)/2.
Given: Range=Median or Mean
So, we can say that
b-a = (a+b)/2
b = 3a or a = b/3

Statement 1 : given smallest no is 5 or a = 5
So, b= 3a = 3*5 = 15.
Hence, we get a set {5,6,7,.....,15} which will satisfy all given conditions
Statement 1 is sufficient.

Statement 2: Similarly, given largest no is 15 or b=15
So, a=b/3 = 5
Hence, we get the same set again as {5,.......,14,15}.
Statement 2 is sufficient.

Ans :D

Kudos [?]: 0 [0], given: 112

Re: When there are consecutive integers and if their range is equal to the   [#permalink] 25 Sep 2017, 21:02
Display posts from previous: Sort by

When there are consecutive integers and if their range is equal to the

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.