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

 It is currently 23 Oct 2019, 13:52

### 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

# There are 5 integers such that the difference of the biggest number an

Author Message
TAGS:

### Hide Tags

Intern
Joined: 02 Oct 2010
Posts: 3
Location: India
GMAT Date: 08-21-2017
GPA: 3.85
There are 5 integers such that the difference of the biggest number an  [#permalink]

### Show Tags

Updated on: 05 Mar 2019, 21:24
1
1
00:00

Difficulty:

95% (hard)

Question Stats:

39% (02:52) correct 61% (02:33) wrong based on 31 sessions

### HideShow timer Statistics

There are 5 integers such that the difference of the biggest number and the median is 4. Is the average (arithmetic mean) of them less than the median of them?

(1) The sum of biggest numbers and the median is 34.
(2) The difference of median and the smallest number is 10

Originally posted by rawat2583 on 05 Mar 2019, 13:16.
Last edited by Bunuel on 05 Mar 2019, 21:24, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
There are 5 integers such that the difference of the biggest number an  [#permalink]

### Show Tags

Updated on: 09 Mar 2019, 17:05
We have 5 integers such that:

$$n_1 , n_2 , n_3 , n_4 , n_5$$

where $$n_3$$ is the median.

We know that $$n_5 - n_3 = 4$$.

$$1. n_5 + n_3 = 34$$. We could find $$n_5$$ and $$n_3$$ but are useless: we can infer nothing about the average.

$$2. n_3 - n_1 = 10$$. Take $$n_3$$ as reference point. On the left, difference is 10. On the right, 4. So, $$10 + 4 = 14$$. It is the range from $$n_1$$ to $$n_5$$. Since $$14 : 2 = 7$$ and $$n_3 = n + 10$$, we conclude that the average is less than the median.

_________________
If you like my post, Kudos are appreciated! Thank you.

MEMENTO AUDERE SEMPER

Originally posted by lucajava on 05 Mar 2019, 16:24.
Last edited by lucajava on 09 Mar 2019, 17:05, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 58464
Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

### Show Tags

05 Mar 2019, 21:24
rawat2583 wrote:
There are 5 integers such that the difference of the biggest number and the median is 4. Is the average (arithmetic mean) of them less than the median of them?

(1) The sum of biggest numbers and the median is 34.
(2) The difference of median and the smallest number is 10

Similar question to practice: https://gmatclub.com/forum/there-are-5- ... 37063.html
_________________
Manager
Joined: 19 Sep 2017
Posts: 204
Location: United Kingdom
GPA: 3.9
WE: Account Management (Other)
Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

### Show Tags

09 Mar 2019, 15:34
lucajava wrote:
We have 5 integers such that:

$$n_1 , n_2 , n_3 , n_4 , n_5$$

where $$n_3$$ is the median.

We know that $$n_5 - n_3 = 4$$.

$$1. n_5 + n_3 = 34$$. We could find $$n_5$$ and $$n_3$$ but are useless: we can infer nothing about the average.

$$2. n_3 - n_1 = 10$$. Take $$n_3$$ as reference point. On the left, difference is 10. On the right, 4. So, $$10 + 4 = 14$$. It is the range from $$n_1$$ to $$n_5$$. Since $$14 : 2 = 7$$ and $$n_3 = 10$$, we conclude that the average is less than the median.

Hi lucajava ,
How did you conclude n3=10? and 14:2 = 7? what is this for?

Thanks.
_________________
Cheers!!
Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

### Show Tags

09 Mar 2019, 17:03
1
Hi Doer01, you're right, my conclusion was too hasty and I should've explained more. What i meant to say was that you do care only about deviations from the mean. So, $$10$$ will be the deviation from the mean as we consider the median; $$\frac{14}{2}$$ is the average deviation from the mean (i took the extreme values: $$\frac{n + (n + 14)}{2}= n + 7$$). Hope it's clear.
_________________
If you like my post, Kudos are appreciated! Thank you.

MEMENTO AUDERE SEMPER
Re: There are 5 integers such that the difference of the biggest number an   [#permalink] 09 Mar 2019, 17:03
Display posts from previous: Sort by