GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Jan 2020, 19:06 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)

Author Message
TAGS:

### Hide Tags

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3219
Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

10 00:00

Difficulty:   95% (hard)

Question Stats: 37% (03:19) correct 63% (02:42) wrong based on 71 sessions

### HideShow timer Statistics

Question of the Week #32

The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set?

A. 52
B. 104
C. 112
D. 208
E. 260

_________________

Originally posted by EgmatQuantExpert on 18 Jan 2019, 01:05.
Last edited by EgmatQuantExpert on 27 Feb 2019, 23:39, edited 1 time in total.
Intern  B
Joined: 22 Jan 2014
Posts: 31
Schools: Johnson '21 (WL)
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

1
If we want maximum range, we want 5x to be as large as possible and x to be as small as possible
x - - - - - - 78 - - - - - - 5x

This is only possible if all the other numbers are 78
13*78 = 1014

Total sum of 15 numbers = 1170
Subtracting sum of 13 no.s from sum of 15 no.s = 1170-1014
= 156

which is equal to x+5x = 6x=156
x=26

Range = 5x-x=4x=4*26=104
Intern  B
Joined: 03 Dec 2018
Posts: 13
WE: Operations (Computer Software)
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

My approach for this problem was

Sum of nos. 78*15=1170
Sum of nos of a sequence= n/2*(a+an)
Where n total nos of digit, a = first digit and an = last digit
Therefore, 15/2*(a+an)= 1170

a+an=156
an = 5a (given in question)
6a=156
a=26, an=130
Range =130-26, 104 (B)

Feel free for correction ?

Posted from my mobile device
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5723
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

2
EgmatQuantExpert wrote:
The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set?

A. 52
B. 104
C. 112
D. 208
E. 260

sequence
XXXXXXX 787878787878 5X = 78* 15
12X+ 78*7 = 1170
X= 52
5X= 260
RANGE = 5X-X = 260-52 = 208
IMO D

Originally posted by Archit3110 on 18 Jan 2019, 08:36.
Last edited by Archit3110 on 21 Jan 2019, 07:34, edited 1 time in total.
Current Student S
Joined: 04 Jun 2018
Posts: 156
GMAT 1: 610 Q48 V25
GMAT 2: 690 Q50 V32
GMAT 3: 710 Q50 V36
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

1
We have to minimise X and maximize 5x.

So
X X X X X X X 78 78 78 78 78 78 78 5X

Is the correct sequence.

Hence
7*(78-X)=5X-78
8*78=12X

Hence X=52
4X=208

Option D is correct.

Originally posted by nitesh50 on 18 Jan 2019, 08:42.
Last edited by nitesh50 on 18 Jan 2019, 12:45, edited 2 times in total.
VP  P
Joined: 07 Dec 2014
Posts: 1229
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set?

A. 52
B. 104
C. 112
D. 208
E. 260

(x+5x)/2=78 mean/median
x=26
5x=130
130-26=104
B
Intern  B
Joined: 06 Jun 2016
Posts: 5
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

2
We have to maximise the value of 5x and minimise the value of x such that the sum of the sequence remains 15*78=1170.

Hence, the sequence can be where mean is equal to median

x,x,x,x,x,x,x, 78, 78,78,78,78,78,78, 5x

The sum of the above sequence is 7x+ 78*7 + 5x = 15*78-----> 12x= 8*78-----> x=52

Hence the maximum range of the value of the set is 5x-x= 4x= 4* 52= 208

Intern  B
Joined: 19 Jul 2018
Posts: 21
Location: India
Schools: IIMB (D)
GMAT 1: 690 Q52 V47
GRE 1: Q162 V167
GPA: 3.9
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

My approach was:
l=5a

Median=(a+l)/2=Mean=78

-->>:::Range=l-a=104

I think I missed the point of maximizing the Range but accidentally did so...!!?
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3219
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

Solution

Given:
• The arithmetic mean of a sequence of 15 integers is 78
• The largest value of the set is five times the smallest value of the set
• The mean of the set is equal to the median

To find:
• The maximum possible value for the range of the set

Approach and Working:
• We know that the range of a set = the largest value – the smallest value

So, for the range to be maximum, we need to maximise the value of largest element of the set and minimise the value of smallest element of the set.
• We know that the mean = the median = the 8th element of the sequence = 78
• So, to minimise the first element of the sequence, all the elements before the median element must be same. Let us assume it be “a”
• And, to maximise the last element of the sequence, all the elements after the median except the last element must be minimum = the median = 78
• The last element of the sequence will be = 5 * a

We are also given that the mean of the set = median = 78
• Implies, sum of all 15 elements in the sequence = 78 * 15
• Thus, a + a + a + a + a + a + a + 78 + 78 + 78 + 78 + 78 + 78 + 78 + 5a = 78 * 15
o 12a = 78 * 15 – 78 * 7
o $$a = 78 * \frac{8}{12} = 52$$

• Therefore, range of the set = 5a – a = 4a = 4 * 52 = 208

Hence the correct answer is Option D.

_________________
Intern  B
Joined: 30 Oct 2018
Posts: 2
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

My question is why is this being assumed
"Thus, a + a + a + a + a + a + a + 78 + 78 + 78 + 78 + 78 + 78 + 78 + 5a = 78 * 15"
Manager  S
Joined: 26 Nov 2018
Posts: 96
Concentration: Technology, Entrepreneurship
GPA: 3.3
WE: Manufacturing and Production (Manufacturing)
Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
Question of the Week #32

The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set?

A. 52
B. 104
C. 112
D. 208
E. 260

Dear Bunuel,

What mistake I have made in the math. In my sense, the answer is B. I would be glad if you help me to find out the mistake.

(x+5x)/2=78 ( Mean and Median is the same)
x=26
5x=130
130-26=104
Intern  B
Joined: 21 Jan 2018
Posts: 11
Location: India
Schools: ISB '21
GMAT 1: 730 Q50 V38 GMAT 2: 690 Q48 V37
GPA: 3.98
Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  [#permalink]

### Show Tags

EgmatQuantExpert

" So, to minimise the first element of the sequence, all the elements before the median element must be same. Let us assume it be a "

Is'nt it that all the elements before the median element must be equal to the median to minimise the first element?

Please correct me if I'm wrong, having tough time understanding these type of questions. Re: Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)   [#permalink] 30 Mar 2019, 00:23
Display posts from previous: Sort by

# Question of the week - 32 (The arithmetic mean of a sequence of 15 ..)  