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# The arithmetic mean of a set of 12 numbers is 65, and the median......

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
The arithmetic mean of a set of 12 numbers is 65, and the median......  [#permalink]

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Updated on: 29 Oct 2018, 23:39
00:00

Difficulty:

75% (hard)

Question Stats:

53% (02:43) correct 47% (02:48) wrong based on 106 sessions

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The arithmetic mean of a set of 12 numbers is 65, and the median of the set is 40. What is the minimum possible value of the largest number of this set?

A. 65
B. 80
C. 100
D. 120
E. 130

_________________

Originally posted by EgmatQuantExpert on 25 Oct 2018, 01:26.
Last edited by EgmatQuantExpert on 29 Oct 2018, 23:39, edited 1 time in total.
Intern
Joined: 28 Aug 2018
Posts: 3
GMAT 1: 520 Q30 V32
GMAT 2: 500 Q34 V24
Re: The arithmetic mean of a set of 12 numbers is 65, and the median......  [#permalink]

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25 Oct 2018, 03:38
1
I considered the set from number x1to x12

As the median of the set is 40 I have considered that all numbers from x1 to x7 are 40. Thus 40x7=280

On the other hand, the sum of all the set is 65*12=780

The subtract is
780-280=500

As we have 5 numbers between x8 to x12, I divided 500/5= 100

C. 100

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e-GMAT Representative
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Posts: 3074
Re: The arithmetic mean of a set of 12 numbers is 65, and the median......  [#permalink]

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29 Oct 2018, 01:45

Solution

Given:
• The arithmetic mean of a set of 12 numbers = 65
• Median of the set = 40

To find:
• The minimum possible value of the largest number of the set

Approach and Working:
• Given, the arithmetic mean of 12 numbers = 65
o Implies, the sum of 12 numbers = 12 * 65 = 780
 $$t_1 + t_2 + … + t_6 + t_7 + …. + t_{11} + t_{12} = 780$$

• We are also given that the median = 40,
o That implies, $$t_6 + t_7 = 2 * 40$$

• So, for the largest number to be minimum, all other numbers must take the maximum possible value
o The maximum value of all the five numbers before the median term = the median itself (since they cannot be greater than the median value)
o The maximum value of all the five numbers after the median term = the value of the largest number

• Thus, 5 * 40 + 2 * 40 + 5 * x =780, where x is the largest number
o Implies, $$x = \frac{500}{5} =100$$

• Therefore, the minimum possible value of the largest number = 100

Hence, the correct answer is option C.

_________________
Re: The arithmetic mean of a set of 12 numbers is 65, and the median......   [#permalink] 29 Oct 2018, 01:45
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