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Updated on: 12 Jun 2024, 02:01
Originally posted by EgmatQuantExpert on 25 Oct 2018, 01:26.
Last edited by Bunuel on 12 Jun 2024, 02:01, edited 2 times in total.
Last edited by Bunuel on 12 Jun 2024, 02:01, edited 2 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:36) correct
32%
(02:46)
wrong
based on 696
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
A. 65
B. 80
C. 100
D. 120
E. 130
29 Oct 2018, 01:45
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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.
Answer: C
General Discussion
25 Oct 2018, 03:38
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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
Posted from my mobile device
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
Posted from my mobile device
