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In a series of four cricket matches, the average number of runs.......

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In a series of four cricket matches, the average number of runs.......  [#permalink]

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New post Updated on: 29 Oct 2018, 22:38
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In a series of four cricket matches, the average number of runs scored by Jack and Jill is same. The number of runs scored by Jill in the four matches are 45, 72, 18 and 25 respectively. If Jack’s median score is 30 and his least score, in the series, is thrice his highest score of the series, then what is the highest score of Jack in the series?

    A. 25
    B. 30
    C. 60
    D. 75
    E. Cannot be determined

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Originally posted by EgmatQuantExpert on 25 Oct 2018, 00:24.
Last edited by EgmatQuantExpert on 29 Oct 2018, 22:38, edited 2 times in total.
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Re: In a series of four cricket matches, the average number of runs.......  [#permalink]

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New post 25 Oct 2018, 03:44
In a series of four cricket matches, the average number of runs scored by Jack and Jill is same. The number of runs scored by Jill in the four matches are 45, 72, 18 and 25 respectively. If Jack’s median score is 30 and his score in the first match is thrice his score in the fourth match, then what is the highest score of Jack in the series?

[list]A. 25
B. 30
C. 60
D. 75
E. Cannot be determined



Average score of Jill is 40 so average score of Jack wll also be 40

1.jack's median score R2+ R3/2 = 30
R2+ R3= 60

2. Jack's runs in R1 = 3 R4

R1+ R2 + R3 + R4/ 4 = 40

after plugging the values

(4R4 + 60)/4 = 40
R 4 = 25
R 1 = 75

So 75 is the highest score of Jack in the series.

Choice D is correct

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Re: In a series of four cricket matches, the average number of runs.......  [#permalink]

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New post 25 Oct 2018, 04:25
2
In a series of four cricket matches, the average number of runs scored by Jack and Jill is same. The number of runs scored by Jill in the four matches are 45, 72, 18 and 25 respectively. If Jack’s median score is 30 and his least score, in the series, is thrice his highest score of the series, then what is the highest score of Jack in the series?

A. 25
B. 30
C. 60
D. 75
E. Cannot be determined

Sol-
Ji- 18,25,45,72 = 160
JA- x,y,z,3x

Now, JA= 4x+y+z =160 (avg score same so total score is same)----(1)

Jack’s median score is 30- (y+z)/2= 30
=> y+z= 60-----(2)

putting value of 2 in 1
4x+y+z=160
4x=100
x=25
=> 3x= 75 (D)
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Re: In a series of four cricket matches, the average number of runs.......  [#permalink]

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New post 25 Oct 2018, 06:38
EgmatQuantExpert wrote:
In a series of four cricket matches, the average number of runs scored by Jack and Jill is same. The number of runs scored by Jill in the four matches are 45, 72, 18 and 25 respectively. If Jack’s median score is 30 and his least score, in the series, is thrice his highest score of the series, then what is the highest score of Jack in the series?

    A. 25
    B. 30
    C. 60
    D. 75
    E. Cannot be determined


Avg of Jill is \(\frac{45 + 72 + 18 + 25}{4} = 40\)

Runs scored by Jack in Ascending Order be \(a + b + c + d\)

\(\frac{b + c}{2} = 30\)

Or, \(b + c = 60\)

Further \(a = 3d\)

So We have \(a + d + ( b + c ) = 160\)

Or, \(3d + d + 60 = 160\)

Or, \(4d = 100\)

Or, \(d = 25\)

Thus, Highest score must be 25*3 = 75 , Answer must be (D)
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Re: In a series of four cricket matches, the average number of runs.......  [#permalink]

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New post 29 Oct 2018, 00:42

Solution


Given:
    • Average runs scored by both Jack and Jill, in the series, is same
    • Runs scored by Jill in four matches = {45, 72, 18, 25}
    • Jack’s median score = 30
    • Jack’s least score in the series = 3 * his highest score in the series

To find:
    • The highest score of Jack in the series

Approach and Working:
    • Average runs scores by Jill = Sum of his scores in all matches/number of matches = \(\frac{(45 + 72 + 18 + 25)}{4}= \frac{160}{4} = 40\)
    • Average runs scored by Jack = \(\frac{Sum of his scores in all matches}{4}\)
    • Given, both averages are same
      o Which implies, \(\frac{sum of all Jack’s scores}{4} = 40\)
      o Thus, sum of Jack’s scores = 40 * 4 = 160

    • Let a, b, c, d be the scores of Jack in increasing order
    • Given, median score = 30
      o Implies, \(\frac{(b + c)}{2} =30\)
      o Thus, b + c = 60

    • And, we are also given that d = 3a
    • Sum of all scores of Jack =a + b + c + d = a + 60 + 3a = 160
      o Thus, \(a = \frac{100}{4} = 25\)

    • Therefore, the highest score of Jack in the series = 3 * 25 = 75

Hence, the correct answer is option D.

Answer: D

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Re: In a series of four cricket matches, the average number of runs.......  [#permalink]

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New post 29 Oct 2018, 02:57
Q should be changed to "his highest score, in the series, is thrice his lowest score of the series" ?
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Re: In a series of four cricket matches, the average number of runs....... &nbs [#permalink] 29 Oct 2018, 02:57
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