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EgmatQuantExpert
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In a series of four cricket matches, the average number of runs....... Updated on: 18 Mar 2019, 22:34
Originally posted by EgmatQuantExpert on 25 Oct 2018, 01:24.
Last edited by EgmatQuantExpert on 18 Mar 2019, 22:34, edited 3 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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77% (02:11) correct 23% (02:33) wrong based on 359 sessions

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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 highest score, in the series, is thrice his least 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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D
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sonusaini1
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In a series of four cricket matches, the average number of runs....... 25 Oct 2018, 04:44
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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 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

Thanks

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In a series of four cricket matches, the average number of runs....... 25 Oct 2018, 05:25
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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

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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In a series of four cricket matches, the average number of runs....... 25 Oct 2018, 07:38
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EgmatQuantExpert
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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In a series of four cricket matches, the average number of runs....... Updated on: 18 Mar 2019, 22:34
Originally posted by EgmatQuantExpert on 29 Oct 2018, 01:42.
Last edited by EgmatQuantExpert on 18 Mar 2019, 22:34, edited 1 time in total.
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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 highest score in the series = 3 * his least 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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In a series of four cricket matches, the average number of runs....... 29 Oct 2018, 03:57
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Q should be changed to "his highest score, in the series, is thrice his lowest score of the series" ?
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In a series of four cricket matches, the average number of runs....... 16 Mar 2019, 19:33
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EgmatQuantExpert

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


Shouldn't the Question be "Highest Score is thrice the least Score"?? Moreover you have repeated this statement in your solution also. Am i not getting it right?
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In a series of four cricket matches, the average number of runs....... 18 Mar 2019, 07:02
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pankajpatwari
Shouldn't the Question be "Highest Score is thrice the least Score"?? Moreover you have repeated this statement in your solution also. Am i not getting it right?

Yes, you are write. At first, I was confused as well. EgmatQuantExpert can you correct it, please, thanks.
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In a series of four cricket matches, the average number of runs....... 18 Mar 2019, 22:37
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Hey mtambiev, pankajpatwari and pandeyashwin,

Thanks for pointing it out. We've made the necessary changes. :)
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In a series of four cricket matches, the average number of runs....... 29 Jul 2019, 16:31
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EgmatQuantExpert
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 highest score, in the series, is thrice his least 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


Since Jill’s total score of the 4 matches is 45 + 72 + 18 + 25 = 160, Jack’s total score of the 4 matches is also 160. Furthermore, since Jack’s median score is 30, the sum of his middle two scores is 60. Therefore, the sum of his lowest and highest scores is 100. We can create the equation where x is his lowest score:

x + 3x = 100

4x = 100

x = 25

Therefore, his highest score is 3(25) = 75.

Answer: D
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