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

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by BTGmoderatorDC » Thu Jan 02, 2020 8:56 pm
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




OA D

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by Jay@ManhattanReview » Thu Jan 02, 2020 9:21 pm
BTGmoderatorDC 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 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

OA D

Source: e-GMAT
Given that the average number of runs scored by Jack and Jill is same, the sum of runs scored by Jack and Jill is same, too.

Thus, in four matches, Jack scored 45 + 72 + 18 + 25 = 160

Say Jack's least score was x, thus, his highest score was 3x. Say the other two scores are y and z such that y ≤ z. Thus, Jack's four scores are x, y, z and 3x.

So, the median = (y + z)/2 = 30 => z = 60 - y

Thus, Jack's four scores are x, y, (60 - y) and 3x.

Sum of scores = x + y + (60 - y) + 3x = 160 => x = 25 => 3x = Highest score = 3*25 = 75.

The correct answer: D

Hope this helps!

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by swerve » Fri Jan 03, 2020 10:30 am
BTGmoderatorDC 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 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




OA D

Source: e-GMAT

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) \( \cdots \) (1)

Jack's median score is \(30 - \frac{y+z}{2} = 30\)
\(\Rightarrow y + z = 60 \cdots\) (2)

Putting value of (2) in (1)
\(4x + y + z = 160\)
\(4x = 100\)
\(x = 25\)
\(\Rightarrow 3x = 75.\) Therefore, __D__
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by Scott@TargetTestPrep » Wed Jan 08, 2020 7:45 pm
BTGmoderatorDC 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 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

OA D

Source: e-GMAT
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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