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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

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

by BTGmoderatorDC » Wed Jul 17, 2019 4:38 pm

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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

OA D

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Wed Jul 17, 2019 4:38 pm

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by Ian Stewart » Thu Jul 18, 2019 6:35 am

If Jill's average is the same as Jack's in 4 games, then their sum is the same. Jill's sum is 160, so Jack's sum must be 160. Jack's median score is the average of his two middle scores, so if his median score is 30, the sum of his two middle scores is 60. His smallest and largest scores therefore add to 100, and if the larger score is 3 times the smaller, the larger score is 75.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jul 29, 2019 3:20 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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