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Five friends Alastair, Bell, Cook, Darren and Eoin appeared

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by BTGmoderatorLU » Tue Aug 21, 2018 3:54 pm

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Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50

The OA is D.
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by Jay@ManhattanReview » Tue Aug 21, 2018 10:49 pm
BTGmoderatorLU wrote:Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50

The OA is D.
Say the scores of Alastair, Bell, Cook, Darren and Eoin are a, b, c, d, and e, respectively.

Thus, from the given information, we have

d = c + 1/5 of c = 6c/5
a = d/2 = 3c/5
e = c + 2/5 of c = 7c/5

d = 3b/2
=> b = 2d/3 = 2/3*(6c/5) = 4c/5

Given, the average score (arithmetic mean) of the group was 50, the total score of all the five students = 5*50 = 250

Thus, a + b + c + d + e = 250

3c/5 + 4c/5 + c + 6c/5 + 7c/5 = 250

=> c = 50

We see that the highest score is 7c/5 = 7/5*50 = 70 and the smallest score is 3c/5 = 3/5*50 = 30

Thus, the range = 70 - 30 = 40.

The correct answer: D

Hope this helps!

-Jay
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by GMATGuruNY » Wed Aug 22, 2018 2:57 am
BTGmoderatorLU wrote:Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50
To determine the ratio of the scores, plug in numbers and reduce the resulting ratio as much as possible.
Let A = Alastair, B = Bell, C = Cook, D = Darren, and E = Eoin.
Let B = the product of the denominators = 2*5*5*2 = 100.

Darren's score was 3/2 times that of Bell's score.
D = 3/2(B) = (3/2)(100) = 150.

Alastair scored exactly 1/2 of Darren's score.
A = (1/2)D = (1/2)(150) = 75.

Darren's score was 1/5th more than Cook's score.
In other words, Darren's score of 150 is 6/5 Cook's score:
150 = (6/5)C
C = (5/6)150 = 125.

Eoin scored 2/5th more than Cook.
In other words, Eoin's score is 7/5 Cook's score of 125:
E = (7/5)125 = 175.

A : B : C : D : E = 75:100:125:150:175 = 3:4:5:6:7.
When the values in the ratio are fully reduced, biggest - smallest = 7-3 = 4.
Implication:
The range of the values must be a MULTIPLE OF 4.

The correct answer is D.
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by Scott@TargetTestPrep » Thu Aug 23, 2018 4:10 pm
BTGmoderatorLU wrote:Source: e-GMAT

Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren's score, whose score was 1/5th more than Cook's score. Eoin scored 2/5th more than Cook and Darren's score was 3/2 times that of Bell's score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

A. 25
B. 30
C. 35
D. 40
E. 50
Let's let Cook's score be x.

Since Darren's score is 1/5th more than Cook's; Darren's score must be x + (x/5) = 6x/5.

Since Alastair's score is 1/2 of Darren's, Alastair's score is (6x/5)(1/2) = 3x/5.

Since Eoin's score is 2/5th more than Cook's; Eoin's score is x + (2x/5) = 7x/5.

Finally, since Darren's score is 3/2 times Bell's score; Bells score is (6x/5)/(3/2) = 4x/5.

Since the average score of the group is 50, the sum of their scores is 50 * 5 = 250.

We can set up the following equation:

3x/5 + 4x/5 + x + 6x/5 + 7x/5 = 250

25x/5 = 250

5x = 250

x = 50

So, the lowest score was 3(50)/5 = 30 and the highest score was 7(50)/5 = 70. The range is 70 - 30 = 40.

Answer: D

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