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A group of 7 students has a combined score of 280 on an aptitude test. If 4 of the students have a score of 60, 50, 30

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A group of 7 students has a combined score of 280 on an aptitude test. If 4 of the students have a score of 60, 50, 30

by Vincen » Mon May 18, 2020 6:23 am

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A group of 7 students has a combined score of 280 on an aptitude test. If 4 of the students have a score of 60, 50, 30 and 20 respectively, what is the median score of the students on the aptitude test?

(1) Out of the remaining three students, two students have a combined score of 80 on the aptitude test.

(2) Out of the remaining three students, one student has a score of 40 on the aptitude test.

[spoiler]OA=D[/spoiler]

Source: e-GMAT
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Source: — Data Sufficiency |
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Re: A group of 7 students has a combined score of 280 on an aptitude test. If 4 of the students have a score of 60, 50,

by deloitte247 » Fri May 22, 2020 6:45 am

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The total score of 7 students = 280
Let 7 students =a, b, c, d, e, f, g
a + b + c + d + e + f + g = 280

Assuming that a, b, c, d = 60, 50, 30 and 20 respectively
Therefore, 60 + 50 + 30 + 20 + e + f + g = 280
160 + (e + f + g) = 280
e + f + g =280 - 160 = 120

Target question => What is the median score of the students on the aptitude test?

Statement 1 => Out of the remaining three students, two students have a combined score of 80 on the aptitude test
Assuming that e + f = 80 then f + g = 12
=> 80 + g = 120
g = 120 - 80 = 40

There are so many variations to the sum of 2 numbers that equals 80; but for c and f, it can be categorized under 3 scenario

When e and f = 40
a, b, c, d, e, f, g = 60, 50, 30, 20, 40, 40, 40
Median = 40

When e is less than 40 and f is greater than 40
a, b, c, d, e, f, g = 60, 50, 30, 20, 10, 70, 40
Median = 40

When e is greater than 40 and f is less than 40
a, b, c, d, e, f, g = 60, 50, 30, 20, 55, 35, 40
Median = 40

Scenario, statement 1 is SUFFICIENT

Statement 2 => Out of the remaining three students, one student has a score of 40 on the aptitude test
Assuming e = 40 then e + f + g = 120 and f + g = 120 - 40 = 80

This is the same instance as statement 1, so we will get the same answer. Therefore, statement 2 is also SUFFICIENT

Answer = D
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