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The students at a school took a math exam. Is the average (a

by Max@Math Revolution » Tue Apr 24, 2018 11:25 pm

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[GMAT math practice question]

The students at a school took a math exam. Is the average (arithmetic mean) score for the exam higher than the median score?

1) The average (arithmetic mean) score is 75.
2) 51% of the students attained more than the average (arithmetic mean) score.
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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Apr 25, 2018 9:10 am

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Max@Math Revolution wrote:[GMAT math practice question]

The students at a school took a math exam. Is the average (arithmetic mean) score for the exam higher than the median score?

1) The average (arithmetic mean) score is 75.
2) 51% of the students attained more than the average (arithmetic mean) score.
Statement 1:
No information about the median.
INSUFFICIENT.

Statement 2:
Let the total number of scores = 100.
Since 51 of the 100 scores are greater than the average, the 50th highest score and the 51st highest score are both greater than the average.
Thus, the median score -- which is halfway between the 50th highest score and the 51st highest score -- must also be greater than the average.
Since the median is greater than the average, the answer to the question stem is NO.
SUFFICIENT.

The correct answer is B.
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by Max@Math Revolution » Fri Apr 27, 2018 12:01 am

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have many variables and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.


Conditions 1) & 2)
The median score is attained or exceeded by 50% of students.
Since 51% of students scored more than the average, the median is more than the average.
Both conditions together are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since we don't know the median, condition 1) is not sufficient.

Condition 2)
Since 51% of students scored more than the average, the median is more than the average.
Condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

In cases where 3 or more additional equations are required, such as for original conditions with "3 variables", or "4 variables and 1 equation", or "5 variables and 2 equations", conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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