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MathRevolution
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The students at a school took a math exam. Is the average (arithmetic 25 Apr 2018, 00:35
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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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B
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The students at a school took a math exam. Is the average (arithmetic 25 Apr 2018, 02:14
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Statement 1:
we don't have any information about the no. of students or about the median
Not sufficient

Statement 2:
51% students have more marks than the arithmetic mean
So, if there are 100 students, median will be the average of 50th and 51st no.
which are more than the arithmetic mean. Hence Median>Arithmetic mean
Sufficient
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The students at a school took a math exam. Is the average (arithmetic 25 Apr 2018, 04:31
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Ans: B

Statement 1 only gives us the average score but not the distribution of the scores. (not sufficient)
Statement 2: tells us that the whatever the avg is 51% scored higher than that means median will be higher than the average score. (sufficient)

ans: B
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The students at a school took a math exam. Is the average (arithmetic 27 Apr 2018, 01:08
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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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