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100 students take a test. 20 students are in class A, 30 students in class B, and 50 students in class C. Wha

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100 students take a test. 20 students are in class A, 30 students in class B, and 50 students in class C. Wha

by Max@Math Revolution » Tue Jul 28, 2020 12:42 am

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[GMAT math practice question]

100 students take a test. 20 students are in class A, 30 students in class B, and 50 students in class C. What is the average of the 100 students?

1) The average of class B is 10 points higher than that of class A.
2) The average of class C is 20 points higher than that of class B.
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Source: — Data Sufficiency |
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Re: 100 students take a test. 20 students are in class A, 30 students in class B, and 50 students in class C. Wha

by Max@Math Revolution » Thu Jul 30, 2020 1:02 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Assume a, b and c are the averages of classes A, B, and C, respectively.

Since we have 3 variables (a, b, and c) and 0 equations, E is most likely 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) together give us that b = a + 10 and c = b + 20:

If a = 60, b = 70 and c = 90, then the average is
60·20 + 70·30 + 90·50/100 = 1200 + 2100 + 4500/100 = 7800/100 = 78

If a = 50, b = 60 and c = 80, then the average is
50·20 + 60·30 + 80·50/100 = 1000 + 1800 + 4000/100 = 6800/100 = 68

The answer is not unique, and both conditions 1) and 2) together are not sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.

Both conditions 1) & 2) together are not sufficient.

Therefore, E is the correct answer.
Answer: E

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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