Data Sufficiency

[GMAT math practice question]

A class consists of 30 students. Among them a students have 90 books, b students have 80 books, c students have 70 books and all the remaining students have 60 books. What is the average number of books the students in the class have?

1) a= b+c
2) a is twice b

=>

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 3 variables (a, b and c) 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 average number of books is
( 90a + 80b + 70c +60(30 - a - b - c) ) / 30
= ( 30a + 20b + 10c + 1800) /30

If a = 2, b = 1 and c = 1, then the average is (60 + 20 + 10 + 1800)/30 = 1890/30 = 63.
If a = 4, b = 2 and c = 2, then the average is (120 + 40 + 20 + 1800)/30 = 1980/30 = 66.

Since both conditions together don't yield a unique solution, they are not sufficient.
Therefore, E is the 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.