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A law firm charges 1500 dollars in total for jobs that take

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A law firm charges 1500 dollars in total for jobs that take

by Max@Math Revolution » Thu Jun 21, 2018 11:32 pm

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[GMAT math practice question]

A law firm charges 1500 dollars in total for jobs that take at most 10 hours to complete, and 100 dollars/hour for jobs that take more than 10 hours to complete. If the firm completed 2 jobs, how many hours did it take to complete the two jobs?

1) The cost of one of the jobs was 1500 dollars
2) The total cost of the two jobs was 3500 dollars
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Jun 24, 2018 6:03 pm

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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.
Let T1 and T2 be the numbers of hours it took to complete the first and second jobs, respectively.
Since we have 2 variables and 0 equations, C 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)
Since the cost of the first job is $1500, the cost of the second job is $3500 - $1500 = $2000. Therefore, it took T2 = 2000/100 = 20 hours to complete the second job. However, we cannot determine how long the first job took. For example, we could have T1 = 5 < 10, or T1 = 1500/100 = 15 hours.
Since we don't have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.
Answer: E

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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