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If operation @ represent addition or subtraction, 3@4=? 1)

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If operation @ represent addition or subtraction, 3@4=? 1)

by Max@Math Revolution » Fri Mar 11, 2016 5:07 am
If operation @ represent addition or subtraction, 3@4=?

1) 3@(0@4)=3@0@4
2) 3@(4@0)=3@4@0


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Mar 13, 2016 9:11 pm
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If operation @ represent addition or subtraction, 3@4=?

1) 3@(0@4)=3@0@4
2) 3@(4@0)=3@4@0


In the original condition, you only need to figure out @, which makes 1 variable. In order to match with the number of equations, you need 1 equation, which is likely to make D the answer.
For 1), only @=+ is possible, which is unique and sufficient.
For 2), only @=+,- is possible, which is not unique and not sufficient.
Therefore, the answer is A.
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by Max@Math Revolution » Sun Mar 13, 2016 9:16 pm
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


Power of Machine A=W/24hrs. Since Machine A does the job for 8 hours, which becomes (W/3)/8hrs and 2W/3 is left. However, as power of Machine B is 2/3 of Machine A, power of B is (2/3)(W/24hrs)=(2W/3)/24hrs. Eventually, it takes 24 hours for Machine B to do the rest of the job.
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