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John wants to put the 78 pencils in the 6 boxes. The number

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John wants to put the 78 pencils in the 6 boxes. The number

by Max@Math Revolution » Tue Apr 19, 2016 5:05 am
John wants to put the 78 pencils in the 6 boxes. The number of the each pencil in the boxes is different one another and there is no empty boxes. The second largest box of the number of the pencils is named to be B, is the pencil's number of the box B more than 9?

1) The largest number box has 40 pencils and the smallest number box has 5 pencils
2) The box B has the pencils less than the number 14


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Apr 27, 2016 12:40 am
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.

John wants to put the 78 pencils in the 6 boxes. The number of the each pencil in the boxes is different one another and there is no empty boxes. The second largest box of the number of the pencils is named to be B, is the pencil's number of the box B more than 9?

1) The largest number box has 40 pencils and the smallest number box has 5 pencils
2) The box B has the pencils less than the number 14


First of all, when it comes to inequality questions, it is important that if range of que includes range of con, that con is sufficient. The question is B>9?, and ,in 2) B<14, the range of que doesn't include the range of con, which is not sufficient. Also, if the question refers to "more than", you need to figure out a minimum value. For 1), 5+x+y+z+B+40=78 -> x+y+z+B=33. In this case, (x,y,z,B)=(6,7,8,9) is impossible and (6,8,9,10) is possible, which makes B=10>9. When it is minimum, it is always yes and sufficient.
Thus, the answer is A.
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