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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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John wants to put the 78 pencils in the 6 boxes. The number of the eac [#permalink]

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19 Apr 2016, 06:05
00:00

Difficulty:

65% (hard)

Question Stats:

71% (01:30) correct 29% (02:13) wrong based on 75 sessions

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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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Joined: 12 Jun 2015
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Re: John wants to put the 78 pencils in the 6 boxes. The number of the eac [#permalink]

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19 Apr 2016, 16:55
1
Since the no. of pencils in each box is supposed to be different and not zero, let the equation be stated as
a+b+c+d+e+f= 78

Statement 1 says the largest box has 40 pencils. The rest of them should add up to 38.
The box with least number of pencil contains 5 pencils.

So , 40+b+c+d+e+5= 78
b+c+d+e= 33

If we take the least values possible for the rest of the boxes apart from box b, we get
b+8+7+6= 33

b=12
Separately, when you take other values for c,d,e , you will find the least value for box B , the box with 2nd highest no. of pencils is 10
Statement 1 is Sufficient

Statement 2 say box B has less than 14 pencils which can either be greater than or less than 9.
Hence, not sufficient

Correct Option : A
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5837
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: John wants to put the 78 pencils in the 6 boxes. The number of the eac [#permalink]

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21 Apr 2016, 01:23
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.
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Re: John wants to put the 78 pencils in the 6 boxes. The number of the eac [#permalink]

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16 Oct 2017, 08:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: John wants to put the 78 pencils in the 6 boxes. The number of the eac   [#permalink] 16 Oct 2017, 08:23
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