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John puts balls in 7 boxes, and put at least 1 ball in each box. Did h

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John puts balls in 7 boxes, and put at least 1 ball in each box. Did h [#permalink]

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New post 29 Mar 2017, 22:14
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Difficulty:

  65% (hard)

Question Stats:

60% (01:14) correct 40% (01:27) wrong based on 57 sessions

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John puts balls in 7 boxes, and put at least 1 ball in each box. Did he put more than 7 balls in at least one box?

1) The number of balls in each of the 7 boxes are different
2) The total number of balls put into box is 29.
[Reveal] Spoiler: OA

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John puts balls in 7 boxes, and put at least 1 ball in each box. Did h [#permalink]

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New post 29 Mar 2017, 22:45
ziyuen wrote:
John puts balls in 7 boxes, and put at least 1 ball in each box. Did he put more than 7 balls in at least one box?

1) The number of balls in each of the 7 boxes are different
2) The total number of balls put into box is 29.


St I
The number of balls in each of the 7 boxes are different
Since the total number of balls is not mentioned, the arrangement can be {1,2,3,4,5,6,7} or {1,2,3,4,5,8,9} -------------Insufficient

St II
The total number of balls put into box is 29.
the arrangement can be {6,4,4,4,4,4,3} or {1,1,2,4,5,8,8} -------------Insufficient

Combining St I and II the only possible arrangement is
{1,2,3,4,5,6,8} ------------Sufficient

Hence option C is correct
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Re: John puts balls in 7 boxes, and put at least 1 ball in each box. Did h [#permalink]

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New post 24 Nov 2017, 15:19
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Expert's post
Hi All,

We're told that John puts balls in 7 boxes and puts at least 1 ball in each box. We're asked if he put MORE than 7 balls in AT LEAST one box. This is a YES/NO question.

1) The number of balls in each of the 7 boxes is DIFFERENT.

Since John put at least 1 ball in each box, there a couple of different possibilities to consider:
IF.... the number of balls in the 7 boxes were:
1, 2, 3, 4, 5, 6 and 7... then the answer to the question would be NO.
1, 2, 3, 4, 5, 6 and 8... then the answer to the question would be YES.
Fact 1 is INSUFFICIENT

2) The total number of balls put into boxes is 29.

With Fact 2, we can have 'duplicate' numbers in boxes, so we now have to consider THAT possibility:

IF.... the number of balls in the 7 boxes were:
4, 4, 4, 4, 4, 4 and 5... then the answer to the question would be NO.
1, 2, 3, 4, 5, 6 and 8... then the answer to the question would be YES.
Fact 2 is INSUFFICIENT

Combined, we know that there are only 29 total balls AND that each box must hold a DIFFERENT number of balls. There's only one option that 'fits':
1, 2, 3, 4, 5, 6 and 8... so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer:
[Reveal] Spoiler:
C


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Re: John puts balls in 7 boxes, and put at least 1 ball in each box. Did h   [#permalink] 24 Nov 2017, 15:19
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