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John puts balls in 7 boxes, and put at least 1 ball...

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by swerve » Tue Nov 07, 2017 11:10 am
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.

The OA is C.

I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced.
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Source: — Data Sufficiency |

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by [email protected] » Tue Nov 07, 2017 7:19 pm
Hi swerve,

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: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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