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Each of the integers from 0 to 9. . . .

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Each of the integers from 0 to 9. . . .

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Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?

A. 3
B. 4
C. 5
D. 6
E. 7

E is OA.

I would like to know how can I solve this PS question. Experts, may you give me an explanation? Thanks.

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GMAT/MBA Expert

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VJesus12 wrote:
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?

A. 3
B. 4
C. 5
D. 6
E. 7
Here are the PAIRS of numbers that yield a sum of 10:
(1 and 9)
(2 and 8)
(3 and 7)
(4 and 6)
Also, 0 and 5 have no other values to pair with to get a sum of 10

Now let's try to AVOID getting a sum of 10.
Notice that, if we choose the numbers 0, 1, 2, 3, 4, and 5, there are no pair of values that yield a sum of 10
Since these 6 values do NOT ensure that two numbers yield a sum of 10, we can conclude that the correct answer is GREATER THAN 6
So, the correct answer must be E

Cheers,
Brent $$$$

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GMAT/MBA Expert

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Hello VJesus12.

The worst scenario you can have is that the extracted splits of paper are: 0, 1, 2, 3 ,4 and 5 (or 5, 6, 7, 8 and 9).

In each case, there are 6 splits extracted and no pair of them sum 10.

So, you have to extract one more split to ensure that two of them sum 10.

In conlcusion, you have to extract 7 splits. The answer is E.

I hope this answer can help you.

I'm available if you'd like any follow up.

Feel free to contact me.

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