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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

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

by VJesus12 » Sat Oct 14, 2017 6:20 am

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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Source: Beat The GMAT — Problem Solving | Sat Oct 14, 2017 6:20 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Oct 14, 2017 6:42 am

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 $$$$

Brent Hanneson - Creator of GMATPrepNow.com

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Fri Oct 20, 2017 2:20 pm

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.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Nov 22, 2019 11:50 am

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

E is OA.

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

We can pull the following slips before getting a sum of 10:

0, 1, 2, 3, 4, 5

No matter what number (6, 7, 8 or 9) we pull on the next card , we are sure that we will obtain a sum of 10. Thus, the minimum number of cards drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 is 7.

Answer: E

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Founder and CEO
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