Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Each of the integers from 0 to 9, inclusive, is written on a [#permalink]

Show Tags

07 May 2005, 00:06

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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 a 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?

3

4

5

6

7

--------------

I did get the ans right, but I hoping there's a better method than the one I used.

with the integers from 0 to 9, you can add 10 with
1+9
2+8
3+7
4+6
other numbers are 0,5

we should find a combination of 7 6 5 4 or 3 that does not add 10.
I started from 5 -> 9 8 7 6 5 (pick one number from first/second column and 0 or 5)
now 6-> pick one number from first/second column and both 0 and 5
0 5 9 8 7 6 or 0 5 1 2 3 4
7 is the answer because you pick
0 and 5 first
6 7 8 9 OR 1 2 3 4
next number will necessarily lead to 10 as a sum

You have to just assume the worst - that you won't get 10 until it's absolutely impossible to get anything else.

So what makes ten?

1-9
2-8
3-7
4-6

That's it. So what if the first number you choose is 0? You'll never get ten. What if the next one is 5? Same problem. So now you've chosen 2 numbers already, and no 10.

Then, what if you pick all the next numbers that don't have a partner? Let's say you pick 1,2,3,4 in a row. None of your number now will add up to 10, and you've chosen 6 numbers.

What's left? The 4 partners to 1,2,3,4 - so the next number you choose, whatever it is, will definately match with one of them to make 10.

Agree with you guys. You have to skip 0 and 5 whixh do not lead to any correct sum. Then the 4 first component of this "10" sum. The following one must at least complete one of the possible sums.

There are 6 numbers (0,1,2,3,4,5) forming a set in which any two numbers do not add up to 10.

So, in the worst case scenario (if you were to be absolutely sure that there are 2 numbers that add to 10), You need to pick these 6 numbers + one more. So, the answer is 7.