Each of the integers from 0 to 9, inclusive, is written on a

Expert replies

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Dec 10, 2019 5:08 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 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 ?

A. Three
B. Four
C. Five
D. Six
E. Seven

OA E

Source: Official Guide

Like this post

Source: Beat The GMAT — Problem Solving | Tue Dec 10, 2019 5:08 am

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Tue Dec 10, 2019 7:26 am

BTGmoderatorDC 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 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 ?

A. Three
B. Four
C. Five
D. Six
E. Seven

OA E

Source: Official Guide

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

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Jan 10, 2020 1:11 pm

BTGmoderatorDC 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 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 ?

A. Three
B. Four
C. Five
D. Six
E. Seven

OA E

Source: Official Guide

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review