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

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

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

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

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

Quote

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 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; 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

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8088; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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]