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

Redeem

Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are drawn

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are drawn

by BTGmoderatorDC » Sat Apr 18, 2020 8:14 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are drawn from the box at random without replacement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?

(A) 19
(B) 12
(C) 11
(D) 10
(E) 3


OA C

Source: Princeton Review
Top
Source: — Problem Solving |
User avatar
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Wed Apr 15, 2020 12:19 pm

Re: Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are draw

by MBABackstage » Sun Apr 19, 2020 4:21 am
The integers from 1-20 contain 10 even and 10 odd numbers

As soon as we pick an even number, we know that the product will be even too. Therefore the "worst case" scenario is if we pick all 10 odd evens first and only get an even number on the 11th pick.

The answer is therefore 11! (C)
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

Re: Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are draw

by Jay@ManhattanReview » Sun Apr 19, 2020 11:00 pm
BTGmoderatorDC wrote: ↑
Sat Apr 18, 2020 8:14 pm
 Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are drawn from the box at random without replacement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?

(A) 19
(B) 12
(C) 11
(D) 10
(E) 3

OA C

Source: Princeton Review
From 1 to 20, there are 10 even and 10 odd integers. Since Odd*Odd = Odd and Odd*Even = Even, we must have at one even no. in the product; however, since we wish to be ENSURED that the product of all the integers drawn is even, we must draw all Odd integers and then any of the even integers would do.

So, we must draw at the max 10 + 1 = 11 integers

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review Test Prep

Locations: Manhattan Review Bangalore | Chennai | GRE Prep Hyderabad | Himayatnagar GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

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

Re: Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are draw

by Scott@TargetTestPrep » Tue Apr 21, 2020 2:27 pm
BTGmoderatorDC wrote: ↑
Sat Apr 18, 2020 8:14 pm
 Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are drawn from the box at random without replacement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?

(A) 19
(B) 12
(C) 11
(D) 10
(E) 3


OA C

Source: Princeton Review
We see that 10 cards have odd integers and the other 10 cards have even integers. If the first 10 cards drawn are all odd integers, then the product of these integers is still odd. Since the next card drawn must be an even integer, then the product of the 11 integers will of necessity be even, and so 11 cards must be drawn to ensure that the product of all the integers drawn is even.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

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

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1