GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 05 Jul 2020, 21:23

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

X and Y are two data sets that contain integers as shown the table abo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64951
X and Y are two data sets that contain integers as shown the table abo  [#permalink]

Show Tags

New post 02 Jun 2020, 08:02
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (02:20) correct 37% (02:14) wrong based on 43 sessions

HideShow timer Statistics

Frequency Distribution of Integers in Data Set X and Data Set Y

Image

X and Y are two data sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

A. 1/15
B. 13/354
C. 1/5
D. 1/2
E. 4/5

Attachment:
1.png
1.png [ 12.87 KiB | Viewed 578 times ]

_________________
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 3182
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
Re: X and Y are two data sets that contain integers as shown the table abo  [#permalink]

Show Tags

New post 02 Jun 2020, 08:10
1
Bunuel wrote:
Frequency Distribution of Integers in Data Set X and Data Set Y

Image

X and Y are two data sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

A. 1/15
B. 13/354
C. 1/5
D. 1/2
E. 4/5

Attachment:
1.png


Given: X and Y are two data sets that contain integers as shown the table above.

Asked: What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even = 1 - Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be odd

Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be odd = \(\frac{18}{30} * \frac{10}{12} = \frac{3}{5} * \frac{5}{6} = \frac{3}{6} = \frac{1}{2 }\)

Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even = 1 - Probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be odd = \(1 - \frac{1}{2 }= \frac{1}{2}\)

IMO D
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
IESE School Moderator
avatar
S
Joined: 11 Feb 2019
Posts: 271
CAT Tests
Re: X and Y are two data sets that contain integers as shown the table abo  [#permalink]

Show Tags

New post 02 Jun 2020, 11:41
IMO D

Product of two number even when: (Even from box 1 * Odd from box 2) OR (Even from box 1 * Odd from box 2) OR (Even from box 1 * Even from box 2)

We need to find the probability for above cases.

OR We can calculate Probability as 1 - Probability the product will be ODD

Product of two number odd when: ODD * ODD
SIMPLE :)

Probability the product will be ODD = (Ways of selecting ODD number from box 1 * Ways of selecting ODD number from box 2) / (Ways of selecting a number from box 1 * Ways of selecting a number from box 2)

= 18 * 10 / 30 *12 = 1/2

Probability that product will be Even = 1 -1/2 = 1/2
_________________

Cheers,
NJ
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11036
Location: United States (CA)
Re: X and Y are two data sets that contain integers as shown the table abo  [#permalink]

Show Tags

New post 06 Jun 2020, 04:35
1
1
Bunuel wrote:
Frequency Distribution of Integers in Data Set X and Data Set Y

Image

X and Y are two data sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Data Set X and a randomly chosen integer from Data Set Y will be even?

A. 1/15
B. 13/354
C. 1/5
D. 1/2
E. 4/5

Attachment:
1.png


Solution:

Notice that set X has 30 numbers, of which 12 are even and 18 are odd. Similarly, set Y has 12 numbers, of which 2 are even and 10 are odd.

P(even product)

= P(odd from X, even from Y) + P(even from X, odd from Y) + P(even from X, even from Y)

= 18/30 x 2/12 + 12/30 x 10/12 + 12/30 x 2/12

= 3/5 x 1/6 + 2/5 x 5/6 + 2/5 x 1/6

= 3/30 + 10/30 + 2/30

= 15/30 = 1/2

Alternate Solution:

We can use the fact that P(even product) = 1 - P(odd product) and that P(odd product) = P(odd from X, odd from Y).

Since X has 30 numbers, of which 12 are even and 18 are odd; P(odd from X) = 18/30 = 3/5. Similarly, since set Y has 12 numbers, of which 2 are even and 10 are odd; P(odd from Y) = 10/12 = 5/6.

So, P(odd product) = 3/5 x 5/6 = 3/6 = 1/2. It follows that P(even product) = 1 - 1/2 = 1/2.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

GMAT Club Bot
Re: X and Y are two data sets that contain integers as shown the table abo   [#permalink] 06 Jun 2020, 04:35

X and Y are two data sets that contain integers as shown the table abo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne