Last visit was: 25 Apr 2026, 05:53 It is currently 25 Apr 2026, 05:53
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ (Hard)|   Probability|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,826
Own Kudos:
811,172
 [10]
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,826
Kudos: 811,172
 [10]
There are two decks of 10 cards each. The cards in each deck are label 28 Oct 2021, 09:00
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

35% (02:59) correct 65% (02:48) wrong based on 106 sessions

History

Date
Time
Result
Not Attempted Yet
There are two decks of 10 cards each. The cards in each deck are labeled with integers from 11 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?

A. 0.23
B. 0.36
C. 0.40
D. 0.42
E. 0.46
ShowHide Answer
Official Answer
D
User avatar
JerryAtDreamScore
User avatar
Dream Score Representative
Joined: 07 Oct 2021
Last visit: 02 Jul 2022
Posts: 378
Own Kudos:
437
 [3]
Given Kudos: 2
Posts: 378
Kudos: 437
 [3]
There are two decks of 10 cards each. The cards in each deck are label Updated on: 31 Oct 2021, 17:10
Originally posted by JerryAtDreamScore on 28 Oct 2021, 11:20.
Last edited by JerryAtDreamScore on 31 Oct 2021, 17:10, edited 1 time in total.
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
There are two decks of 10 cards each. The cards in each deck are labeled with integers from 11 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?

A. 0.23
B. 0.36
C. 0.40
D. 0.42
E. 0.46
Show more

Breaking Down the Info:

We have \(10 * 10 = 100\) possible products in total. We need (i) a factor of 6, or (ii) a factor of 2 with a factor of 3 to create a multiple of 6.

(i) We can start from 12 and 18, they can take any number so 12 * X, 18 * X, X * 12, and X * 18 are all easy multiples of 6. That is 40 possible options but remove 4 of them as we double-counted 12*12, 18*18, 12*18, and 18*12, hence 36 options.

(ii) Next, we can try a multiple of 2 times a multiple of 3. The multiples of 2 are {14, 16, 20} (remove 12 and 18 as we used them earlier).

The only multiple of 3 is {15} (again remove 12 and 18 as we used them earlier).

Hence that is only 6 more options if we permutate them and reverse their orders.

Then we have 36 + 6 = 42 options in total.

Answer: D
User avatar
QuantMadeEasy
User avatar
Joined: 28 Feb 2014
Last visit: 01 Mar 2026
Posts: 502
Own Kudos:
802
 [1]
Given Kudos: 78
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE:Engineering (Education)
Posts: 502
Kudos: 802
 [1]
There are two decks of 10 cards each. The cards in each deck are label 29 Oct 2021, 00:25
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Quote:
There are two decks of 10 cards each. The cards in each deck are labeled with integers from 11 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?
Show more

Total number of possible outcomes: 10*10 = 100

There are 4 possible cases:

(1) first card is not multiple of 6, cards are 11, 13, 17, 19; 4 ways. The other card has to be multiple of 6, that is 12, 18; 2 ways. For elaboration these are (11,12), (11,18), (13,12), (13,18), (17,12), (17,18), (19,12), (19,18). There are 8 ways

(2) first card multiple of 6, cards are 12, 18; 2 ways. The other is any card out of 10 cards; 10 ways. There are 2*10 = 20 ways

(3) first card multiple of 2 but not of 3, cards are 14, 16, 20; 3 ways. The other card is multiple of 3, cards are 12, 15, 18; 3 ways. There are 3*3 = 9 ways

(4) first card multiple of 3 but not of 2, cards are 15; 1 ways. The other card is multiple of 2, cards are 12, 14, 16, 18, 20; 5 ways. There are 1*5 = 5 ways

Total number of required outcomes i.e. picking a card which is multiple of 6 are 8+20+9+5 = 42 ways

Required probability = 42/100 = 0.42

D is correct
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 25 Apr 2026
Posts: 4,847
Own Kudos:
9,183
 [2]
Given Kudos: 226
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,847
Kudos: 9,183
 [2]
There are two decks of 10 cards each. The cards in each deck are label 29 Oct 2021, 00:55
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In questions like this, you can also list down the possibilities and add the favorable possibilities to answer the question.

Lets list out the possibilities here.

We have the following situations:

For the product of the numbers on the picked cards to be a multiple of 6,either the picked card from deck 1 is a multiple of 6 and any number from deck 2 would still make the product a multiple of 6

OR

If a card from deck 1 is a multiple of 3, we must pull a multiple of 2 from deck 2 (& vice versa).

If the card from Deck 1 is not a multiple of 2 or 3, we must pick a multiple of 6 from Deck 2 to ensure that the product is a multiple of 6.

Card from deck 1
(i) 11
(ii) 12
(iii)13
(iv)14
(v) 15
(vi)16
(vii)17
(viii)18
(ix)19
(x) 20

Card from deck 2
(i) 12, 18
(ii) ANY CARD
(iii) 12, 18
(iv) 12, 15, 18
(v) 12, 14, 16, 18, 20
(vi) 12, 15, 18
(vii) 12, 18
(viii) ANY CARD
(ix) 12, 18
(x) 12, 15, 18

Number of card pairs for product to be multiple of 6

(i) 2 (11,12) & (11,18)

(ii)10

(iii)2

(iv)3

(v)5

(vi)3

(vii)2

(viii)10

(ix)2

(x)3

Total = 42

Sample space in this case is 10 * 10 =100 possibilities

(If you have 1 card choice from deck 1,you have 10 for deck 2 = > for 10 cards from deck 1, you have 10 * 10 =100 choices)

Probability = Favorable ways /Sample Space

= 42 / 100

=0.42
(option d)

D.S
GMAT SME
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,981
Own Kudos:
1,117
Posts: 38,981
Kudos: 1,117
There are two decks of 10 cards each. The cards in each deck are label 14 Jul 2025, 11:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109826 posts
Krunaal
Tuck School Moderator
852 posts