Last visit was: 10 Jul 2025, 15:59 It is currently 10 Jul 2025, 15:59
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
avatar
konayuki
avatar
Joined: 17 Aug 2009
Last visit: 30 Sep 2009
Posts: 8
Own Kudos:
59
 [39]
Posts: 8
Kudos: 59
 [39]
In a deck of 52 cards, each card is one of 4 different color 28 Aug 2009, 17:21
3
Kudos
Add Kudos
36
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

64% (01:17) correct 36% (01:29) wrong based on 344 sessions

History

Date
Time
Result
Not Attempted Yet
In a deck of 52 cards, each card is one of 4 different colors and there are 13 cards of each color. If cards are to be selected at random from the deck, what is the least number of cards that must be selected to ensure that these are at least 3 cards of each color among selected?

A. 40
B. 41
C. 42
D. 43
E. 44
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
LenaA
User avatar
Joined: 10 Aug 2009
Last visit: 11 Dec 2009
Posts: 58
Own Kudos:
101
 [13]
Given Kudos: 10
Posts: 58
Kudos: 101
 [13]
In a deck of 52 cards, each card is one of 4 different color 28 Aug 2009, 20:38
7
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
konayuki
42 is right... but I do not get it.

Help me with the logic!

The logic is the following.
The worst case scenario is that you draw the first 13 cards of the same colour, then another 13 of the same color then another 13 of the same color. After 39 cards, you draw all 3 colors. Then to ensure that you have at least 3 of each, you need to take another 3 cards of the 4th left colour. So in total after 42 card you can be sure you have at least 3 cards of each color (since we considered here the worst case scenario).

By the same logic, if you are asked how many cards you have to draw to ensure you have three of the same colour (not 3 of EACH), the answer is 9.
Here the worst case scenario is that you draw first 4 cards of different colour, then another 4 of different color. After 8 cards, you have two of each colour. So when you draw the 9th card, you are sure you have at least 3 cards of the same colour.
Hope this helps.
General Discussion
User avatar
LenaA
User avatar
Joined: 10 Aug 2009
Last visit: 11 Dec 2009
Posts: 58
Own Kudos:
101
 [2]
Given Kudos: 10
Posts: 58
Kudos: 101
 [2]
In a deck of 52 cards, each card is one of 4 different color 28 Aug 2009, 18:51
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nikhilpoddar
42
Thanks. I didn't notice they ask about three of EACH color. I thought they ask about first three of the same color...If three of each, it is 42.
avatar
konayuki
avatar
Joined: 17 Aug 2009
Last visit: 30 Sep 2009
Posts: 8
Own Kudos:
59
 [1]
Posts: 8
Kudos: 59
 [1]
In a deck of 52 cards, each card is one of 4 different color 28 Aug 2009, 20:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
42 is right... but I do not get it.

Help me with the logic!
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 09 Jul 2025
Posts: 6,375
Own Kudos:
15,575
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,375
Kudos: 15,575
 [1]
In a deck of 52 cards, each card is one of 4 different color 08 Aug 2015, 07:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
konayuki
In a deck of 52 cards, each card is one of 4 different colors and there are 13 cards of each color. If cards are to be selected at random from the deck, what is the least number of cards that must be selected to ensure that there are at least 3 cards of each color among selected?

Total Cards to be picked (In Worst Case scenario) = 13(All card of First color)+13(All card of Second color)+13(all card of Third color)+2(Both card of Forth color)

i.e. Total cards Picked = 41 and still We don't have 3 cards of each colour

Butthe next card picked will be of forth color and then we will have atleast 3 cards of each colours

i.e. Minimum cards to be picked to ensure the desired scenario = 41+1 = 42 cards
User avatar
azhrhasan
User avatar
Joined: 13 Apr 2019
Last visit: 13 Sep 2024
Posts: 122
Own Kudos:
164
Given Kudos: 93
Location: Canada
Concentration: Marketing, Operations
Schools: Rotman '23 (D) Ivey '22 (D) Schulich Sept '23 (WA)
GMAT 1: 690 Q49 V35
GPA: 3.5
WE:General Management (Retail: E-commerce)
Products:
My Reviews
Schools: Rotman '23 (D) Ivey '22 (D) Schulich Sept '23 (WA)
GMAT 1: 690 Q49 V35
Posts: 122
Kudos: 164
In a deck of 52 cards, each card is one of 4 different color 04 Aug 2019, 04:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
konayuki
In a deck of 52 cards, each card is one of 4 different colors and there are 13 cards of each color. If cards are to be selected at random from the deck, what is the least number of cards that must be selected to ensure that these are at least 3 cards of each color among selected?

42.

worst case + 1

(13+13+13+2)+1
User avatar
akadiyan
User avatar
Retired Moderator
Joined: 31 May 2017
Last visit: 20 Jun 2025
Posts: 740
Own Kudos:
696
Given Kudos: 53
Concentration: Technology, Strategy
Schools: IIMA PGPX'23 Bayes Said '23
Products:
My Reviews
Schools: IIMA PGPX'23 Bayes Said '23
Posts: 740
Kudos: 696
In a deck of 52 cards, each card is one of 4 different color 26 Nov 2020, 14:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is a worst case scenario , so consider picking 13 cards from 3 color , even then we would not have selected 3 cards from all colours.

So, we have 13 from 3 colors, so 3*13 = 39
Plus 3 from 4th color , so in total we have 39+3 = 42

Ans: 42
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 10 Jul 2025
Posts: 21,070
Own Kudos:
26,129
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,070
Kudos: 26,129
In a deck of 52 cards, each card is one of 4 different color 21 Jun 2024, 10:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
konayuki
In a deck of 52 cards, each card is one of 4 different colors and there are 13 cards of each color. If cards are to be selected at random from the deck, what is the least number of cards that must be selected to ensure that these are at least 3 cards of each color among selected?

A. 40
B. 41
C. 42
D. 43
E. 44
­
To ensure that at least 3 cards of each color are selected, we could select 13 of one color, then 13 of another color, and 13 of another color. At this point 39 cards have been selected and we have accounted for three of the four colors. Next, to ensure that we have 3 cards selected of EACH color, we would select 3 cards of the final color.

Thus, the total number of cards that must be selected to ensure at least 3 cards of each color is

13 + 13 + 13 + 3 = 42.

Answer: C
Moderators:
Bunuel
Math Expert
102631 posts
Krunaal
PS Forum Moderator
685 posts