Last visit was: 28 Apr 2026, 11:37 It is currently 28 Apr 2026, 11:37
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,950
Own Kudos:
811,765
 [2]
Given Kudos: 105,927
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: 109,950
Kudos: 811,765
 [2]
Caleb and Dan play a game in which the loser of each round gives one 13 Jun 2018, 12:09
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

92% (01:31) correct 8% (01:21) wrong based on 92 sessions

History

Date
Time
Result
Not Attempted Yet
Caleb and Dan play a game in which the loser of each round gives one half of his marbles to the other player. They start out with 4C and 4D marbles, respectively. If Caleb wins the first round and Dan wins the second round, how many marbles does Dan have at the end of the second round?

(A) 2D
(B) 2C + D
(C) 2D + C
(D) 3D + C
(E) 3D + 2C
ShowHide Answer
Official Answer
E
avatar
Sri21
avatar
Joined: 27 Oct 2016
Last visit: 10 Sep 2018
Posts: 8
Own Kudos:
9
Given Kudos: 54
Posts: 8
Kudos: 9
Caleb and Dan play a game in which the loser of each round gives one 13 Jun 2018, 12:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
After first round Dan = 4D/2 =2D
Caleb = 4C+2D
After second round Caleb = (4C+2D)/2 = 2C+D
Dan= 2D+2C+D = 3D+2C
Option E
User avatar
gmatzpractice
User avatar
Joined: 07 Feb 2017
Last visit: 25 Nov 2024
Posts: 122
Own Kudos:
82
Given Kudos: 11
GMAT 1: 710 Q48 V40
GMAT 1: 710 Q48 V40
Posts: 122
Kudos: 82
Caleb and Dan play a game in which the loser of each round gives one 13 Jun 2018, 15:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
E
Caleb has 4C; Dan has 4D
Caleb has 4C + 2D; Dan has 2D
Caleb has 2C + D; Dan has 2C + 3D
User avatar
KSBGC
User avatar
Joined: 31 Oct 2013
Last visit: 10 Mar 2022
Posts: 1,240
Own Kudos:
1,510
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Posts: 1,240
Kudos: 1,510
Caleb and Dan play a game in which the loser of each round gives one 13 Jun 2018, 18:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Caleb and Dan play a game in which the loser of each round gives one half of his marbles to the other player. They start out with 4C and 4D marbles, respectively. If Caleb wins the first round and Dan wins the second round, how many marbles does Dan have at the end of the second round?

(A) 2D
(B) 2C + D
(C) 2D + C
(D) 3D + C
(E) 3D + 2C
Show more


Caleb = 4C
Dan = 4D

1. Caleb win the first round : so, Dan will provide half of his marbles. = 4D / 2 = 2D. Remaining Marbles of Dan = 4D - 2D = 2D.

So, Caleb has total of 4C + 2D marbles .

2. Dan win the second round. So, Caleb will provide half of his marbles to Dan .

Caleb =\(\frac{4C + 2D}{2}\) = 2C+D

We are asked to determine the total marbles Dan has = 2C+D +2D = 3D + 2C.

Thus the best answer is E.
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,900
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,900
Caleb and Dan play a game in which the loser of each round gives one 13 Jun 2018, 23:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Solution



Given:
    • Caleb and Dan play a game where the loser of each round gives one half of his marbles to the other players
    • They start with 4C and 4D marbles respectively
    • Caleb wins the first round, and Dan wins the second round

To find:
    • Number of marbles Dan has, at the end of second round

Approach and Working:
We can collate the proceedings of the game in the following table:



Hence, the correct answer is option E.

Answer: E
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 21 Feb 2026
Posts: 1,387
Own Kudos:
898
Given Kudos: 243
Posts: 1,387
Kudos: 898
Caleb and Dan play a game in which the loser of each round gives one 27 Nov 2024, 22:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can this be solved via number substitution? I tried and but couldn't solve it, as numbers kept messing up
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,950
Own Kudos:
811,765
 [1]
Given Kudos: 105,927
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: 109,950
Kudos: 811,765
 [1]
Caleb and Dan play a game in which the loser of each round gives one 28 Nov 2024, 00:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sam1001
Caleb and Dan play a game in which the loser of each round gives one half of his marbles to the other player. They start out with 4C and 4D marbles, respectively. If Caleb wins the first round and Dan wins the second round, how many marbles does Dan have at the end of the second round?

(A) 2D
(B) 2C + D
(C) 2D + C
(D) 3D + C
(E) 3D + 2C

Can this be solved via number substitution? I tried and but couldn't solve it, as numbers kept messing up
Show more


If C = D = 1, each starts with 4 marbles.

After Caleb wins the first round, Caleb will have 4 + 2 = 6 marbles, and Dan will have 4 - 2 = 2 marbles.
After Dan wins the second round, Caleb will have 6 - 3 = 3 marbles, and Dan will have 2 + 3 = 5 marbles.

Substituting C = D = 1, only E, 3D + 2C, gives 5 as the answer.

Answer: E.

Hope it helps.
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 21 Feb 2026
Posts: 1,387
Own Kudos:
898
Given Kudos: 243
Posts: 1,387
Kudos: 898
Caleb and Dan play a game in which the loser of each round gives one 28 Nov 2024, 04:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Bunuel, this is super helpful. You are the best!
Bunuel
Sam1001
Caleb and Dan play a game in which the loser of each round gives one half of his marbles to the other player. They start out with 4C and 4D marbles, respectively. If Caleb wins the first round and Dan wins the second round, how many marbles does Dan have at the end of the second round?

(A) 2D
(B) 2C + D
(C) 2D + C
(D) 3D + C
(E) 3D + 2C

Can this be solved via number substitution? I tried and but couldn't solve it, as numbers kept messing up


If C = D = 1, each starts with 4 marbles.

After Caleb wins the first round, Caleb will have 4 + 2 = 6 marbles, and Dan will have 4 - 2 = 2 marbles.
After Dan wins the second round, Caleb will have 6 - 3 = 3 marbles, and Dan will have 2 + 3 = 5 marbles.

Substituting C = D = 1, only E, 3D + 2C, gives 5 as the answer.

Answer: E.

Hope it helps.
Show more
Moderators:
Bunuel
Math Expert
109950 posts
Krunaal
Tuck School Moderator
852 posts