Last visit was: 08 Aug 2024, 15:37 It is currently 08 Aug 2024, 15:37
Toolkit
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.
Request Expert Reply

In a certain game, a player can accumulate points only by scoring eith

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94837
Own Kudos [?]: 647980 [24]
Given Kudos: 86892
Retired Moderator
Joined: 19 Oct 2018
Posts: 1868
Own Kudos [?]: 6719 [1]
Given Kudos: 705
Location: India
Intern
Joined: 07 Apr 2020
Posts: 44
Own Kudos [?]: 87 [1]
Given Kudos: 2
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8026
Own Kudos [?]: 4270 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
Bunuel wrote:
In a certain game, a player can accumulate points only by scoring either an X, which counts 3 points, or a Y, which counts 2 points. If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have?

A. Four
B. Five
C. Six
D. Seven
E. Eight

PS20410

given
3x+2y =24
x = 24-2y/3
x= 2 * ( 12-y)/3
so x can be 0 with y = 12
and value of y =0, 3,6,9,
total 5 values OPTION B
IESE School Moderator
Joined: 11 Feb 2019
Posts: 270
Own Kudos [?]: 174 [1]
Given Kudos: 53
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
1
Kudos
Say 3x: points by X
2y: Points by Y

3x + 2y =24

x = (24-2y)/3
for x to be integer: y can take values: 12, 9, 6, 3, 0

x can take 5 values.

x = 2(12-y)/3

only values for x: 0,
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3710
Own Kudos [?]: 17468 [1]
Given Kudos: 165
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
1
Bookmarks
Expert Reply

Solution

Given
In this question, we are given that
• In a certain game,
o A player can accumulate points only by scoring either an X, which counts 3 points, or
o A Y, which counts 2 points

To find
We need to determine
• If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have

Approach and Working out
• Total points should be of the form 3X + 2Y
• Thus, 3X + 2Y = 24, where X and Y must be ≥ 0
• Possibilities are (X, Y) = (0, 12) or (2, 9) or (4, 6) or (6, 3) or (8, 0)

Thus, option B is the correct answer.

Correct Answer: Option B
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5328
Own Kudos [?]: 4280 [0]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
Given: In a certain game, a player can accumulate points only by scoring either an X, which counts 3 points, or a Y, which counts 2 points.

Asked: If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have?

Let x be the times X was scored and y be the times Y was scored

t = 3x

3x + 2y = 24

(x,y) = {(0,12),(2,9),(4,6),(6,3),(8,0)}: 5 set of values

t will have 5 different values.

IMO B
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30981 [0]
Given Kudos: 799
Location: Canada
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
Expert Reply
Top Contributor
Bunuel wrote:
In a certain game, a player can accumulate points only by scoring either an X, which counts 3 points, or a Y, which counts 2 points. If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have?

A. Four
B. Five
C. Six
D. Seven
E. Eight
PS20410

So, if X's are worth 3 points and Y's are worth 2 points, then the TOTAL points = 3X + 2Y (where X and Y represent the number of X's and Y's scored, respectively)
So, we want to determine the number of different integer solutions to 3X + 2Y = 24
Let's list them in the form (X, Y):
(0, 12)
(2, 9)
(4, 6)
(6, 3)
(8, 0)

So, X can equal 0, 2, 4, 6, or 8, then t can equal 0, 6, 12, 18 or 24

Answer: B
Non-Human User
Joined: 09 Sep 2013
Posts: 34303
Own Kudos [?]: 859 [0]
Given Kudos: 0
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
Moderator:
Math Expert
94837 posts