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Math Expert
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In a certain game, a player can accumulate points only by scoring eith
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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
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Posts: 1938
Location: India
Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
3x+2y=24
3x = 24 - 2y = 2(12-y)
Since 3x is a multiple of 3, '12-y' or 'y' must be a multiple of 3.
y can take 5 values (0, 3, 6, 9 , 12) and so does x.
B
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
Intern
Joined: 07 Apr 2020
Posts: 46
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
Let y be the number of Y score i.e., 2 point
- 3t + 2y = 28
3t = 28 – 2y
- 28- 2y is an even number.
3t must be an even number.
t must be an even number such that 3t ≤ 28
- There are 5 different possible
values of t.
Answer: Option B.
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Posts: 7288
Location: India
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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: 295
Re: In a certain game, a player can accumulate points only by scoring eith
[#permalink]
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,
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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3757
Re: In a certain game, a player can accumulate points only by scoring eith
[#permalink]
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
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Posts: 4825
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
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Kinshook Chaturvedi
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Joined: 11 Sep 2015
Posts: 6875
Location: Canada
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
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
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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink]
15 Feb 2022, 05:34
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