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

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Bunuel
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In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  22 May 2020, 11:27
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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


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nick1816
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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  22 May 2020, 12:07
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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
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Enchanting
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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  22 May 2020, 12:34
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
    t can be 0, 2, 4, 6, and 8
      There are 5 different possible values of t.
Answer: Option B.
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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  22 May 2020, 20:16
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
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NitishJain
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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  23 May 2020, 17:35
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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,
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EgmatQuantExpert
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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  30 May 2020, 22:35
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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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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  03 Dec 2021, 22:36
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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BrentGMATPrepNow
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Re: In a certain game, a player can accumulate points only by scoring eith [#permalink] New post  15 Feb 2022, 06:34
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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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