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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

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by BTGmoderatorDC » Mon Feb 14, 2022 5:19 pm

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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


OA B

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Re: In a certain game, a player can accumulate points only by scoring either an X, which counts 3 points, or a Y, which

by Brent@GMATPrepNow » Tue Feb 15, 2022 5:34 am
BTGmoderatorDC wrote: ↑
Mon Feb 14, 2022 5:19 pm
 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


OA B

Source: GMAT Prep
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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