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In a certain game, a player can accumulate points only by s
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07 Feb 2020, 04:52
07 Feb 2020, 04:52
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64% (01:44) wrong based on 45 sessions
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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
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
Re: In a certain game, a player can accumulate points only by s
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07 Feb 2020, 10:59
07 Feb 2020, 10:59
Expert Reply
KAPLAN OFFICIAL SOLUTION:
The quickest solution is to pick numbers for n and m. Since n = 1 and m = 1 would amount to 7 points, and since we want to minimize the difference between n and m,
and since 50/7 is just a bit more than 7, we'll start with values near 7. The key is to discover what values for n, when multiplied by 2 points, will leave a multiple of 5 as the remaining points. The solution turns out to be 5 for n (10 points), which allows for 8 for m (40 points). That's a total of 50 points, and the positive difference between the two values is only 3.
Answer: B.
Please, specify exactly the source the question comes from. It is a Kaplan question NOT other resources.. In any case , even others must be specified.
Thank you so much for your collaboration
The quickest solution is to pick numbers for n and m. Since n = 1 and m = 1 would amount to 7 points, and since we want to minimize the difference between n and m,
and since 50/7 is just a bit more than 7, we'll start with values near 7. The key is to discover what values for n, when multiplied by 2 points, will leave a multiple of 5 as the remaining points. The solution turns out to be 5 for n (10 points), which allows for 8 for m (40 points). That's a total of 50 points, and the positive difference between the two values is only 3.
Answer: B.
Please, specify exactly the source the question comes from. It is a Kaplan question NOT other resources.. In any case , even others must be specified.
Thank you so much for your collaboration
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Re: In a certain game, a player can accumulate points only by s
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23 Mar 2022, 12:01
23 Mar 2022, 12:01
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Asif123 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
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
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
