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In a certain game, each player scores either 2 points or 5

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In a certain game, each player scores either 2 points or 5 [#permalink] New post 17 Oct 2005, 18:56
00:00
A
B
C
D
E

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(N/A)

Question Stats:

50% (01:04) correct 50% (00:00) wrong based on 1 sessions
In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?


A. 1

B. 3

C. 5

D. 7

E. 9
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 [#permalink] New post 17 Oct 2005, 19:06
I get B) 3

2n + 5m =50 .. n=5, m=8 gives the smallest difference
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 [#permalink] New post 17 Oct 2005, 19:09
multiple of 5 could be, 10, 20, 30, 40
If m=8 (8*5=40), n=5 (5*2=10) -> total 50 -> m-n = 3
If m=6 (6*5=30), n=10 (10*2=20) -> total 50 -> m-n = 4
For other values, it increases.
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 [#permalink] New post 17 Oct 2005, 19:16
I took way more than 2 minutes

n + 2.5 m = 25

By picking the numbers I found

n = 5 and m = 8 is the required set, is B OA?
n = 1 not possible
n = 2 not possible
n = 3 not possible
n= 4 not possible

Any easy way?
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 [#permalink] New post 17 Oct 2005, 19:49
jainvineet wrote:
I took way more than 2 minutes

n + 2.5 m = 25

By picking the numbers I found

n = 5 and m = 8 is the required set, is B OA?
n = 1 not possible
n = 2 not possible
n = 3 not possible
n= 4 not possible

Any easy way?


n+2.5m = 25---> m<10 ...look at 2.5 , it's can only be rounded of by multiplying 4,6 or 8 ....check each and find answer.
I like your solution.
OA is B.
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 [#permalink] New post 18 Oct 2005, 01:04
2n+5m = 50

n=15, m= 4 -- too big <-- i pick this choice randomly
n=10, m m=6
n=5, m =8

smallest diference = 3

Once you pick the first choice, it's very fast to narrow down because the number 50-2n must be divisible by 5 and it must either end in 5 or 0.
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 [#permalink] New post 18 Oct 2005, 15:17
B it is ....
2n+5m=50...and now by picking numbers, we can find out the difference
  [#permalink] 18 Oct 2005, 15:17
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