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

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Konstantin1983
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Re: In a certain game, each player scores either 2 points or 5 points. If [#permalink] New post   01 May 2015, 13:50
Hello Konstantin1983.
I've found another task that exploit this trick with wording "difference between X and Y".
Think it'll be interesting for you )

a-certain-salesman-s-yearly-income-is-determined-by-a-base-126533.html[/quote]
Hello Harley1980!
Thanks! Really good question! Absolute Value is a trick here
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Re: In a certain game, each player scores either 2 points or 5 points. If [#permalink] New post   12 Jan 2017, 10:42
Each Game Players
2 n

5 m
Total Points 50
Case m and n are
1 m - n = 5-2 = 3
m = 0 , n = 1 ; difference 2
m = 1, n = 0 ; difference 5

B
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Re: In a certain game, each player scores either 2 points or 5 points. If [#permalink] New post   24 Sep 2019, 15:36
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Bunuel wrote:
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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We can create the equation:

2n + 5m = 50

Since 2n and 50 are even, then 5m must also be even. Since 5 is not even, m must be even. Therefore, m could be 0, 2, 4, 6, 8, 10.

Since we want the least possible difference between n and m, let’s let m = 6, and we have:

2n + 5(6) = 50

2n = 20

n = 10

We see the difference between n and m is 4.

If m = 8, then we have:

2n + 5(8) = 50

2n = 10

n = 5

We see the difference between n and m is 3.

If m = 10, then we have:

2n + 5(10) = 50

2n = 0

n = 0

We see the difference between n and m is 10.

Thus, the smallest possible difference between n and m is 3 (when n = 5 and m = 8).

Answer: B
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Re: In a certain game, each player scores either 2 points or 5 points. If [#permalink] New post   24 Sep 2019, 19:11
Bunuel wrote:
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

Kudos for a correct solution.


(5+2)*7=49
If m = 8; n=5;n-m=3
If m=6;n=10; n-m=4

IMO B

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Re: In a certain game, each player scores either 2 points or 5 points. If [#permalink] New post   04 Apr 2021, 09:28
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Bunuel wrote:
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

Kudos for a correct solution.


With "x" is the difference between n and m, we have:
2n+5m=50 <-> 2n+5(n+x)=50 <-> 7n+5x=50 <-> n=(50-5x)/7
Now the task becomes: what is x to make n an integer (because n is the number of players who score 2 points, n must be an integer)
if x=1: n= 45/7 --> out
if x=3: n= (50-15)/7 = 5 (integer) --> correct!

Hope this helps :)
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Re: In a certain game, each player scores either 2 points or 5 points. If [#permalink] New post   20 Mar 2023, 20:18
I did it a bit differently:

2n + 5m = 50
=> 2n = 50 - 5m
=> 2n = 5 (10-m).

Now... m MUST be positive, so really the largest m can be is 9 but then the equation is not possible.
So we go to the next number, 8, and then n = 5.
Then we go to 7; the equation is not possible..
Then we go to 6; n = 10 ...
You can technically STOP here because the difference between 8 and 5 (3) is smaller than the difference between 10 and 6 (4).
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Re: In a certain game, each player scores either 2 points or 5 points. If [#permalink]
20 Mar 2023, 20:18
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