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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In a certain game
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sanju09
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eaakbari
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We can set up the equations
2n + 5m = 50
n - m = x
Solving for m
7m = 50 -2x
If we look at the answer choices none will satisfy, then maybe m is greater than n
2n + 5m = 50
m - n = x
Solving
7m = 50 + 2x
While looking at the answer choices we find B turns out as 56 which is a multiple of 7
Hence B
2n + 5m = 50
n - m = x
Solving for m
7m = 50 -2x
If we look at the answer choices none will satisfy, then maybe m is greater than n
2n + 5m = 50
m - n = x
Solving
7m = 50 + 2x
While looking at the answer choices we find B turns out as 56 which is a multiple of 7
Hence B
Last edited by eaakbari on Mon Apr 12, 2010 7:53 pm, edited 2 times in total.
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thephoenix
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solving for meaakbari wrote:We can set up the equations
2n + 5m = 50
n - m = x
Solving for m
7m = 50 -x
If we look at the answer choices only x = 1 will give us a multiple of 7 and obviously points scored is an integer.
Hence A
7m=50-2x
and therefore none is possible
i think somewhere some thing is modified in the question
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eaakbari
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Ahh Silly mistakes, silly mistakes, Thank you so much phoenix. I shall edit my post. Let us wait for sanju to replythephoenix wrote:solving for meaakbari wrote:We can set up the equations
2n + 5m = 50
n - m = x
Solving for m
7m = 50 -x
If we look at the answer choices only x = 1 will give us a multiple of 7 and obviously points scored is an integer.
Hence A
7m=50-2x
and therefore none is possible
i think somewhere some thing is modified in the question
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liferocks
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I am getting the ans as B ie 3sanju09 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
we can write the question as
2n+5m=50
different values are
n m
0 10
5 8
10 6
15 4
20 2
25 0
clearly minimum is (8-5)=3
@Sanju can you please confirm the answere
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thephoenix
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thanks i missed that oneliferocks wrote:I am getting the ans as B ie 3sanju09 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
we can write the question as
2n+5m=50
different values are
n m
0 10
5 8
10 6
15 4
20 2
25 0
clearly minimum is (8-5)=3
@Sanju can you please confirm the answere
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kstv
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In this game
2m + 5n = 50 have to find the least value of |m-n|
n cannot be a odd number , so possible values of n are 0,2,4,6,8,10 the corresponding values of m are 25,20,15,10,5,0
list out the possible values
m---n--m-n
25---0--25
20---2--18
15---4--11
10---6--4
5 ----8--3
0---10--10
IMO (B)
2m + 5n = 50 have to find the least value of |m-n|
n cannot be a odd number , so possible values of n are 0,2,4,6,8,10 the corresponding values of m are 25,20,15,10,5,0
list out the possible values
m---n--m-n
25---0--25
20---2--18
15---4--11
10---6--4
5 ----8--3
0---10--10
IMO (B)
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ironstar37
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Can just choose numbers for this.
Let m = 8, therefore points scored from m players = 40 (8x5)
Therefore, n = 5 (5 x 2 = 10) and 40+10 = 50.
Difference between m and n = 3.
You can see that 8 would work for m, but not 9 or 7 (points would be 45, and 5 is not divisible by 2).
IMO (B)
Let m = 8, therefore points scored from m players = 40 (8x5)
Therefore, n = 5 (5 x 2 = 10) and 40+10 = 50.
Difference between m and n = 3.
You can see that 8 would work for m, but not 9 or 7 (points would be 45, and 5 is not divisible by 2).
IMO (B)
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eaakbari
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We can set up the equations
2n + 5m = 50
n - m = x
Solving for m
7m = 50 -2x
If we look at the answer choices none will satisfy, then maybe m is greater than n
2n + 5m = 50
m - n = x
Solving
7m = 50 + 2x
While looking at the answer choices we find B turns out as 56 which is a multiple of 7
Hence B
2n + 5m = 50
n - m = x
Solving for m
7m = 50 -2x
If we look at the answer choices none will satisfy, then maybe m is greater than n
2n + 5m = 50
m - n = x
Solving
7m = 50 + 2x
While looking at the answer choices we find B turns out as 56 which is a multiple of 7
Hence B
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Scott@TargetTestPrep
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We can create the equation:sanju09 wrote: ↑Mon Apr 12, 2010 5:20 amIn 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
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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