In a certain game

[sanju09]

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

[eaakbari]

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

[thephoenix]

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

solving for m
7m=50-2x
and therefore none is possible
i think somewhere some thing is modified in the question

[eaakbari]

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

solving for m
7m=50-2x
and therefore none is possible
i think somewhere some thing is modified in the question

Ahh Silly mistakes, silly mistakes, Thank you so much phoenix. I shall edit my post. Let us wait for sanju to reply

[liferocks]

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

I am getting the ans as B ie 3
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

[thephoenix]

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

I am getting the ans as B ie 3
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

thanks i missed that one

[kstv]

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)

[ironstar37]

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)

[eaakbari]

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

[Scott@TargetTestPrep]

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 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