In a certain game

Question

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 · Answer

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

Whether you think you can or can't, you're right.
- Henry Ford

thephoenix · Answer

eaakbari 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

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

eaakbari · Answer

thephoenix wrote:eaakbari 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 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 · Answer

sanju09 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

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 · Answer

liferocks wrote:sanju09 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 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 · Answer

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 · Answer

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 · Answer

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

Whether you think you can or can't, you're right.
- Henry Ford

Scott@TargetTestPrep · Answer

sanju09 wrote: ↑Mon Apr 12, 2010 5:20 am 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

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