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

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

Kudos for a correct solution.

A. 1
B. 3
C. 5
D. 7
E. 9

Kudos for a correct  solution .

hsbinfy · Answer

is it B?

multiple of 2 always even so we need multiples of 5 ending with 0.

i see only one case in which the difference can be minimizd

5*8 +2*5=50
8-5=3

Harley1980 · Answer

We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2 
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15 
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0

third variant give us the mininal difference 
n - m = 10 - 6 = 4

And there is some mistake in my way of thinking because we don't have such answer )

If we change the task and will seek for difference between m and n
than minimal result will be 8 - 5 = 3
And answer B

Harley1980 · Answer

You've made final calculation as m - n 
But question asks about n - m

AmoyV · Answer

2n+5m=50

Now m will always be even.

m 2 4 6 8
n 20 15 10 5

Lowest |n-m|=3

Answer: B

adityadon · Answer

2n+5m=50

I put some values here , 
i put m=6 , so n=10 .. difference is 4
so options C,D,E are out.
lets increase value of m now , 
let m=7 , but n is non-integer , 
let m=8 so n =5 .. differnce is 3. 
also looking at equation , differnce of 1 is not possible 
So answer is option B =3

Divyadisha · Answer

I think answer is 'A'

The question is asking the difference between n and m and NOT the difference between scores of n and m.

2n+5m=50
2*5+5*4=50
5-4=1

I hope i am thinking right. Please suggest

Chimka · Answer

2n+5m=50(n+m)

2n+5m=50n+50m

-45m=48n so, the lowest difference will be 3 if you substitute 1 for m and n. Is it right way?

Thanks.

Harley1980 · Answer

2*5+5*4 is not equal to 50
2*5+5*4 = 30

Harley1980 · Answer

You make mistake in the first equation 
2n+5m=50n+50m

Tasks says that 
so 2n + 5m = 50 points

Your equation shows variant if each player score 50 points
50n + 50m scores

lipsi18 · Answer

2n+3m=50; least positive n-m=?

1. 2.10+5.6=>n-m=4
2. 2.5+5.8=>n-m=3

Hence answer is B

Thanks,

Chimka · Answer

you're right. Thanks. I got it now

KS15 · Answer

Required equation is 2n+5m=50
Different combinations of n and m are 
0,10
25,0
5,8
10,6
15,4
20,2

Least difference =8-5=3. Answer=B

Bunuel · Answer

KAPLAN OFFICIAL SOLUTION:

The quickest solution is to pick numbers for n and m. Since n = 1 and m = 1 would amount to 7 points, and since we want to minimize the difference between n and m,
and since 50/7 is just a bit more than 7, we'll start with values near 7. The key is to discover what values for n, when multiplied by 2 points, will leave a multiple of 5 as the remaining points. The solution turns out to be 5 for n (10 points), which allows for 8 for m (40 points). That's a total of 50 points, and the positive difference between the two values is only 3.

Answer: B.

Konstantin1983 · Answer

Yes i agree. Does it matter if the question asks about n-m or m-n? If about n-m then answer should be 4. If about m-n then 3. Please correct if i am wrong

manishkhare · Answer

If we create an equation then it will be 2n+5m=50 . It implies n=(50-5m)/2 so m is a multiple of 2 .
Similarly m=(50-2n)/5 so n is a multiple of 5 .Minimum difference can be the case when n= 5 and m=2 so difference is 5-2=3. 
Note: Number of players is a integer ,so this approach will work fine.

Harley1980 · Answer

Hello  Konstantin1983 
When we have such formulation "least possible positive difference between n and m" it means both variants  m - n  and  n - m 
And yes, you are right: if question asks exactly about  n - m  than answer will be  4

Konstantin1983 · Answer

Hello Harley1980!
Thanks for reply. Valuable info. I didn't know that. It will help me. Дякую!=))

MarkusKarl · Answer

To fit the equation 2n+5m=50, 2n must be divisible by 10 and the same goes for 5m.

For every 2n to be 10, it will take n=5,10,15,20 etc.
For every 5m to be 10, it will take m=2,4,6,8 etc.

I want to have more 5m's than 2n's and thus start trying with n=10 and m=6, giving me 4 as a difference. I try with n=5 and m=8 (and notice that at this point n is smaller than m and making n smaller further will result in a larger difference) and get the difference of 3. Which was the answer.

Harley1980 · Answer

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

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