In a certain game

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

In a certain game

by sanju09 » Mon Apr 12, 2010 5:20 am

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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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Source: Beat The GMAT — Problem Solving | Mon Apr 12, 2010 5:20 am

eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 am; Thanked: 32 times; Followed by:1 members

by eaakbari » Mon Apr 12, 2010 5:46 am

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

Last edited by eaakbari on Mon Apr 12, 2010 7:53 pm, edited 2 times in total.

Whether you think you can or can't, you're right.
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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Mon Apr 12, 2010 7:27 am

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

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eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 am; Thanked: 32 times; Followed by:1 members

by eaakbari » Mon Apr 12, 2010 7:36 am

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

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

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pm; Thanked: 97 times; Followed by:1 members

by liferocks » Mon Apr 12, 2010 7:55 am

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

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Mon Apr 12, 2010 8:04 am

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

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 am; Thanked: 47 times; Followed by:2 members

by kstv » Mon Apr 12, 2010 8:24 am

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)

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ironstar37: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Thu Nov 19, 2009 6:08 pm

by ironstar37 » Mon Apr 12, 2010 11:46 am

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)

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eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 am; Thanked: 32 times; Followed by:1 members

by eaakbari » Mon Apr 12, 2010 7:54 pm

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: In a certain game

by Scott@TargetTestPrep » Thu Apr 02, 2020 10:07 am

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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