need help

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ttv: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Fri Jan 04, 2008 1:19 pm; Location: florida, FL

by ttv » Fri Jan 04, 2008 2:20 pm

In a certain game, each player scores either 2 points or 5 points. if n players score 2 points and m player score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m ?

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Source: Beat The GMAT — Problem Solving | Fri Jan 04, 2008 2:20 pm

cris: Master | Next Rank: 500 Posts; Posts: 128; Joined: Sat Nov 17, 2007 11:59 am; Thanked: 1 times

by cris » Fri Jan 04, 2008 3:12 pm

is it 3?

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Tud: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Tue Dec 04, 2007 12:04 pm; Location: Nova Scotia; Thanked: 6 times

by Tud » Fri Jan 04, 2008 3:20 pm

I agree with 3.
2+5=7
50/7=7 remainder 1
Since nothing gets you 1 point you need to take something away. By removing 2 of the 2 pointers you add up to 45, then add 1 5 pointer to get to 50.

7-2=5 2pointers
7+1=8 5pointers.

8-5=3

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Auzbee: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Mon Jul 09, 2007 6:54 pm; Location: US of A

by Auzbee » Sat Jan 05, 2008 12:33 am

To crack this problem, since the point denominations are in 2 and 5, the LCM is 10. Hence the 2's will be in multiple of 5 and 5's in multiple of 2.
Least difference between n and m will be
8 of 5's - 5 of 2's = 3
If you take the next level it becomes:
6 of 5's - 10 of 2's = 4

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