by stupidityismygam » Sun Feb 03, 2008 1:45 pm
Another approach:
We have mn=4n+2m so mn-2m-4n=0
By SFFT (simons favorite factoring trick)
(m-4)(n-2)=8
So, m-4=8,n-2=1 OR m-4=4,n-2=2 OR m-4=2,n-2=4 OR m-4=1,n-2=8
Which is 4 solutions!
Point Count:
mathslug: 3
Quelloquialism: 5
collegebookworm: 2
Roel: 1/2
Very long-winded
Problem #11:
Three cards, each with a positive integer written on it, are lying face-down on a table. Casey, Stacy, and Tracy are told that
i) the numbers are all different
ii) they sum to 13, and
iii) they are in increasing order, left to right
First, Casey looks at the number on the leftmost card and says, "I don't have enough information to determine the other two numbers." Then
Tracy looks at the number of the rightmost card and says, "I don't have enough information to determine the other two numbers." Finally, Stacy looks at the number on the middle card and says, "I don't have enough information to determine the other two numbers." Assume that each person knows that the other two reason perfectly and hears their comments. What number is on the middle card?
a) 2 b) 3 c) 4 d) 5 e) There is not enough information to determine the number.
Source: 1998 AHSME
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tytia