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Equation

by dtweah » Mon May 18, 2009 3:40 pm
. The equation 5x + 51y = 551 has two solution pairs where x and y are positive integers. One solution pair is (100,1). If (x,y) is the other solution pair then x + y equals
(a) 43
(b) 62
(c) 55
(d) 75
(e) 67
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by francopiccolo » Mon May 18, 2009 4:58 pm
Working on the equation:

x = 551 - 51y

y must be such that 51y is 51 + a multiple of 5 so it is y = 1 + 5k

For k = 1 the solution is (49,6), thus the sum is 55.
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by singhr10 » Mon May 18, 2009 5:00 pm
Is OA = c
Well the answer is 55

55*6 = 306 and the remaining 245/5 = 49

So X+Y = 49+5 = 55
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by dumb.doofus » Tue May 19, 2009 12:09 am
To write this in terms of x we get
x = (551 - 51y)/5

For x to be an integer.. 551-51y needs to be a multiple of 5.. for that to happen it should either end with a 0 or a 5..

For ending with a 0 51*y should yield a number ending with 1.. we already know that 1 satisfies it.. the next number would be 11.. but that gives a number greater than 551.. so can't take that..

So now we should check another number that when subtracted from 551 should yield a number ending with 5.. so that means, 51y should be a number ending with 6..
the closest we have is itself.. and so that gives us y =6 and x = 49

total = 55.

Notice that the next number after 6 would be 16 and that too will give a number greater than 551, so not allowed..
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by Svedankae » Tue May 19, 2009 1:41 am
how long do top scorers take on these kinds of questions? are these the questions considered "hard" or does it get way harder than that? i found the solution by working my way up from 1 until i reached 6.... but i guess to score high one needs to do it a smart way like you guys :-/
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