Q) If x and y are integers, how many sets of (x,y) satisfy 3x+5y=84?
A) 2
B) 3
C) 4
D) 6
E) none of the above
Is there a better way to answer these questions without plugging in different values of x and y?
number of (x,y) sets
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EDITED:
to reflect that integers can be negative
rewrite equations as:
x + (5/3)y=28
y has to be zero or a multiple of 3
therefore,
your positive sets are
28,0; 23,3; 18,6; 13,9; 8,12; 3,15
if y is negative, then additional sets
to reflect that integers can be negative
rewrite equations as:
x + (5/3)y=28
y has to be zero or a multiple of 3
therefore,
your positive sets are
28,0; 23,3; 18,6; 13,9; 8,12; 3,15
if y is negative, then additional sets
Last edited by gmatjedi on Sat May 15, 2010 11:54 am, edited 1 time in total.
it must be E because the number of integers that satisfy the equation is more than 6.
I solved the problem by plugging in numbers. Does anyone know easier and less time consuming way to solve it?
thanks
I solved the problem by plugging in numbers. Does anyone know easier and less time consuming way to solve it?
thanks
gmatjedi wrote:is the answer 6?
rewrite equations as:
x + (5/3)y=28
y has to be zero or a multiple of 3
therefore,
your sets are
28,0; 23,3; 18,6; 13,9; 8,12; 3,15
Why didn't you consider possible negative values of x and y?