## number of (x,y) sets

##### This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 77
Joined: 08 Jan 2010
Thanked: 2 times
GMAT Score:700

### number of (x,y) sets

by pharmxanthan » Sat May 15, 2010 11:28 am
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?

Senior | Next Rank: 100 Posts
Posts: 85
Joined: 15 Aug 2009
Thanked: 19 times
by gmatjedi » Sat May 15, 2010 11:39 am
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
Last edited by gmatjedi on Sat May 15, 2010 11:54 am, edited 1 time in total.

Master | Next Rank: 500 Posts
Posts: 247
Joined: 27 Jul 2008
Thanked: 2 times
GMAT Score:660
by orel » Sat May 15, 2010 11:47 am
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

Master | Next Rank: 500 Posts
Posts: 247
Joined: 27 Jul 2008
Thanked: 2 times
GMAT Score:660
by orel » Sat May 15, 2010 11:49 am
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,
28,0; 23,3; 18,6; 13,9; 8,12; 3,15

Why didn't you consider possible negative values of x and y?

Senior | Next Rank: 100 Posts
Posts: 85
Joined: 15 Aug 2009
Thanked: 19 times
by gmatjedi » Sat May 15, 2010 11:55 am
orel, you are correct
i edited my post
you can have an infinite number of negative sets

• Page 1 of 1