number of (x,y) sets

Expert replies

pharmxanthan: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Fri Jan 08, 2010 7:55 am; Thanked: 2 times; GMAT Score:700

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?

Like this post

Source: Beat The GMAT — Problem Solving | Sat May 15, 2010 11:28 am

gmatjedi: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Sat Aug 15, 2009 4:36 am; 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.

Like this post

orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; 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

Like this post

orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; 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,
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?

Like this post

gmatjedi: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Sat Aug 15, 2009 4:36 am; 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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review