How to determine Suff/NotSuff with *single* two-variables equation

[acutetrader]

Hi all,

 

I have found that several DS GMAT equations that have two-variables can determine the X and Y value when assuming that X and Y are positive integer.

 

For example,

 

5x + 3y = 76 , given that X and Y are positive interger

We can determine X and Y value with only one equation above.

 

The problem is : I'm curious "How to check whether the provided 2-variables equations, if X&Y are positive integer, are sufficient to determine both X and Y value?".

 

It's still possible to try pick&test the X and Y for equation above, but it will consume too much time if the equation is more complicated such as "16x+24y = 2200".

 

Thank you very much

[arjmen]

5x + 3y = 76 , given that X and Y are positive interger

We can determine X and Y value with only one equation above.

We can't establish unique values for x and y from just that equation!

 

For the following multiples of 3, "x" and "y" will be positive integers:

3y = {6, 21, 36, 51, 66}

 

(x,y)= {(14,2), (11,7), (5,17), (2,22)}

[Dimas]

Geometrically 5x + 3y = 76 is an equation of line. Saying x>0 and y>0 makes this line in the positive quarter. But it is still a line. and there are infinite number of points located on this line.

[pirate]

While we are at it, I also came across this "strange" question in OG:

Given that r

(a) s-r = 5

(b) r and s are not integers.

 

The solution says C, as if r and s are decimals there will be 5 such numbers. Else, if r and s are integers, there will be 4 integers.

 

Now, my confusion is that the stub never said that r and s are constants. If they are variables, infinite solutions are possible!

[chix475ntu]

Its C.

 

about 1 equation with 2 variables, there is one problem in OG which tests this, its about buying something with 2 different amounts, initially i thought that we need 2 equations but on a second thought tried out the numbers and that equation doesnt need another equatino to solve. this might be rare but you got to look out and esp as this problem in in OG, there are chances that thay type might come, so try to apply some logic and calculation before deciding.

 

pirate.. r and s are positive, so they will be decimals or intergers(no imaginary number here).

I didnt understand what you meant by r and s are constants. there will be infinite solutions if they asked to give the numbers between r and s, but the question asks how many intergers are there, its just saying that there will be 5 or 4 or some other number of intergers. No need to tell what those intergers are.

[acutetrader]

WOW! Thank you very much all