singhpreet1 wrote:oops sorry i got it now, i missed out that the price was provided for each of the bottles and the sizes as well. so St.2 is sufficient independently to answer the question. .52x+. 58y= 4.92 i hope i got right this time around!

thanks.

Patrick_GMATFix wrote:Hello osirus,

Indeed (2) is sufficient. It allows you to write the equation 52x + 58y = 492 --> 26x+29y=246 where x and y are the number of lemonade drinks sold at 52 cents and 58 cents respectively.

In general when you have two variables, you don't have enough info to solve. The key here is that x and y must be integers; this severely limits the range of possible values (actually it limits the range to a unique solution).

Under certain circumstances, you will have sufficiency even though there are two variables. I've discussed these circumstances in two posts in another thread:

• Post 1

• Post 2

In short, because 246 in the equation above is smaller than the LCM(26,29) + 26, and because x and y are integers, you can be certain that there is a unique set of values that can work.

Hope that helps,
-Patrick

Patrick_GMATFix wrote:My apologies. I was being careless. Thank you for pointing it out. In fact, I meant LCM(26,29)+26. If this value is greater than the sum, then we'll have a unique solution. Otherwise, it depends.

-Patrick

osirus0830 wrote:Julie opened a lemonade stand and sold lemonade in two different sizes, a 52-cent (12oz) size and a 58-cent (16 oz) size. How many 52-cent lemonade drinks did Julie sell?

(1) Julie sold a total of 9 lemonades.

(2) The total value of the lemonade drinks Julie sold was $4.92

OA [spoiler]B I got this answer correct. My question is how can you determine that there is only one value integer value for the 52 cent drinks that would also allow the value for the 58 cent drinks to be an integer, without testing each individual integer cases? The book says that you don't have to calculate each case, you know that there is only one value for the 52 cent drinks that would allow the 58 cent drinks to also be an integer, my question is how do you know this?[/spoiler]

Haaress wrote: If 246 was more than the LCM(x, y) + min(x,y), would that mean that there are more than one set solution for the equation?