Data Sufficiency

Question 123 of OG 12 Ed.

Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?
(1) She bought $4.40 worth of stamps
(2) She bought an equal number of $0.15 stamps and $0.29 stamps

OA : A

I read the explanation but didn't particularly like it because the thought process is long and it's very unlikely that I can go through the thought process in 2 minutes.

Anyone has a much shorter solution?

Also, it seems like this question shows that for 2 variables, you don't need two equations to solve?

Hi,

Check this post. You could find a detailed explanation here.

https://www.beatthegmat.com/word-transla ... 15309.html

15x + 29y = 440

Y should be modified by 0,5,10 because no other value can result in 440 while keeping x an integer.

440/15 = not an integer
440-145/15 = not an integer

So Y=10 and X=10

I is sufficient. A

Also, it seems like this question shows that for 2 variables, you don't need two equations to solve?

You have to be careful about applying this tactic to word problems in data sufficiency. The reason is the nature of many word problems necessitates positive integers. (When we are dealing with objects or people, usually we can't cut up the objects or people into pieces!)

This extra restriction (ie, only positive integers) in these kinds of problems often means that only one pair of positive integers will satisfy an equation even if there are two unknowns in the equation.