Problem Solving

Joanna bought only 0.15$ stamps and 0.29$ stamps. how many 0.15$ and 0.29$ stamps did she buy?

1) she bought 4.4$ worth of stamps
2) she bought an equal number of 0.15$ stamps and 0.29$ stamps

Let's assume Joanna bought X number of $0.15 stamps and Y number of $0.29 stamps.

Statement 1 : she bought 4.4$ worth of stamps

This implies:
(0.15)X + (0.29)Y = 4.4
15X + 29Y = 440 (multiply both sides by 100)
15X = 440 - 29Y
X = (440 - 29Y) / 15

This tells that the subtraction (440 - 29Y) will be a multiple of 15, because we can't have fractional amount of stamps.
Now list out various multiples of 15
0,15,30,45,60,75,90....
Notice that every time the number ends in either a 5 or a 0. This should mean that 440 - 29Y must also end in either a 5 or a 0

The unit digit of 440 is 0 , so the only way to subtract something from it (to get a number which ends with a 5 or 0) is to subtract a number whose unit digit ends in a 5 or 0

Now its fairly simple. 29 * 5 = 145 or 29 * 10 = 290 (9 multiplied by a 5 or a multiple of 5 or a 0 will satisfy this ,notice that only those two will give us the desired result)

440 - 145 = 295 --> Not divisible by 15
440 - 290 = 150 --> Divisible by 15

So, X = 10 and from our previous equation Y = 10

SUFFICIENT

Statement 2 : she bought an equal number of 0.15$ stamps and 0.29$ stamps

Joanna could have bought any number of both $0.15 and $0.29 stamps

NOT SUFFICIENT

Correct Answer : A

For an alternate approach, check my second post here:
https://www.beatthegmat.com/to-find-the- ... 73004.html

Here's a quick way that doesn't require much casework.

If we have 15x + 29y = 440, and we know that x and y are integers, we can do a little manipulation to start.

15x + 15y + 14y = 440

15x + 15y + 15y - y = 440

15*(x + 2y) - y = 440

Now let's look at multiples of 15 in the vicinity of 440. We have 15 * 30 and 15 * 31, or 450 and 465.

But if 465 is our answer, then y = 25. If y = 25, then Joanna bought 25 29¢ stamps ... but that's $7.25!

So the only possible solution is 450. This gives us

15*(x + 2y) = 450

and 15*(x + 2y) - y = 440

so y = 10. From there, x = 10, and we're done; S1 is sufficient.