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.

Statement 2 is clearly insufficient.

Statement 1: She bought $4.40 worth of stamps.
Let $F = the total revenue from the 15¢ stamps and $T = the total revenue from the 29¢ stamps.

Since the two statements cannot contradict each other, it must be possible in statement 1 that the 440¢ in total revenue is divided according to the ratio indicated in statement 2.
Statement 2 indicates that the ratio of 15¢ stamps to 29¢ stamps = 1:1.
If an equal number of each type of stamp is purchased, we get:
$F : $T = 15:29 = 150:290, for a total of 440¢ in revenue.
Here, the number of 15¢ stamps = 150/15 = 10, and the number of 29¢ stamps = 290/29 = 10.

Check whether OTHER revenue ratios are also possible.
Since the stamp values are 15¢ and 29¢, the revenue ratio can be altered only by adding a multiple of 15 and 29 to $F or $T, while subtracting this same multiple from the other value.
The LCM of 15 and 29 = 15*29 = 435.
If 435¢ is added to either 150¢ or 290¢, the sum will exceed 440¢.
Thus, the revenue ratio CANNOT be altered, implying that only ONE revenue ratio will satisfy statement 1:
$F = 150¢ and $T = 290¢.
Thus, the number of 15¢ stamps = 10.
SUFFICIENT.

The correct answer is A.