Bunuel wrote:

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

Let \(x\) be the # of $0.15 stamps and \(y\) the # of $0.29 stamps. Note that \(x\) and \(y\) must be an integers. Q: \(x=?\)

(1) She bought $4.40 worth of stamps --> \(15x+29y=440\). Only one integer combination of \(x\) and \(y\) is possible to satisfy \(15x+29y=440\): \(x=10\) and \(y=10\). Sufficient.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps --> \(x=y\). Not sufficient.

Answer: A.

So when we have equation of a type \(ax+by=c\) and we know that x and y are integers, there can be multiple solutions possible for x and y (eg \(5x+6y=12900\)) OR just one combination (eg \(15x+29y=440\)). Hence in some cases \(ax+by=c\) is NOT sufficient and in some cases it's sufficient.

Hope it helps.

How can one identify one or multiple solution for \(ax+by=c\)? (i.e. how did you arrive at the conclusion that only one integer combo satisfy \(15x+29y=440\)?

Trial and error plus some logic and knowledge of basics of number properties should help you to identify this.