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.