Say AP = asking price
OC = original cost
You have that AP = 40%*OC + 100%*OC = 140%OC

1 tells us that AP - 10%*AP = OC + 403. This means that 0.9 (or 90%) of AP = OC + 403. Use this equation and the one above to make a system of two equations with two unknown factors, which could be easily solved:
AP = 1.4OC
0.9AP = OC + 403
So 1 is sufficient.

2 is not sufficient since we do not know if the dealer sold the bracelet for the asking price or if he had to reduce it.

So I'd go with B

1) Lets say x is the original price. So 0.4x should be the initial profit expected.

Asking price would be x+0.4x.
Now the dealer decides to give 10% discount on the asking price, so the new asking price would be 0.9(x+0.4x).

Now, (the new discounted asking price) - (the original price) is the profit the dealer gained by selling this bracelet. The profit he gained is $403. So..

(0.9(x+0.4x)) - x = 403

You can solve this equation and find out the value of x, which is the original price. So (1) is sufficient.

2) is insufficient since we do not know whether any discount was given on the asking price.

So I'd go with A.

@Dana: Shouldn't the answer be A since you followed the same logic like i did?

agree with jadeja.

Sorry guys... Of course it's A, I just missed the correct letter...

thankyou Danaj and jadeja.....very clear explanation