Discount on belt and tie

[Redhorsep]

Hi,

Please help me with this problem, I believe it's from Princeton Review, but can't find or remember the answer at the moment, sorry:

A shopper bought a tie and a belt during a sale. Originally, the tie cost more than the belt, which item did he buy at the greater dollar discount?

1. He bought the tie at a 20% discount
2. He bought the belt at a 25% discount

Thanks!

[goalevan]

Dollar discount = discount percentage * sales price
For the tie, D = R * P
For the belt, d = r * p

We are given that price P > p.

D > d? (or d > D?)

Statement 1) R = 20%, but nothing is said about r:

It could be that D = 20% * 10, and d = 100,000,000% * 9, d > D
but could also be that D = 20% * 10, and d = 1% * 1 D > d

Insufficient.

Statement 2) r = 25%, but nothing is said about R:

It could be that D = 1% * 10, and d = 25% * 9, d > D
but could also be that D = 100,000% * 10, and d = 25% * 1 D > d

Insufficient.

Combined) Even knowing that D = 20% * P, d = 25% * p, and P > p does not tell us whether D > d.

D > d ?
20% * P > 25% * p ?
P > (5/4)p ?

In order for the discount for the tie to exceed that for the belt, the price of the tie must be greater than 120% of the price of the belt. We only know that the price of the tie exceeds that of the belt, but not to what extent.

Insufficient.

E

[Redhorsep]

Thanks, very clear and helpful!