Ps discount rate

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Mon Jun 02, 2008 3:49 pm

Ps discount rate

by andreasonlinegr » Thu Jan 01, 2009 6:16 pm
Fox jeans regularly sell for 15$ a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of 9$ is saved by purchasing 5 pairs of jeans: 3 pairs of fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?

Answer: 10%
Source: — Problem Solving |

Senior | Next Rank: 100 Posts
Posts: 37
Joined: Wed Sep 17, 2008 8:17 pm
Location: India
Thanked: 4 times

by Sachindh » Thu Jan 01, 2009 9:55 pm
cost of 3 fox jeans = 45
cost of 2 pony jeans = 36

let x be discount on fox jeans and y be on pony jeans
therefore
45*x/100 + 36*y/100 = 9
15x + 12y=300 ----- eq i

also x+y = 22 ----- eq ii
solving both equation, we get x=12, y=10.

User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Thu Jan 01, 2009 11:23 pm
Sachindh wrote:cost of 3 fox jeans = 45
cost of 2 pony jeans = 36

let x be discount on fox jeans and y be on pony jeans
therefore
45*x/100 + 36*y/100 = 9
15x + 12y=300 ----- eq i

also x+y = 22 ----- eq ii
solving both equation, we get x=12, y=10.
Good job on the algebra.

If we could actually see all the choices, it would also be incredibly quick to solve this via backsolving, i.e. working backwards from the answers.

Using the correct answer as an example:

if Pony is 10%, then fox is 12%.

2 pairs of pony @ $18 each = $36. 10% savings = $3.60
3 pairs of fox @ $15 each = $45. 12% savings = $4.50 + $0.90 = $5.40

Total savings = $9, which matches the question stem. Correct answer!

If we had gotten savings of less than $9, we would have looked for a smaller answer, since the pony jeans make up the smaller part of the purchase, so increasing the discount on fox would increase the overall discount. If we had gotten savings greater than $9, we'd have looked for a bigger answer. By starting with either (B) or (D), we'd guarantee only having to check 2 choices and have a 40% chance of getting it right on the first shot.

Moral of the story: if the algebra jumps out at you, it's probably fastest to do the algebra; if the algebra doesn't jump out at you, look for an alternative method like backsolving, picking numbers or strategic guessing.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course