A shopkeeper bought an article for Rs.1000 and marked its price as Rs.

maximum value: when successive discounts are equal, (a,b,c)=50/3%
minimum value: largest possible successive discount, (a,b,c)=50,0,0%

original net%=sale/cost-1=2160/1000-1=2.16-1=1.16=116%
min. net%=2160(1-50/100)/1000-1=1.08-1=0.08=8%
max. net%=2160(1-50/3/100)^3/1000-1=216(5/6)^3/100-1…
max. net%=216(125/216)/100-1=1.25-1=0.25=25%
max-min net%=25-8=17%

Ans (B)

Bunuel Please explain.

VeritasKarishma Can u plz explain this? How to approach this problem?

Recall that the order in which we apply the discount doesn’t matter (for example, a discount of 10% followed by a discount of 20% is same as a discount of 20% followed by a discount of 10%). Also, let’s assume that any values of a, b, and c can be 0 and they can also be decimals or fractions.

The minimum discounted price of the article after 3 discounts occurs when a, b, and c are as far apart as possible. That is, if we let a = 50, b = 0, and c = 0, then the minimum discounted price is 2160 x 0.5 x 1 x 1 = 1080.

The maximum discounted price of the article after 3 discounts occurs when a, b, and c are as close to each other as possible. That is, if we let a = b = c = 50/3 = 16⅔ (notice that 16⅔% = 1/6), then the maximum discounted price is 2160 x 5/6 x 5/6 x 5/6 = 2160 x 125/216 = 1250.

In the first case (minimum discounted price), the profit is 80, so the profit margin is 8%. In other words, the minimum value of x is 8. In the latter case (maximum discounted price), the profit is 250, so the profit margin is 25%. In other words, the maximum value of x is 25.

So the difference between the maximum and minimum values of x is 25 - 8 = 17.

Answer: B

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.