Problem Solving

Rastis wrote:When sold at a 40% discount, a sweater nets the merchant a 20% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?

a) 20%

b) 40%

c) 50%

d) 80%

e) 100

Let's work BACKWARDS.

Let's say the WHOLESALE price was $100

the merchant made a net profit of 20% on the wholesale cost (which was $100)
So, the merchant sold the sweater for $120

[the sweater] sold at a 40% discount
Let M = the markup price on the label (before any discounts).
So, 40% less than M = $120
In other words, 60% of M = $120
Or we can write 0.6M = 120
So, M = 200
In other words, the markup price (before any discounts) was $200

If the wholesale price was $100, and the markup price was $200, then the sweater was originally marked up by [spoiler]100%[/spoiler]

Answer: E

Cheers,
Brent

Hi Jesse,

I'm a bit fan of using a combination of TEST IT and TEST THE ANSWERS (as Mitch and Brent have both shown) and that's exactly how I would have solved this problem. It can also be approached with algebra though:

X = wholesale cost of the sweater.

[1 + (N/100)]X = retail price --> N/100 is the percent markup in price

We're told that the sweater is sold at a 40% discount of the retail price, which means that the discount price is 60% of the original retail price. The discounted price of the sweater is:

.6{1 + (N/100)]X

We're told that this price nets the merchant a 20% profit on the wholesale cost, so we have one big equation....

.6[1 + (N/100)]X = 1.2X

Now we can cancel out the Xs:

.6[1 + (N/100)] = 1.2

And do algebra....

[1 + (N/100)] = 2

N/100 = 1

N = 100

Meaning that the original percent markup was 100%

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

rsarashi wrote:

In other words, 60% of M = $120
Or we can write 0.6M = 120

Hi Brent ,

Can you please explain why did you do 60% of M?

Why not Discount = 120* 40/100? If we can do this, then what will be the next step we have to do?

Please explain.

Thanks.

We're told that 40% less than M = $120
In other words: M - (40% of M) = $120
Or we can write: M - (0.4M) = $120
Simplify: 0.6M = $120

Why not Discount = 120* 40/100? If we can do this, then what will be the next step we have to do?

In this calculation, you are finding 40% of the ALREADY-DISCOUNTED price of $120
We are need to find 40% of the marked-up price.

Cheers,
Brent