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
Sweater price
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We can PLUG IN THE ANSWERS, which represent the markup when the sweater is sold at its regular price.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
When the correct answer choice is plugged in, the discounted price of the sweater will net a 20% profit.
Let the wholesale cost = 100.
Answer choice D: 80%
Regular price = 100 + (0.8)(100) = 180.
Discounted price = 180 - (0.4)(180) = 108.
Discounted price - wholesale cost =108-100 = 8.
The profit is too small.
For the profit to increase, the required markup must be greater than 80%.
The correct answer is E.
Answer choice E: 100%
Regular price = 100 + 1(100) = 200.
Discounted price = 200 - .4(200) = 120.
Discounted price - wholesale cost = 120-100 = 20.
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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
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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
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
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Here's the proper algebra. Suppose that the merchant's purchase cost is x. We know the sale price is 20% greater than x, or 1.2x. We also know that 1.2x is 40% LESS than the full price.
Now we have to be careful, since we can't ADD 40% to 1.2x: percents DON'T do the same thing going up that they do going down. (For instance, $100 + 40% = $140, but $140 - 40% = $84.)
Let's call the full price y. We know that y - 40% = 1.2x, or .6y = 1.2x. This gives us y = 2x.
Hence the FULL price is 2x, the sale price is 1.2x, and the cost is x. Since 2x is 100% greater than x, the answer is E.
Now we have to be careful, since we can't ADD 40% to 1.2x: percents DON'T do the same thing going up that they do going down. (For instance, $100 + 40% = $140, but $140 - 40% = $84.)
Let's call the full price y. We know that y - 40% = 1.2x, or .6y = 1.2x. This gives us y = 2x.
Hence the FULL price is 2x, the sale price is 1.2x, and the cost is x. Since 2x is 100% greater than x, the answer is E.
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Wholesale Cost = W
F = Full selling price
1.2W = 0.6F
F/W = 1.2/0.6 = 2 = = 200%
200% = 100%W + 100%Mark up
Answer (E) 100%
F = Full selling price
1.2W = 0.6F
F/W = 1.2/0.6 = 2 = = 200%
200% = 100%W + 100%Mark up
Answer (E) 100%
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A few points for some student who gets stuck at these questionsRastis 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
1) Discount is offered at Marked Price/List price
2) The Price after the discount is called Selling Price
3) Profit/loss is calculated on Cost Price
4) Cost Price + Profit/Loss = Selling Price
5) List Price - Discount = Selling Price
MP - (40/100) x MP = (120/100) x CP
i.e. 0.6 MP = 1.2 CP
i.e. MP = 2 x CP
i.e. Markup by 100%
Answer: Option E
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Hi Brent ,In other words, 60% of M = $120
Or we can write 0.6M = 120
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.
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We're told that 40% less than M = $120rsarashi wrote:Hi Brent ,In other words, 60% of M = $120
Or we can write 0.6M = 120
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.
In other words: M - (40% of M) = $120
Or we can write: M - (0.4M) = $120
Simplify: 0.6M = $120
In this calculation, you are finding 40% of the ALREADY-DISCOUNTED price of $120Why not Discount = 120* 40/100? If we can do this, then what will be the next step we have to do?
We are need to find 40% of the marked-up price.
Cheers,
Brent