Problem Solving

Need help with this one:

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40 percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?

a - 40
b- 60
c - 80
d - 90
e -100

The answer is e

p=purchase price=150
s=selling price

150+.40s=s (.40s is the markup)
150=1s-.4s
150=.6s
s=250

Gross profit = Selling price - purchase price
=250-150=100

Hey Luke,

Just a quick strategic point to tack on to hyl0428's post - if you're wondering about this question, I'd say that you most likely want to focus on this:

The most important word in most percentage questions is the word "of". "Of" tells you which value is the basis of your percentage - it's what you multiply the percentage by to determine the value.

In this case, they say that the markup is 40% "of" the selling price, so we know that the item is sold for:

Purchase price ($150) plus 40% of selling price, so:

S = 150 + 40/100 * S

S - 40/100 * S = 150

60/100 * S = 150

3/5 S = 150

S = 150 * 5/3

S = 250

The authors of the GMAT know that we're usually in a rush to "do math", so they can be pretty crafty in setting up the "of" in percentage problems to correspond to a variable (S) and not to the number (150) - they know that you'd much rather multiply 40% by 150 than by S, but if you pay strict attention to the position of the word "of", you'll know exactly where to multiply the percentage and can set up the algebra accordingly.

lukeposada wrote:Need help with this one:

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40 percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?

a - 40
b- 60
c - 80
d - 90
e -100

The answer is e

Another approach would be to plug in the answers, which represent the profit.

Let P=profit, S=selling price, M=mark up.
With each answer, we need to see whether S = 150 + M (because the selling price needs to equal purchase price + markup.)

Answer choice C:
P = 80
S= 80+150 = 230
M = .4(230) = 92.
Does 230 = 150 + 92? No.
We need more profit.

Answer choice D:
P = 90
S= 90+150 = 240
M = .4(240) = 96.
Does 240 = 150 + 96? No.
We need more profit.

The correct answer is E.

Answer choice E:
P = 100
S= 100+150 = 250
M = .4(250) = 100
Does 250 = 150 + 100? Success!