Percentag Problems

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GMAT-Zenith: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Thu May 27, 2010 2:04 am; Thanked: 1 times

by GMAT-Zenith » Fri Jul 27, 2012 11:30 pm

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?
$40 $60 $80 $90 $100

Bobby bought two shares of stock, which sold for $96 each. If he had a profit of 20 percent on the sale of
one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares
combined Bobby had:
a profit of $10 a profit of $8 a loss of 8
a loss of 10 neither profit nor loss

In May Mr. Lee's earings were 60 percent of the Lee family's total income. In June Mr. Lee earned 20 percent
more than in May. If the rest of the family's income was the same both months, then, in June, Mrs.Lee's
earnings were approximately what percent of the Lee Family's total income?

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Source: Beat The GMAT — Problem Solving | Fri Jul 27, 2012 11:30 pm

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Jul 28, 2012 2:36 am

GMAT-Zenith wrote: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?
$40 $60 $80 $90 $100

Purchase price = 1x = 150
Selling price = 1.4x

Profit = 1.4x - 1x = x(1.4-1) = x(0.4)= 150*0.4 = 60

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Jul 28, 2012 2:50 am

GMAT-Zenith wrote: Bobby bought two shares of stock, which sold for $96 each. If he had a profit of 20 percent on the sale of
one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares
combined Bobby had:
a profit of $10 a profit of $8 a loss of 8
a loss of 10 neither profit nor loss

Purchase Price = A + B
Selling Price = 96 + 96

Profit of 20% means
(96 - A) / A = 20%
96 - A = 0.2 A
96 = 1.2 A -------- A = 80

Loss of 20% means
(96 - B) / B = -20%
96 - B = -0.2B
96 = 0.8 B ------- B = 120

Purchase price = 80 + 120 = 200
Selling price = 96 + 96 = 192
Profit = 192 - 200 = -8
Loss of $8 between transactions

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Jul 28, 2012 3:02 am

GMAT-Zenith wrote: In May Mr. Lee's earings were 60 percent of the Lee family's total income. In June Mr. Lee earned 20 percent
more than in May. If the rest of the family's income was the same both months, then, in June, Mrs.Lee's
earnings were approximately what percent of the Lee Family's total income?

In May:
Lee's income = 0.6T ---- T is the family total income
Rest of the family's income = T - 0.6T = 0.4T

In June:
Lee's income = 1.2 * 0.6T = 0.72T
Rest of the family's income = 0.4T
Total family income = 0.72T + 0.4T = 1.12T

Lee's income = (0.72T / 1.12T) * 100 = 64%

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niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Sat Jul 28, 2012 3:06 am

GMAT-Zenith wrote: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?
$40 $60 $80 $90 $100

Cost Price = $150
Selling Price = S
S = $150 + .4S
=> .6S = $150 => S = $250

Gross profit = S - $150 = $250 - $150 = $100

The correct answer is E

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Jul 28, 2012 3:17 am

niketdoshi123 wrote:
GMAT-Zenith wrote: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?
$40 $60 $80 $90 $100
Cost Price = $150
Selling Price = S
S = $150 + .4S
=> .6S = $150 => S = $250

Gross profit = S - $150 = $250 - $150 = $100

The correct answer is E

I must be thinking like a computer programmer

".....and then set the selling price equal to the purchase price"
means Selling Price = purchase price

"....plus a markup that was 40 percent of the selling price"
means new selling price = selling price + 0.4 * selling price = selling price (1+0.4)

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jul 28, 2012 3:21 am

A furniture dealer purchased a desk@$150 and set the selling price equal to purchase price plus a markup that was 40% of the selling price.If the dealer sold the desk at selling price what was the ampunt of dealer's gross profit from the purchase and sale of the desk?
a.40 b.60 c.80 d.90 e.100

We can plug in the answers, which represent the profit.
When the current answer choice is plugged in, the profit must be equal to the markup.
To be efficient, we should start with C, the middle answer choice.
If C is incorrect, we'll know whether the correct answer must be smaller or greater.

Answer choice C: profit = 80.
Selling price = profit + purchase price = 80+150 = 230.
Markup = 40% of the selling price = .4(230) = 92.
The profit is too small.
Eliminate A, B and C.

Answer choice D: profit = 90.
Selling price = profit + purchase price = 90+150 = 240.
Markup = 40% of the selling price = .4(240) = 96.
The profit is too small.
Eliminate D.

The correct answer is E.

Note that we had to try only 2 answer choices, an efficient way to determine the correct answer.

Answer choice E: profit = 100.
Selling price = profit + purchase price = 100+150 = 250.
Markup = 40% of the selling price = .4(250) = 100.
Profit = markup = 100. Success!

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by GMATGuruNY » Sat Jul 28, 2012 3:27 am

Bobby bought two shares of stock, which sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined bobby had:

a: a profit of $ 10
b: a profit of $ 8
c: a loss of $8
d: a loss of $ 10
e: neither profit nor loss

Many students struggle with this type of question.
An efficient way to solve that involves very little algebra is to GUESS AND CHECK.

Since all of the values in the problem and in the answer choices are integers, the purchase prices are almost certainly each a multiple of a 10.

Stock sold at a 20% profit:
Since this stock is sold at a PROFIT, the purchase price = a multiple of 10 LESS than 96.
90 + .2(90) = 108. Too big.
80 + .2(80) = 96.
Success!
The purchase price = 80.
Profit = 96-80 = 16.

Stock sold at a 20% loss:
Since this stock is sold at a LOSS, the purchase price = a multiple of 10 GREATER than 96.
100 - .2(100) = 80. Too small.
110 - .2(110) = 88. Too small.
120 - .2(120) = 96.
Success!
The purchase price = 120.
Loss = 96-120 = -24.

Profit + loss = 16 + (-24) = -8.
A loss of $8.

The correct answer is C.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jul 28, 2012 3:32 am

In May, Mrs. Lee's earnings were 60% of the Lee family's total income. In June, Mrs. Lee earned 20% more than in May. If the rest of the family's income was the same both months, then, in June, Mrs. Lee's earnings were approximately what percent of the Lee family's total income ?

a. 64
b. 68
c .72
d. 76
e. 80

OA A

Let the family income in May = 100.
Mrs. Lee in May = .6*100 = 60.
Rest of the family = 100-60 = 40.
Mrs. Lee in June = 1.2(60) = 72.
Rest of the family is unchanged = 40.
Total family income in June = 72+40 = 112.
Percentage for Mrs. Lee in June = 72/112 * 100 â‰ˆ 64%.

The correct answer is A.

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