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A shipment of 1500 heads of cabbage, each of which was approximately

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A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 10 Feb 2011, 23:16
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A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

(A) $100
(B) $115
(C) $125
(D) $130
(E) $135

Total number of heads=1500
cost=600

Cost per head=1500/600=2.5
2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help

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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 11 Feb 2011, 02:36
3
Quote:
Total number of heads=1500
cost=600

Cost per head=1500/600=2.5; not correct

\(1500\quad head = \$600\)
\(1 head = \frac{600}{1500}\)


2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help


I recommend one should use fractions to solve this one rather than converting it into decimals

Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)

25% more of (2/5) -> 125/100 * 2/5 = $(1/2)

He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500

Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225

Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600

Profit = 725-600 = $125

Ans: "C"
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 12 Feb 2011, 13:23
1
fluke wrote:
Quote:
Total number of heads=1500
cost=600

Cost per head=1500/600=2.5; not correct

\(1500\quad head = \$600\)
\(1 head = \frac{600}{1500}\)


2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help


I recommend one should use fractions to solve this one rather than converting it into decimals

Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)

25% more of (2/5) -> 125/100 * 2/5 = $(1/2)

He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500

Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225

Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600

Profit = 725-600 = $125

Ans: "C"

Thanks
I was wrong while calculating cost per head
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 13 Feb 2011, 04:29
1.25 * 2/3 * 1500 * 600/1500 - Day 1 Total SP

0.9 * 1.25 * 1/3 * 1500 * 600/1500 - Day 2 total SP


=> Total SP = 600/1500 * 1500 * 1.25 (2/3 + 0.9 * 1/3)

= 600 * 5/4 * (2 + 0.9)/3

= 3000 * 2.9/12 = 725

=> Profit = 725 - 600 = $ 125
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 29 Apr 2015, 12:11
:arrow: :arrow: This sol might help, its faster if we solve this way , might save you some time :-D

Prob:
Total number of heads=1500
Cost Price =$600
Sale Price = 2/3 sold at 25% profit & 1/3 sold at price (10% less than the price each head sold for the day before)

Sol: will calculate these in bulks only (will try not to go down to single level)

    2/3 of 1500 ~ 1000 --> sold on day 1
    1/3 of 1500 ~ 500 --> sold on day 2

Day 1: Sale price of 2/3 sold at 25% profit = 1000 * 600/1500 * 125/100 = $500

~~now 1000 heads sold at $500, with the same price could have sold remaining 500 heads for = $500/2 = $250*

Day 2:Sale price of 1/3 (=500 heads) sold at 10% less than previous day price, that's 10% less of $250 = $225 (90% of $250)

Total sale price (Day1 + Day2) = $500 + $225 = $725

Profit = SP - CP = $725 - $600 = $125

Ans C
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 25 May 2017, 15:57
Quote:
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

a) $100
b) $115
c) $125
d) $130
e) $135



We are given that a shipment of 1500 heads of cabbage costs 600 dollars, or 600/1500 = $0.40 per cabbage.

We are given that 2/3 x 1500 = 1,000 heads of cabbage sold for 1.25 x $0.40 = $0.50. So, a total of 1,000 x $0.50 = $500 was made on the sale of those heads of cabbage.

The next day, 500 heads of cabbage were sold at a price of 0.9 x $0.50 = $0.45, so a total of 500 x $0.45 = $225 dollars was made on the sale of those heads.

Thus, a total of 500 + 225 = $725 was made.

Thus, profit = 725 - 600 = $125.

Answer: C
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post Updated on: 10 Jun 2017, 00:15
GMATD11 wrote:
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

a) $100
b) $115
c) $125
d) $130
e) $135

Total number of heads=1500
cost=600

Cost per head=1500/600=2.5
2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help

Profit per unit works well with these numbers.

(Profit per item) * (# items) = gross profit

Cost per cabbage is $600 for 1500 heads = 40¢ per head

Sell Price A is 25% above cost: 40¢ * 1.25 = 50¢. Profit per head for price A = 10¢ = .10

Sell Price B is 10% less than Sell Price A: 50¢ *.90 = 45¢. Profit per head for price B = 5¢ = .05

Number of items at price A = 2/3 of 1,500 = 1,000

Number of items at price B = 1/3 of 1,500 = 500

1,000 * .10 = $100
500 * .05 = $25

Gross profit = 100 + 25 = $125

Answer C
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Originally posted by generis on 09 Jun 2017, 21:15.
Last edited by generis on 10 Jun 2017, 00:15, edited 1 time in total.
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 09 Jun 2017, 23:33
1
genxer123 wrote:
GMATD11 wrote:
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

a) $100
b) $115
c) $125
d) $130
e) $135

Total number of heads=1500
cost=600

Cost per head=1500/600=2.5
2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help

Profit per unit works well with these numbers.

(Profit per item) * (# items) = gross profit

Cost per cabbage is $600 for 1500 heads = 40¢ per head

Sell Price A is 10% above cost: 40¢ * 1.1 = 50¢. Profit per head for price A = 10¢ = .10

Sell Price B is 10% less than Sell Price A: 50¢ *.90 = 45¢. Profit per head for price B = 5¢ = .05

Number of items at price A = 2/3 of 1,500 = 1,000

Number of items at price B = 1/3 of 1,500 = 500

1,000 * .10 = $100
500 * .05 = $25

Gross profit = 100 + 25 = $125

Answer C


The rest of your calculations are correct.
But its 40 * 1.25 = 50(because its 25% more than the cost)

Please make the necessary change!
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 10 Jun 2017, 00:19
pushpitkc wrote:

The rest of your calculations are correct.
But its 40 * 1.25 = 50(because its 25% more than the cost)

Please make the necessary change!

Thanks for catching my typo! Edited.
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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 08 Apr 2018, 05:24
GMATD11 wrote:
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

(A) $100
(B) $115
(C) $125
(D) $130
(E) $135



hello highly intellectally smart people :) please help a passionate problem solver :)

here is my solution which is wrong, but i dont understand why its wrong:) why why why :)

total number of gabbage 1500

original cost per gabbage \(600/1500\) = 0.30 cents

2/3 of gabbage sold at 0.25 % more than it was bought --> 0.30*1.25 = 37.5 (profit of 2/3 of gabbage sold 7,5 * 1000 = 7500 -->7500/100 = 75

rest of gabbage is sold at 10 % less than day before ---> 37.5 * 0.1 = 3.75 ---> 37,5-3,75 = 33.75 so profit 3.75*500 =1875 --> 1875/100 = 18.75

total profit 75+18,75 = 93.75 :shocked :? why :roll: :-)
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A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 08 Apr 2018, 10:51
1
dave13 wrote:
GMATD11 wrote:
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

(A) $100
(B) $115
(C) $125
(D) $130
(E) $135


hello highly intellectally smart people :) please help a passionate problem solver :)

here is my solution which is wrong, but i dont understand why its wrong:) why why why :)

total number of gabbage 1500

original cost per gabbage \(600/1500\) = 0.30 cents

2/3 of gabbage sold at 0.25 % more than it was bought --> 0.30*1.25 = 37.5 (profit of 2/3 of gabbage sold 7,5 * 1000 = 7500 -->7500/100 = 75

rest of gabbage is sold at 10 % less than day before ---> 37.5 * 0.1 = 3.75 ---> 37,5-3,75 = 33.75 so profit 3.75*500 =1875 --> 1875/100 = 18.75

total profit 75+18,75 = 93.75 :shocked :? why :roll: :-)

Hi dave13 , you are indeed a passionate problem solver, which is admirable.

It looks to me as if you mostly understand how to solve the problem. You have a couple of arithmetic mistakes.

Quote:
original cost per gabbage \(600/1500\) = 0.30 cents

Try that arithmetic again. :)

Quote:
rest of gabbage is sold at 10 % less than day before ---> 37.5 * 0.1 = 3.75

Whoops. 10 % LESS than means
90 percent OF
(1 - .10) = .90
Not one-tenth

X percent less = (1 - Xpercent)
See below for links on GMAT and percents

If you get stuck trying to decide what "10% less than" means, take a simple example.

A cake cost $100
Next day it is on sale for10% LESS than before
Did the cake cost $10? No.

(1.00 - .10) = .90
The cake sold for .90 * $100 = $90

Finally, I don't understand this part
Quote:
37.5 (profit of 2/3 of gabbage sold 7,5 * 1000 = 7500 -->7500/100 = 75

37.5 CENTS (wrong number, but that's not the point) = .375 DOLLARS
Total revenue on 1,000 = (.375 * 1,000) = $375
??? I think? Am I missing something?

Try again? You'll get it.

See mikemcgarry Percents on the GMAT
And more on GMAT percents HERE:
"For example, the multiplier for a 40% increase would be: 1 + 0.40 = 1.4, and the multiplier for a 40% decrease would be 1 – 0.40 = 0.6 . . ."

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Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

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New post 08 Apr 2018, 11:02
GMATD11 wrote:
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

(A) $100
(B) $115
(C) $125
(D) $130
(E) $135

Total number of heads=1500
cost=600

Cost per head=1500/600=2.5
2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help


Cost per cabbage = $600/1500 = $0.40
1000 cabbages sold for 25% above cost on day 1: profit on day 1 = 1000*0.25*0.40 = 100
500 cabbages sold for 10% less than day before on day 2: profit on day 2 = 500*(0.50*0.90 - 0.40) = 500*(0.05) = 25
Profit = 100 + 25 = 125
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Re: A shipment of 1500 heads of cabbage, each of which was approximately &nbs [#permalink] 08 Apr 2018, 11:02
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