GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2018, 05:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 196
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

10 Feb 2011, 23:16
8
00:00

Difficulty:

35% (medium)

Question Stats:

79% (03:12) correct 21% (03:35) wrong based on 249 sessions

### HideShow timer Statistics

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

cost=600

2/3(1500)=1000

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

_________________

The proof of understanding is the ability to explain it.

Retired Moderator
Joined: 20 Dec 2010
Posts: 1835
Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

11 Feb 2011, 02:36
3
Quote:
cost=600

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

2/3(1500)=1000

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

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"
_________________
Manager
Joined: 10 Nov 2010
Posts: 196
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

12 Feb 2011, 13:23
1
fluke wrote:
Quote:
cost=600

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

2/3(1500)=1000

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

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
_________________

The proof of understanding is the ability to explain it.

Retired Moderator
Joined: 16 Nov 2010
Posts: 1436
Location: United States (IN)
Concentration: Strategy, Technology
Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

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 _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Manager Joined: 18 Nov 2013 Posts: 79 Concentration: General Management, Technology GMAT 1: 690 Q49 V34 Re: A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] ### Show Tags 29 Apr 2015, 12:11 This sol might help, its faster if we solve this way , might save you some time 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 _________________ _______ - Cheers +1 kudos if you like Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2830 Re: A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] ### Show Tags 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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior SC Moderator
Joined: 22 May 2016
Posts: 2040
Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

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

cost=600

2/3(1500)=1000

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

_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

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.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3194
Location: India
GPA: 3.12
Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

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

cost=600

2/3(1500)=1000

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

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

_________________

You've got what it takes, but it will take everything you've got

Senior SC Moderator
Joined: 22 May 2016
Posts: 2040
Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

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)

Thanks for catching my typo! Edited.
_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

Director
Joined: 09 Mar 2016
Posts: 946
Re: A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

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

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 why
Senior SC Moderator
Joined: 22 May 2016
Posts: 2040
A shipment of 1500 heads of cabbage, each of which was approximately  [#permalink]

### Show Tags

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

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 why

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 . . ." _________________ ___________________________________________________________________ For what are we born if not to aid one another? -- Ernest Hemingway Intern Joined: 28 Apr 2015 Posts: 6 Re: A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] ### Show Tags 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
_________________

Dan Morgan
MBA Wisdom
http://www.mbawisdom.com

Re: A shipment of 1500 heads of cabbage, each of which was approximately &nbs [#permalink] 08 Apr 2018, 11:02
Display posts from previous: Sort by