Last visit was: 17 Jul 2024, 05:44 It is currently 17 Jul 2024, 05:44
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 10 Apr 2012
Posts: 244
Own Kudos [?]: 4545 [26]
Given Kudos: 325
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE:Project Management (Telecommunications)
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94372
Own Kudos [?]: 641620 [15]
Given Kudos: 85662
Send PM
General Discussion
avatar
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7294 [1]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
avatar
Manager
Manager
Joined: 14 Sep 2014
Posts: 74
Own Kudos [?]: 97 [4]
Given Kudos: 51
WE:Engineering (Consulting)
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
4
Kudos
guerrero25 wrote:
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

A. 1:4
B. 1:5
C. 2:3
D. 1:2
E. 2:5


Lets say he bought mangoes worth '$z'
so total no. of mangoes = 5z

he made a stash of 3 mangoes to be sold at $x,
total no. of mangoes in this stash = 3x

and a second stash of 6 mangoes to be sold at $y
total no. of mangoes in this stash = 6y

so we get two equations
z = x+ y &
5z = 3x+ 6y

solving these two
we get x/y = 1/2 (WHICH IS PRICE)
for no. of mangoes i.e. 3x/6y = x/2y = 1/4
OA : A
User avatar
Manager
Manager
Joined: 20 Jan 2014
Posts: 108
Own Kudos [?]: 193 [0]
Given Kudos: 120
Location: India
Concentration: Technology, Marketing
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
PareshGmat wrote:
rate of 3 for a dollar means 3 mangoes in 1 dollar

Say x mangoes are sold for rate of 3 for a dollar means
price of 1 mango = 1/3 &
price of x mangoes = 1/3 . x .................. (1)

y mangoes are sold for rate of 6 for a dollar means
price of 1 mango = 1/6 &
price of y mangoes = 1/6 . y ......................... (2)

Total selling price = 1/3 x + 1/6 y ........................ (3)
Adding (1) & (2)

Total Mangoes procured = (x+y); rate of 5 for a dollar means 5 mangoes in 1 dollar
Total Cost Price = 1/5 . (x+y) ........................... (4)

Equating (3) & (4)

we get x:y = 1:4 = Answer = A


nice explanation. When equating (3) and(4)

1/3 x + 1/6 y = 1/5 . (x+y)
(2y+x)/6xy = 1/(5x+5y)
5(2y+x)(x+y)=6xy
10y^2 + 5x^2 + 9xy = 0

i got stuck here
User avatar
Retired Moderator
Joined: 16 Jun 2012
Posts: 869
Own Kudos [?]: 8615 [2]
Given Kudos: 123
Location: United States
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
2
Kudos
him1985 wrote:
PareshGmat wrote:
rate of 3 for a dollar means 3 mangoes in 1 dollar

Say x mangoes are sold for rate of 3 for a dollar means
price of 1 mango = 1/3 &
price of x mangoes = 1/3 . x .................. (1)

y mangoes are sold for rate of 6 for a dollar means
price of 1 mango = 1/6 &
price of y mangoes = 1/6 . y ......................... (2)

Total selling price = 1/3 x + 1/6 y ........................ (3)
Adding (1) & (2)

Total Mangoes procured = (x+y); rate of 5 for a dollar means 5 mangoes in 1 dollar
Total Cost Price = 1/5 . (x+y) ........................... (4)

Equating (3) & (4)

we get x:y = 1:4 = Answer = A


nice explanation. When equating (3) and(4)

1/3 x + 1/6 y = 1/5 . (x+y)
(2y+x)/6xy = 1/(5x+5y)
5(2y+x)(x+y)=6xy
10y^2 + 5x^2 + 9xy = 0

i got stuck here


Hello buddy.

I think you put wrong equation.

Assume we have total mangoes = T
Pack 1 has x mangoes
Pack 2 has y mangoes

=> T = x + y
Cost = T/5 = (x +y)/5 [you put 5/(x+y)]
Revenue pack 1 = x/3 [you put 3/x]
Revenue pack 2 = y/6 [you put 6/y]
=> (x+y)/5 = x/3 +y/6
=> 4x = y
=> Ratio 1:4

A is correct.
User avatar
Manager
Manager
Joined: 03 Jul 2013
Posts: 76
Own Kudos [?]: 728 [0]
Given Kudos: 14
GMAT 1: 660 Q48 V32
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Please explain whats the issue with my approach. Break even means no profit no loss.

3 mangoes bought at 5$ per mango = 15$ cost price.
1 mango sold at 3$ per mango = 3 $
2 Mangoes sold at 6$ per mango = 12 $

Ratio should be 1:2
Math Expert
Joined: 02 Sep 2009
Posts: 94372
Own Kudos [?]: 641620 [0]
Given Kudos: 85662
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Expert Reply
aadikamagic wrote:
Please explain whats the issue with my approach. Break even means no profit no loss.

3 mangoes bought at 5$ per mango = 15$ cost price.
1 mango sold at 3$ per mango = 3 $
2 Mangoes sold at 6$ per mango = 12 $

Ratio should be 1:2


Please re-read the question.

A grocery store bought some mangoes at a rate of 5 for a dollar --> 5 mangoes for a dollar --> the cost price of a mango = 1/5 dollars.

One stack was sold at a rate of 3 for a dollar (3 mangoes for 1 dollar) --> the selling price of a mango from the first stack = 1/3 dollars.

Another stack was sold at a rate of 6 for a dollar (6 mangoes for 1 dollar) --> he selling price of a mango from the second stack = 1/6 dollars
avatar
Manager
Manager
Joined: 14 Sep 2014
Posts: 74
Own Kudos [?]: 97 [0]
Given Kudos: 51
WE:Engineering (Consulting)
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
aadikamagic wrote:
Please explain whats the issue with my approach. Break even means no profit no loss.

3 mangoes bought at 5$ per mango = 15$ cost price.
1 mango sold at 3$ per mango = 3 $
2 Mangoes sold at 6$ per mango = 12 $

Ratio should be 1:2


Please re-read the Question
it says he bought 5 mangoes for $1
and sold at 3 mangoes for $1
sold at 6 mangoes for $1
Senior Manager
Senior Manager
Joined: 24 Jun 2016
Posts: 334
Own Kudos [?]: 135 [0]
Given Kudos: 21
GMAT 1: 770 Q60 V60
GPA: 4
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Each mango from the first stack sold generates (1/3-1/5) = 2/15 profit
Each mango from the second stack sold generates (1/5-1/6) = 1/30 loss

Since 2/15 / (1/30) = 4, to break even, we need to sell 1 mango from the first stack for each 4 sold from the second stack.

Answer choice A.
VP
VP
Joined: 07 Dec 2014
Posts: 1067
Own Kudos [?]: 1608 [0]
Given Kudos: 27
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
1/3*x+1/6*y=1/5(x+y)
x/y=1/4
Tutor
Joined: 16 Oct 2010
Posts: 15121
Own Kudos [?]: 66687 [0]
Given Kudos: 436
Location: Pune, India
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Expert Reply
guerrero25 wrote:
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

A. 1:4
B. 1:5
C. 2:3
D. 1:2
E. 2:5


To avoid fractions, assume there were 45 mangoes. So the store bought them for 45/5 = 9 dollars.

To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these.

45 split in the ratio 1:4 gives 9 and 36.

9 mangoes split into 3 mangoes each will give $3.
36 mangoes split into 6 mangoes each will give $6.
They add up to $9 so we have hit the right answer.

Answer (A)
Manager
Manager
Joined: 24 Jun 2017
Posts: 87
Own Kudos [?]: 165 [0]
Given Kudos: 130
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Resolved it through primes
some mangoes at a rate of 5 for a dollar - so 5 is the known prime factor
one stack was sold at a rate of 3 for a dollar - so 3 is the known prime factor
and the other at a rate of 6 for a dollar - so 2 and 3 are prime factors

total (avoiding duplicating 3) - 5 * 2 * 3 = 30
so if 30 mangoes were bought then the dollar amount is 6

how we can divide 30 in 2 stacks by keeping the same total dollar amount
2*3 = 2$ and 6 * 4 = 4$

Then ration between first stack and the second one: 6 mangoes / 24 mangoes = 1:4
Senior Manager
Senior Manager
Joined: 02 Apr 2014
Posts: 369
Own Kudos [?]: 493 [0]
Given Kudos: 1227
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Let initial number of mangoes = 60
cost of 60 mangoes = 60/5 = 12
stack 1 = x mangoes, stack 2 = y mangoes
x + y = 60 ----------------(1)
store broke even, 12 = (x/3) + (y/6) ------(2)
solving two equations x = 12, y = 48, ratio of x:y = 1:4 -> (A)
Manager
Manager
Joined: 15 Oct 2017
Posts: 248
Own Kudos [?]: 247 [0]
Given Kudos: 338
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
5 mangoes @ 1/5$, x mangoes @ 1/3$ and y mangoes @ 1/6$. Also, x + y=5.
Therefore, 5*1/5= x*1/3 + y*1/6 to breakeven.
Hence, x=3-y/2 & x+y=5, thus, 5-y=3-y/2, y=4. x=1.

B.
VP
VP
Joined: 07 Dec 2014
Posts: 1067
Own Kudos [?]: 1608 [0]
Given Kudos: 27
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
guerrero25 wrote:
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

A. 1:4
B. 1:5
C. 2:3
D. 1:2
E. 2:5


let x=number of 3 for a dollar mangoes sold
y=number of 6 for a dollar mangoes sold
x/3+y/6=(x+y)/5
x/y=1/4
x:y=1:4
A
Intern
Intern
Joined: 01 Feb 2019
Posts: 10
Own Kudos [?]: 2 [0]
Given Kudos: 22
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Bunuel's explanation is clear. Thank you Bunuel.

If I may add, I think the trickiest part of this problem is the " reading comprehension " bit of understanding the question.

In practice mode, to be honest I spent 3 minutes reading and re-reading the question stem to no avail.

To be specific, the part that threw me off was the first sentence " A grocery store bought some mangoes at a rate of 5 for a dollar ". It did not occur to me on my first read that this is a prompt for " COGS of 1 mango is 0.2 USD ".

To benefit the GMATclub community, I would suggest reading Bunuel's explanation and at least my way of studying this for exam, is to build a mental framework should this type of question occur in the GMAT exam.

If we use just plain logic, my framework for the exam is:
Step 1: identify input - process - output -> get COGS (0.2 USD per mango) and ASP (0.333 USD per mango for the first basket and 0.167 USD per mango for the second basket)
Step 2: identify unit profit and/or unit loss for all basket -> (the first basket yields us (0.333 - 0.2 = 0.133 USD per mango; the second basket we lose 0.033 USD per mango)
Step 3: see, we if we sell 4 mangoes from the second basket, it annihilates any profit we make from selling 1 mango from the first basket.

Thus, the answer is A.

Apologies for the simplistic language. At least for my brain, this is digestible. Hope this post is useful.
VP
VP
Joined: 10 Jul 2019
Posts: 1385
Own Kudos [?]: 577 [0]
Given Kudos: 1656
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
The question is essentially a disguised weighted averages/mixture type of question.


The Data Points = ($) per Mango sold

“Weighted Average” or the Break-Even Cost Point = $1 dollar per 5 mangoes

And the “Weighting” for each Data Point is the number of mangoes sold at each price


Price A: $1 dollar / per 3 mangoes ———Sold A Mangoes and broke even


Price B: $1 dollar / per 6 mangoes——- Sold B mangoes and broke even


The Total mangoes purchased = (A + B)

And the Cost (i.e., “weighted average”) is = $1 / per 5 mangoes

The following equation would describe the break-even point and the Ratio of Mangoes Sold at the two different price structure is given by (A/B) ———>

$1/3(A) + $1/5(B) = $1/6(A + B)

20A + 10B = 12A + 12B

8A = 2B

A/B = 2/8 = 1/4

Answer (A)
1 : 4

Posted from my mobile device
CR Forum Moderator
Joined: 25 Jan 2022
Posts: 824
Own Kudos [?]: 654 [0]
Given Kudos: 559
Location: Italy
GPA: 3.8
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
With these problems, I find converting to cents helps.

Sale Price: \(\frac{100}{5}\) (100 cents=1 dollar per 5)

Stack 1 (x) Sale Price:\(\frac{100}{3}\)(1 dollar per 3)
Profit X:\(\frac{100}{3}-\frac{100}{5}=\frac{200}{15}\)

Stack 2 (y) Sale Price: \(\frac{100}{6}\)(1 dollar per 6)
Profit Y: \(\frac{100}{6}-\frac{100}{5}=-\frac{100}{30}\)


Now, we are told that the store breaks even, implying a 0 profit level.
Profit Y+Profit X=0
\(-\frac{100}{30}y+\frac{200}{15}x=0\)
\(-\frac{100}{30}y+\frac{400}{30}x=0\)
\(\frac{400}{30}x=\frac{100}{30}y\)
Which solves to y/x=4/1, which is not a choice but the equivalent (x/y=1/4) is. Note that since the question only asks for the ratio of mangos, and doesn't specify the type of ratio, both types work. (So if it had asked, for say the ratio of stack 1 to stack 2, 4:1 would be incorrect)
A.
Intern
Intern
Joined: 11 Apr 2023
Posts: 2
Own Kudos [?]: 6 [0]
Given Kudos: 29
Location: India
Concentration: General Management
WE:Sales (Manufacturing)
Send PM
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

A. 1:4
B. 1:5
C. 2:3
D. 1:2
E. 2:5

Buying price 5 $/ pc ; stacking into 2 different rate i.e., $ 3 & $ 6.
Mango stacking at price $3 would require 2 times than stacking at $6.
For break even distribution, equation shall follow = Total Buying / Stacking
For $ 3 stacking equation = (5 x 3) / 2 = 7.5
And for $ 6 stacking equation = (5 x 6) / 1 = 30
Therefore; $ 3 : $ 6 = 7.5:30 = 1:4.
GMAT Club Bot
Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
Moderator:
Math Expert
94371 posts