Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 07 Jun 2020, 02:42 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A grocery store bought some mangoes at a rate of 5

Author Message
TAGS:

### Hide Tags

Senior Manager  Joined: 10 Apr 2012
Posts: 261
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

2
17 00:00

Difficulty:   95% (hard)

Question Stats: 42% (02:25) correct 58% (02:02) wrong based on 203 sessions

### HideShow timer Statistics

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
Math Expert V
Joined: 02 Sep 2009
Posts: 64322
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

3
8
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

The cost price of a mango = 1/5 dollars.

The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/3 - 1/5 = 2/15 = 4/30 dollars.
The selling price of a mango from the second stack = 1/6 dollars --> the loss from one mango = 1/5 - 1/6 = 1/30 dollars.

The profit from one mango from the first stack is 4 times the loss from one mango from the second stack. Thus, to break even, 4 times as many mangoes must be sold at loss as at profit. The ratio = 1:4. For example, if one one mango was sold at a profit of 4/30 dollars, 4 mangoes must be sold at a loss of 1/30 dollars to break even.

_________________
##### General Discussion
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1707
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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)

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
Manager  Joined: 13 Sep 2014
Posts: 86
WE: Engineering (Consulting)
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

3
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
Manager  Joined: 20 Jan 2014
Posts: 136
Location: India
Concentration: Technology, Marketing
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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)

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
Retired Moderator Joined: 15 Jun 2012
Posts: 968
Location: United States
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

2
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)

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.
Manager  Joined: 03 Jul 2013
Posts: 80
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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
_________________
Sometimes standing still can be, the best move you ever make......
Math Expert V
Joined: 02 Sep 2009
Posts: 64322
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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

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
_________________
Manager  Joined: 13 Sep 2014
Posts: 86
WE: Engineering (Consulting)
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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

it says he bought 5 mangoes for \$1
and sold at 3 mangoes for \$1
sold at 6 mangoes for \$1
Senior Manager  S
Joined: 24 Jun 2016
Posts: 344
GMAT 1: 770 Q60 V60
GPA: 4
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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.

_________________
Stuck in the 600's and want to score 700+ on the GMAT?
If this describes you, we should talk. I specialize in getting motivated students into the 700's.

\$90/hour as of August 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out!

HanoiGMATTutor@gmail.com
VP  D
Joined: 07 Dec 2014
Posts: 1253
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

1/3*x+1/6*y=1/5(x+y)
x/y=1/4
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10506
Location: Pune, India
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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.

_________________
Karishma
Veritas Prep GMAT Instructor

Manager  B
Joined: 24 Jun 2017
Posts: 113
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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  P
Joined: 02 Apr 2014
Posts: 453
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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)
Senior Manager  P
Joined: 15 Oct 2017
Posts: 291
GMAT 1: 560 Q42 V25 GMAT 2: 570 Q43 V27 GMAT 3: 710 Q49 V39 Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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  D
Joined: 07 Dec 2014
Posts: 1253
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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  B
Joined: 01 Feb 2019
Posts: 13
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

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.

Apologies for the simplistic language. At least for my brain, this is digestible. Hope this post is useful.
Non-Human User Joined: 09 Sep 2013
Posts: 15108
Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: A grocery store bought some mangoes at a rate of 5   [#permalink] 05 Apr 2020, 02:21

# A grocery store bought some mangoes at a rate of 5  