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

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

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25 Jan 2014, 04:54
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Difficulty:

95% (hard)

Question Stats:

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

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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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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25 Jan 2014, 09:43
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.

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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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04 Mar 2014, 03:38
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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22 Sep 2014, 00:40
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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22 Sep 2014, 05:21
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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23 Sep 2014, 00:19
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.
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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23 Sep 2014, 02:03
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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23 Sep 2014, 05:36
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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23 Sep 2014, 05:59
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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26 Jun 2016, 01:46
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.

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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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27 Jun 2016, 18:04
1/3*x+1/6*y=1/5(x+y)
x/y=1/4
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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27 Jun 2016, 20:17
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.

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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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10 Aug 2017, 13:57
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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14 Feb 2018, 11:06
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)
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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14 Feb 2018, 12:16
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.
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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14 Feb 2018, 16:48
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
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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22 Mar 2019, 01:28
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.
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Re: A grocery store bought some mangoes at a rate of 5  [#permalink]

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Re: A grocery store bought some mangoes at a rate of 5   [#permalink] 05 Apr 2020, 02:21