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Price of a Belgian chocobar has increased by x percent

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Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 08 Apr 2017, 03:28
1
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A
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  85% (hard)

Question Stats:

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Price of a Belgian chocobar has increased by x percent but the number of units sold is decreased by y percent. Was the revenue collected at new price more than the revenue collected at original price?

(1) x = y.

(2) 100x − 100y − xy < 0

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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 08 Apr 2017, 06:57
2
1
Let P be the price and Q be the number of units sold

Original revenue = PQ
New revenue = P(1 + x/100)Q(1 - y/100)

Question: P(1 + x/100)Q(1 - y/100) > PQ?
(1 + x/100)(1 - y/100) > 1?
(100 + x)(100 - y) > 10000?
100x - 100y - xy > 0?

St1: x = y --> 100x - 100x - x^2 > 0?
-x^2 > 0? Answer is a clear no.
Sufficient

St2: 100x − 100y − xy < 0 --> Clearly sufficient as it directly answers the prompt with a No

Answer: D
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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 10 Apr 2017, 07:33
Hi,

I guess the ans is B. From Statement 1, there is always a possibility of x=y=0. In that case, before and after revenue are unchanged.
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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 10 Apr 2017, 23:25
arunavamunshi1988 wrote:
Hi,

I guess the ans is B. From Statement 1, there is always a possibility of x=y=0. In that case, before and after revenue are unchanged.


Hey mate,

You're correct in the assumption that x=y=0 and hence there won't be any change in the revenue.

The question is : Was the revenue collected at new price more than the revenue collected at original price? Using your assumption, the answer for this is 'NO' (revenues before and after will be equal). Using any number for x and y other than 0 will yield an answer and that's again a 'NO' (new revenue will be lesser than old one).

So this statement is sufficient.

Cheers!
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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 26 Aug 2017, 06:22
Diwakar003 wrote:
arunavamunshi1988 wrote:
Hi,

I guess the ans is B. From Statement 1, there is always a possibility of x=y=0. In that case, before and after revenue are unchanged.


Hey mate,

You're correct in the assumption that x=y=0 and hence there won't be any change in the revenue.

The question is : Was the revenue collected at new price more than the revenue collected at original price? Using your assumption, the answer for this is 'NO' (revenues before and after will be equal). Using any number for x and y other than 0 will yield an answer and that's again a 'NO' (new revenue will be lesser than old one).

So this statement is sufficient.

Cheers!

not able to understand why option 1 sufficient? can you explain with example?
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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 27 Aug 2017, 07:35
r19 wrote:
not able to understand why option 1 sufficient? can you explain with example?


Hey mate, see whether the below explanation helps.
Let the initial no of chocolates be N. Let the price per chocolate be P.
Initial revenue = NxP.
Given the increase in price is x% and decrease in the amount of chocolates sold is y%.

New revenue = [(100+x)/100] x [(100-y)/100] x N x P

Question: Whether the new revenue is more than the old revenue?

A) Given x=y.
If x=y=0
New revenue=Old revenue. There is no increase in revenue after the change so new revenue is not more than old revenue. So the answer for question asked is 'no'.
If x=y=Any value other than 0
The new revenue will be lesser than old revenue. So the answer for the question is again 'no'
Hence A is sufficient.

Cheers!
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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 27 Aug 2017, 19:03
Vyshak wrote:
Let P be the price and Q be the number of units sold

Original revenue = PQ
New revenue = P(1 + x/100)Q(1 - y/100)

Question: P(1 + x/100)Q(1 - y/100) > PQ?
(1 + x/100)(1 - y/100) > 1?
(100 + x)(100 - y) > 10000?
100x - 100y - xy > 0?

St1: x = y --> 100x - 100x - x^2 > 0?
-x^2 > 0? Answer is a clear no.
Sufficient

St2: 100x − 100y − xy < 0 --> Clearly sufficient as it directly answers the prompt with a No

Answer: D


Hi
I didnt get why statement 2 is a clear no, can you please elaborate
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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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New post 29 Aug 2017, 00:44
New Revenue=(1+0.01x)OldPrice*(1-0.01y)OldUnitsSold.
=(1+{-0.01y+0.01x-0.0001xy})*OldPrice*OldUnitsSold
=(1+{-0.01y+0.01x-0.0001xy})*OldRevenue

From statement 2, we know that expression in curly bracket above is less than 0. So we always know new revenue will be lesser than the old one. Hope this helps.
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Re: Price of a Belgian chocobar has increased by x percent  [#permalink]

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Re: Price of a Belgian chocobar has increased by x percent   [#permalink] 01 Nov 2018, 09:03
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