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Problem Solving — algebra and arithmetic
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by sachindia » Sat Oct 13, 2012 9:31 pm
If price decreases by 25%, by what % should consumption increase so that the expenditure does
not increase?
Regards,
Sach
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by Brent@GMATPrepNow » Mon Oct 15, 2012 6:42 am
sachindia wrote:If price decreases by 25%, by what % should consumption increase so that the expenditure does
not increase?
I think you might need to rephrase the question. It's unclear what you're asking.
Also, it would be useful to include the answer choices. In many cases, the fastest way to solve a GMAT math question is to work with the answer choices.

Cheers,
Brent
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by sachindia » Mon Oct 15, 2012 5:38 pm
Brent@GMATPrepNow wrote:
sachindia wrote:If price decreases by 25%, by what % should consumption increase so that the expenditure does
not increase?
I think you might need to rephrase the question. It's unclear what you're asking.
Also, it would be useful to include the answer choices. In many cases, the fastest way to solve a GMAT math question is to work with the answer choices.

Cheers,
Brent
Thanks for responding Brent. Here's a similar Question with options:

If the price of sugar is raised by 25%, find by how much percent a householder must reduce his consumption of sugar so as not to increase his expenditure?
(A) 10 (B) 20 (C) 18 (D) 25
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Sach
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by Brent@GMATPrepNow » Mon Oct 15, 2012 6:01 pm
sachindia wrote: If the price of sugar is raised by 25%, find by how much percent a householder must reduce his consumption of sugar so as not to increase his expenditure?
(A) 10 (B) 20 (C) 18 (D) 25
This is a great question for plugging in numbers.
Let's say that, each day, Joe buys 100 pounds of sugar at a cost of $1.00/pound.
So, his total expenditure is $100.

If the price of sugar increases 25%, then the new cost is $1.25/pound.
So, if Joe's expenditure is to remain at $100, how many pounds of sugar can he buy?
In other words, how many pounds of sugar can Joe get for $100 at a price of $1.25/pound.
We need to calculate 100/1.25
This is equal to 100/(5/4) = 100(4/5) = 80
So, Joe can buy 80 pounds of sugar at a price of $1.25/pound.

Joe went from 100 pounds to 80 pounds.
This represents a [spoiler]20%[/spoiler] decrease
The answer is B

Cheers,
Brent
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by \'manpreet singh » Wed Oct 17, 2012 10:06 pm
If the price of sugar is raised by 25%, find by how much percent a householder must reduce his consumption of sugar so as not to increase his expenditure?
(A) 10 (B) 20 (C) 18 (D) 25[/quote]

Take initial values as E=100 , P=100 and C=1

We know that Expenditure(E)= Price(P)X Consumption(C)
PLUG THE VALUES:
initially we have 100 = 100 X 1

now, P=125 , C=1-x , E=100(CONSTANT)

the equation becomes:

100 = 125 X (1-x)

x= 1/5
x=0.20

x%= 20% decrease in consumption
Ans: B
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