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Percentage Increase and decrease

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Percentage Increase and decrease

by melguy » Tue Jun 18, 2013 12:21 am
Please help me with the questions below. Thanks

Q1. If price decreases by 25%, by what % should consumption increase so that the expenditure does not
increase?

a. 20%
b. 25%
c. 33.33%
d. 40%
e. 75%

Q2. If speed increases by 33.33%, what is the percent reduction in the time taken to travel the same
distance?

a. 20%
b. 25%
c. 33.33%
d. 66.66%
e. 75%
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by Brent@GMATPrepNow » Tue Jun 18, 2013 5:52 am
melguy wrote: Q1. If price decreases by 25%, by what % should consumption increase so that the expenditure does not
increase?

a. 20%
b. 25%
c. 33.33%
d. 40%
e. 75%
A fast approach is to choose some nice numbers to work with.
Say, some item costs $4 each, and you typically buy 6 items for a total cost (expenditure) of $24

If the price decreases by 25%, then the new price per item is $3.
If the total cost (expenditure) must be $24, we can now buy 8 items.

So, to keep the expenditure the same, we must increase consumption from 6 to 8. This represents a [spoiler]33 1/3%[/spoiler] increase.
Answer = C



melguy wrote: Q2. If speed increases by 33.33%, what is the percent reduction in the time taken to travel the same distance?

a. 20%
b. 25%
c. 33.33%
d. 66.66%
e. 75%
Choose nice values and plug in.

Time = distance/speed

Let distance = 12 miles, and let original speed = 3 miles per hour.
So time = 12/3 = 4 hours


If speed increases by 33 1/3%, then the new speed is 4 miles per hour.
So time = 12/4 = 3 hours

So, the travel time decreased from 4 hours to 3 hours.
This represents a [spoiler]25%[/spoiler] decrease.
Answer = B


Cheers,
Brent
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by GMATGuruNY » Tue Jun 18, 2013 7:17 am
Each problem is a variation of the following equation:
(number)(average) = sum.

Q1: (number of units sold)(average price per unit) = revenue.
Q2: (number of hours)(average miles per hour) = distance.

In each case, the goal is to keep the product CONSTANT.
Thus, if one factor on the left is multiplied by x/y, the other factor on the left must be multiplied by y/x, so that the product doesn't change.
Q1. If price decreases by 25%, by what % should consumption increase so that the expenditure does not
increase?

a. 20%
b. 25%
c. 33.33%
d. 40%
e. 75%
To decrease the price by 1/4 is to multiply the price by 3/4.
Thus, to keep the product constant, the number of sales must be multiplied by 4/3 -- an increase of 1/3 = 33.33%.

The correct answer is C.
Q2. If speed increases by 33.33%, what is the percent reduction in the time taken to travel the same
distance?

a. 20%
b. 25%
c. 33.33%
d. 66.66%
e. 75%
To increase the speed by 1/3 is to multiply the speed by 4/3.
Thus, to keep the product constant, the time must be multiplied by 3/4 -- a decrease of 1/4 = 25%.

The correct answer is B.
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