Percent Problem

[talaangoshtari]

At the begining of the year, a certain computer problem requires 3.6 X 10^11 calculations to solve, And a computer used to solve it is capable of 1,000,000 calculations per second.At the end of the year, a new algorithm comes out which reduces the number of calculations by the factor of 10, and a new computer is buit capable of perfoming twice as many calculations per second.What percent decrease in computing time(in hrs) has been achived?

A. 60%
B. 75%
C. 85%
D. 90%
E. 95%

w2 = 9/10 w1
r2 = 2 r1

percent decrease = (t1-t2)/t1 = [(w1/r1) - (w2/r2)]/t1
= [(w1/r1) - (.9w1/2r1)]/t1 = 11/20 × 100 = 55%

[GMATGuruNY]

At the begining of the year, a certain computer problem requires 3.6 X 10^11 calculations to solve, And a computer used to solve it is capable of 1,000,000 calculations per second.At the end of the year, a new algorithm comes out which reduces the number of calculations by the factor of 10, and a new computer is buit capable of perfoming twice as many calculations per second.What percent decrease in computing time(in hrs) has been achived?

A. 60%
B. 75%
C. 85%
D. 90%
E. 95%

The values in red are IRRELEVANT.
Plug in EASY VALUES for the original number of calculations and the original rate.

Let the original number of calculations = 100 calculations.
Let the original rate = 1 calculation per hour.
Original time to solve the problem = w/r = 100/1 = 100 hours.

Number of calculations reduced by a factor of 10 = 100/10 = 10 calculations.
Double the rate = 2*1 = 2 calculations per hour.
New time to solve the problem = w/r = 10/2 = 5 hours.

Percent decrease from 100 hours to 5 hours = 95%.

The correct answer is E.

[talaangoshtari]

Why w2 is equal to 1/10w1, but not 9/10w1?

[GMATGuruNY]

Why w2 is equal to 1/10w1, but not 9/10w1?

To INCREASE by a factor of 10 means to MULTIPLY by 10.
To DECREASE by a factor of 10 means to DIVIDE by 10.
Thus, when w� is decreased by a factor of 10, we get:
w�/10 = (1/10)(w�).

[nikhilgmat31]

At the begining of the year, a certain computer problem requires 3.6 X 10^11 calculations to solve, And a computer used to solve it is capable of 1,000,000 calculations per second.At the end of the year, a new algorithm comes out which reduces the number of calculations by the factor of 10, and a new computer is buit capable of perfoming twice as many calculations per second.What percent decrease in computing time(in hrs) has been achived?


so w2 = 9/10 of w1

also factor of 10 can be 2 or 5 or 1 or 10, Please clarify

[theCEO]

At the begining of the year, a certain computer problem requires 3.6 X 10^11 calculations to solve, And a computer used to solve it is capable of 1,000,000 calculations per second.At the end of the year, a new algorithm comes out which reduces the number of calculations by the factor of 10, and a new computer is buit capable of perfoming twice as many calculations per second.What percent decrease in computing time(in hrs) has been achived?


so w2 = 9/10 of w1

also factor of 10 can be 2 or 5 or 1 or 10, Please clarify

by a factor of " is used commonly to mean the same as "multiplied by" or "divided by."

[nikhilgmat31]

so does reduced by factor of 10 means divided by 10

[theCEO]

so does reduced by factor of 10 means divided by 10

yes it does.