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The price of a certain computer is discounted by 20% every

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by gmat_winter » Wed Mar 25, 2015 8:28 am
The price of a certain computer is discounted by 20% every year. After 3 years have passed the price of the computer will have been discounted by what fraction of the original price?

A)9/25

B)61/125

C)64/125

D)3/5

E)16/25

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by Brent@GMATPrepNow » Wed Mar 25, 2015 8:51 am
gmat_winter wrote:The price of a certain computer is discounted by 20% every year. After 3 years have passed the price of the computer will have been discounted by what fraction of the original price?

A)9/25
B)61/125
C)64/125
D)3/5
E)16/25

OAB
If the computer price decreases 20%, then it retains 80% of its value.
So, for example, if the original price is $50, then after 1 year, the reduced price = 80% of $50 (i.e., $40)
NOTE: 80% = 4/5

Year 0: let the price = x
After 1 year: the price = x(4/5)
After 2 years: the price = x(4/5)(4/5)
After 3 years: the price = x(4/5)(4/5)(4/5)

So, after 3 years the price = x(64/125)
So, the price is now 64/125 of the original price.
BE CAREFUL, the question actually asks us how much the price has been DISCOUNTED.
So, if the computer RETAINS 64/125 of its original value, then it has been DISCOUNTED by 61/125

Answer: B

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by GMATGuruNY » Wed Mar 25, 2015 10:00 am
gmat_winter wrote:The price of a certain computer is discounted by 20% every year. After 3 years have passed the price of the computer will have been discounted by what fraction of the original price?

A)9/25

B)61/125

C)64/125

D)3/5

E)16/25

OAB
Let the original price = 1000.
1st year price = 1000 - 20% of 1000 = 1000-200 = 800.
2nd year price = 800 - 20% of 800 = 800-160 = 640.
3rd year price = 640 - 20% of 640 = 640-128 = 512.
Total discount = 1000-512 = 488.
Resulting fraction:
(discount)/(original) = 488/1000 = 61/125.

The correct answer is B.
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by [email protected] » Wed Mar 25, 2015 6:10 pm
Hi gmat_winter,

In these types of questions, TESTing VALUES is a great way to get to the correct answer. Typically, when you see percents in these types of questions, it's best to TEST the number 100. However, the answer choices to this question point to the number 125 as the likely "perfect" starting number (since all of the answers are either out of 125 or reduced from 125).

We're told that the price of a computer is discounted 20% each year for 3 years. We're asked for the fraction of the DISCOUNT (relative to the original price) at the end of 3 years...

Starting Price = $125

Year 1: 125 - .2(125) = 100

Year 2: 100 - .2(100) = 80

Year 3: 80 - .2(80) = 64

Since the ending price is $64, the discount was $61

The discount relative to the original price is 61/125

Final Answer: B

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by Brent@GMATPrepNow » Sat Jan 13, 2018 6:24 am
gmat_winter wrote:The price of a certain computer is discounted by 20% every year. After 3 years have passed the price of the computer will have been discounted by what fraction of the original price?

A)9/25

B)61/125

C)64/125

D)3/5

E)16/25

OAB
If the computer price decreases 20%, then it retains 80% of its value.
So, for example, if the original price is $50, then after 1 year, the reduced price = 80% of $50 (i.e., $40)
NOTE: 80% = 4/5

Year 0: let the price = x
After 1 year: the price = x(4/5)
After 2 years: the price = x(4/5)(4/5)
After 3 years: the price = x(4/5)(4/5)(4/5)

So, after 3 years the price = x(64/125)
So, the price is now 64/125 of the original price.
BE CAREFUL, the question actually asks us how much the price has been DISCOUNTED.
So, if the computer RETAINS 64/125 of its original value, then it has been DISCOUNTED by 61/125

Answer: B

Cheers,
Brent
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by Scott@TargetTestPrep » Sun Aug 11, 2019 6:51 pm
gmat_winter wrote:The price of a certain computer is discounted by 20% every year. After 3 years have passed the price of the computer will have been discounted by what fraction of the original price?

A)9/25

B)61/125

C)64/125

D)3/5

E)16/25

OAB
After 3 years, the discounted price of the computer is 4/5 x 4/5 x 4/5 = 64/125 of the original price. So the computer will have been discounted by 1 - 64/125 = 125/125 - 64/125 = 61/125 of the original price.

Answer: B

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