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A baseball card decrease in value 20% in its first year...

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A baseball card decrease in value 20% in its first year...

by BTGmoderatorLU » Mon Mar 19, 2018 2:51 pm
A baseball card decrease in value 20% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?

A. 28%
B. 30%
C. 32%
D. 36%
E. 72%

The OA is A.

I'm confused by this PS question, is there a formula to solve it? Experts, any suggestion? Thanks in advance.
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by ErikaPrepScholar » Tue Mar 20, 2018 4:51 am
Let's say the original value of the baseball card is x. If it decreases in value by 20% in the first year, that means its value at the end of the first year is 80% of the original value, or 0.8x.

Then the value decreases by 10% in the second year. This means that its value at the end of the second year is 90% of its value at the end of the first year, or 0.9(0.8x).

Simplifying gives us 0.72x - so at the end of the second year, the value of the card is 72% of its original value. This means the card has lost 28% of its value, or answer choice A.

When you see percents, your best best is often to turn the percents into decimals and start making equations. However, we can also solve logically - we lose 20% of the original value, then we lose 10% of the reduced value. 10% of the reduced value is less than 10% of the original value, so the value must decrease by less that 30% in total. This leaves us with A as the only possible answer.
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by GMATGuruNY » Tue Mar 20, 2018 5:02 am
LUANDATO wrote:A baseball card decrease in value 20% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?

A. 28%
B. 30%
C. 32%
D. 36%
E. 72%
Let the original value of the card = 100.
After a 20% decrease, the card = 100 - (20% of 100) = 100 - 20 = 80.
After an additional 10% decrease, the card = 80 - (10% of 80) = 80 - 8 = 72.
Total decrease = 100 - 72 = 28.
Since the card loses $28 of its original $100 value, the total percent decrease = 28/100 = 28%.

The correct answer is A.
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by Jeff@TargetTestPrep » Wed Mar 21, 2018 3:21 pm
LUANDATO wrote:A baseball card decrease in value 20% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?

A. 28%
B. 30%
C. 32%
D. 36%
E. 72%
In two years the card is worth 0.8 x 0.9 = 0.72 = 72% of its original value, which is a 28% decrease from its original value.

Answer: A

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by BTGmoderatorRO » Sun Mar 25, 2018 6:43 am
The decrease of 20% in the first year = 80%=0.8
The decrease of 10% in the second year = 90%= 0.9

So, in 2 years the card is worth 0.8*0.9=0.72= 72% of its original value.
This implies it is 28% decrease from its original value.
Hence, the correct answer is A
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