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If x = 80%, by what percent is x larger than x^2?
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20 Dec 2022, 07:59
20 Dec 2022, 07:59
Expert Reply
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Question Stats:
62% (01:03) correct
37% (01:32) wrong based on 37 sessions
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If x = 80%, by what percent is x larger than \(x^2\)?
(A) 8 %
(B) 16 %
(C) 20 %
(D) 25%
(E) 80%
(A) 8 %
(B) 16 %
(C) 20 %
(D) 25%
(E) 80%
If x = 80%, by what percent is x larger than x^2?
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22 Dec 2022, 06:21
22 Dec 2022, 06:21
2
Expert Reply
OE
First you should write x as a decimal in order to calculate x^2. This gives x = 0.8 and x^2 = 0.64. The percent difference is equal to the actual difference divided by the basis of the comparison. The basis of the comparison is what follows the word “than” in the problem statement
percent difference 0.8-0.64/0.64=1/4=25 %
Note that if the problem had instead been worded as “by what percent is 0.64 smaller than 0.8?” the basis of the comparison would have been 0.8. The answer in that case would have been 20 %.
D is the answer
First you should write x as a decimal in order to calculate x^2. This gives x = 0.8 and x^2 = 0.64. The percent difference is equal to the actual difference divided by the basis of the comparison. The basis of the comparison is what follows the word “than” in the problem statement
percent difference 0.8-0.64/0.64=1/4=25 %
Note that if the problem had instead been worded as “by what percent is 0.64 smaller than 0.8?” the basis of the comparison would have been 0.8. The answer in that case would have been 20 %.
D is the answer
If x = 80%, by what percent is x larger than x^2?
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27 Jan 2024, 19:35
27 Jan 2024, 19:35
If \(x=80\)%, then \(x=\frac{80}{100} = \frac{4}{5}\)
\(x=\frac{4}{5}\)
\(x^2=\frac{16}{25}\)
First, let us find out how much is \(x\) larger than \(x^2\) in absolute terms
\(x-x^2 = \frac{4}{5}-\frac{16}{25} = \frac{20-16}{25} = \frac{4}{25}\)
In terms of percentage, \(x\) is larger than \(x^2\) by
\(\frac{x-x^2}{x^2} \times 100 = \dfrac{\frac{4}{25}}{\frac{16}{25}} \times 100 = \dfrac{1}{4} = 25\)%
The correct answer is D.
\(x=\frac{4}{5}\)
\(x^2=\frac{16}{25}\)
First, let us find out how much is \(x\) larger than \(x^2\) in absolute terms
\(x-x^2 = \frac{4}{5}-\frac{16}{25} = \frac{20-16}{25} = \frac{4}{25}\)
In terms of percentage, \(x\) is larger than \(x^2\) by
\(\frac{x-x^2}{x^2} \times 100 = \dfrac{\frac{4}{25}}{\frac{16}{25}} \times 100 = \dfrac{1}{4} = 25\)%
The correct answer is D.
