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If 10^x equals 0.1 percent of 10^y, where x and y are integers, which

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If 10^x equals 0.1 percent of 10^y, where x and y are integers, which  [#permalink]

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New post 15 Jul 2018, 08:42
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If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?

A. y = x + 2
B. y = x + 3
C. x = y + 3
D. y = 1,000x
E. x = 1,000y
Spoiler: OA

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If 10^x equals 0.1 percent of 10^y, where x and y are integers, which  [#permalink]

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New post 15 Jul 2018, 08:49
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Bunuel wrote:
If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?

A. y = x + 2
B. y = x + 3
C. x = y + 3
D. y = 1,000x
E. x = 1,000y


\(10^x=0.1\)%\(*10^y\)

\(=>10^x=\frac{0.1}{100}*10^y=>10^x*100=10^{-1}*10^y\)

\(=>10^{x+2}=10^{y-1}\)

\(=>x+2=y-1 => y=x+3\)

Option B
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If 10^x equals 0.1 percent of 10^y, where x and y are integers, which  [#permalink]

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New post 15 Jul 2018, 10:44
Bunuel wrote:
If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?

A. y = x + 2
B. y = x + 3
C. x = y + 3
D. y = 1,000x
E. x = 1,000y



Given

10^x equals 0.1 percent of 10^y.

So, we can translate into equation.


\(10^x\) = 0.1% * \(10^y\)

\(10^x\) = (0.1 /100)* \(10^y\)

\(10^x\) = 0.001 *\(10^y\)

\(10^x\) = 1*\(10^{y-3}\)

\(10^x\) = \(10^{y-3}\)

x = y-3

y = x+3

Thus the best answer is B.
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Re: If 10^x equals 0.1 percent of 10^y, where x and y are integers, which  [#permalink]

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New post 20 Jul 2018, 01:13
Bunuel wrote:
If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?

A. y = x + 2
B. y = x + 3
C. x = y + 3
D. y = 1,000x
E. x = 1,000y


\(10^x\) \(=\) \(\frac{0.1}{100}\) \(*\) \(10^y\)

\(10^x = \frac{1}{1000} * 10^y\)

\(10^x = 10^{-3} * 10^y\)

\(x = -3 + y\)

\(y = x + 3\)

(B)
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Re: If 10^x equals 0.1 percent of 10^y, where x and y are integers, which &nbs [#permalink] 20 Jul 2018, 01:13
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