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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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Joined: 02 Sep 2009
Posts: 47977
If 10^x equals 0.1 percent of 10^y, where x and y are integers, which  [#permalink]

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15 Jul 2018, 08:42
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25% (medium)

Question Stats:

69% (01:12) correct 31% (01:16) wrong based on 48 sessions

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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

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Location: India
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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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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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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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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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