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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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Math Expert
Joined: 02 Sep 2009
Posts: 52917
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, 07:42
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:26) correct 37% (01:25) wrong based on 120 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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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, 07:49
1
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, 09:44
1
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, 00:13
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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Posts: 417
Location: Germany
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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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05 Jan 2019, 04:36
selim wrote:
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.

Thank you for the explanation, that made the problem quite clear.

Although, I have to admit it feels weird learning math from Johnny Sins.
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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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27 Jan 2019, 04:48
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=10^-3*10^y
x=-3+y
y=x+3
IMO B
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Re: If 10^x equals 0.1 percent of 10^y, where x and y are integers, which   [#permalink] 27 Jan 2019, 04:48
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