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# QOTD#12 If 10x equals 0.1 percent of 10y, where x and y are

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QOTD#12 If 10x equals 0.1 percent of 10y, where x and y are [#permalink]  19 Aug 2016, 05:28
Expert's post
00:00

Question Stats:

67% (00:57) correct 32% (01:05) wrong based on 34 sessions
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

Practice Questions
Question: 14
Page: 152
[Reveal] Spoiler: OA

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Re: QOTD#12 If 10x equals 0.1 percent of 10y, where x and y are [#permalink]  23 Aug 2016, 14:07
Expert's post
Explanation

ASIDE: p% can be written as the fraction p/100
So, 3% = 3/100, 17% = 17/100, 255% = 255/100, and 0.1% = 0.1/100

10^x equals 0.1 percent of 10^y
Write as: 10^x = (0.1/100)(10^y)
Rewrite fraction with integers to get: 10^x = (1/1000)(10^y)
Multiply both sides by 1000 to get: (10^x)(1000) = 10^y
Rewrite 1000 as power of 10 to get: (10^x)(10^3) = 10^y
Apply Product Law to get: 10^(x+3) = 10^y
Since both sides have the same base, we can conclude that: x+3 = y

[Reveal] Spoiler:
B

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Re: QOTD#12 If 10x equals 0.1 percent of 10y, where x and y are   [#permalink] 23 Aug 2016, 14:07
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