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Which of the following equals 5,000 ?

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Bunuel
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Which of the following equals 5,000 ? [#permalink] New post   16 Aug 2023, 03:00
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A
B
C
D
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Which of the following equals 5,000 ?

A. \(\frac{0.03}{0.00006}\)

B. \(\frac{0.3}{0.06}\)

C. \(\frac{3}{0.0006}\)

D. \(\frac{30}{0.6}\)

E. \(\frac{300}{0.006}\)
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C
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AryaSwagat
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Which of the following equals 5,000 ? [#permalink] New post   Updated on: 20 Aug 2023, 22:09
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Here we see 3 in the numerator of all and 6 in the denominator.
\(\frac{3}{6} = 0.5\)
to make it 5000 we need to multiply 0.5 by \(10^4\).
So among the options if the difference of the exponents of 10 between numerator and denominator is 4 irrespective of everything else, then it is the answer.

For example
(a) \(\frac{0.030}{0.00006}= \frac{{3*10^-3}}{{6*10^-5}}= \frac{3*10^{5-3}}{6}=\frac{3*10^{2}}{6}\)
Not correct
(c) \(\frac{3}{0.0006}=\frac{{3}}{{6*10^-4}}=\frac{{3*10^4}}{{6}}=0.5*10^4=5000\)

So C

Originally posted by AryaSwagat on 16 Aug 2023, 03:57.
Last edited by AryaSwagat on 20 Aug 2023, 22:09, edited 1 time in total.
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JeffTargetTestPrep
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Re: Which of the following equals 5,000 ? [#permalink] New post   20 Aug 2023, 17:10
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Bunuel wrote:
Which of the following equals 5,000 ?

A. \(\frac{0.03}{0.00006}\)

B. \(\frac{0.3}{0.06}\)

C. \(\frac{3}{0.0006}\)

D. \(\frac{30}{0.6}\)

E. \(\frac{300}{0.006}\)


30,000/6 = 5,000

We can multiply the numerator and the denominator of the above fraction by the same power of 10 so that the numerator of the resulting fraction matches the numerator of the fraction in each answer choice:

30,000/6 × 10ˉ⁶/10ˉ⁶ = 0.03/0.000006 ≠ A

30,000/6 × 10ˉ⁵/10ˉ⁵ = 0.3/0.00006 ≠ B

30,000/6 × 10ˉ⁴/10ˉ⁴ = 3/0.0006 = C

Answer: C

Note: We don’t need to check the other answer choices because there can be only one correct answer.
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MihirBathia
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Re: Which of the following equals 5,000 ? [#permalink] New post   21 Aug 2023, 08:18
STARTED WITH 30000/6=5000, THEN WENT ON TO REMOVE ONE ZERO FROM THE NUMERATOR AND ADDING A DECIMAL TO THE DENOMINATOR..3000/.6 THEN AGAIN 300/.06 UNTIL THE ANSWER WITH AN OPTION TURNED UP
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Re: Which of the following equals 5,000 ? [#permalink]
21 Aug 2023, 08:18
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