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Re: Of the following, which is least? [#permalink]

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26 May 2016, 22:12

3

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nalinnair wrote:

Of the following, which is least?

A. \(\frac{0.03}{0.00071}\) B. \(\frac{0.03}{0.0071}\) C. \(\frac{0.03}{0.071}\) D. \(\frac{0.03}{0.71}\) E. \(\frac{0.03}{7.1}\)

Each of these can be written as a multiple of (3/71)

A) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-5}\))], which is nothing but [(\(10^{-2}\))X(\(10^5\))], which is \(10^3\) B) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-4}\))], which is nothing but [(\(10^{-2}\))X(\(10^4\))], which is \(10^2\) C) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-3}\))], which is nothing but [(\(10^{-2}\))X(\(10^3\))], which is \(10^1\) D) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-2}\))], which is nothing but [(\(10^{-2}\))X(\(10^2\))], which is \(10^0\) = 1 E) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-1}\))], which is nothing but [(\(10^{-2}\))X(\(10^1\))], which is \(10^-1\)= 0.1

Re: Of the following, which is least? [#permalink]

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27 Sep 2016, 12:29

nalinnair wrote:

Of the following, which is least?

A. \(\frac{0.03}{0.00071}\) B. \(\frac{0.03}{0.0071}\) C. \(\frac{0.03}{0.071}\) D. \(\frac{0.03}{0.71}\) E. \(\frac{0.03}{7.1}\)

all the possible answers' nominators are 0.03

therefore, the one with the bigger denominator has to be the one with the lowest value (value of the fraction and value of the denominator are always negatively correlated)

All 5 numerators are 0.03 So, we'll use the property that says "the bigger the denominator, the smaller the value of the fraction" For example, 17/31 is less than 17/30 And 321/555 is less than 321/534 And 12/6 is less than 12/4

Now let's check the denominators among the answer choices.... The biggest denominator is 7.1, so the correct answer is E

If students didn't see the fast answer (in my above post), here's another (slightly longer approach):

Let's create equivalent fractions with the same denominator. Let's make each denominator 7.1

A. \(\frac{0.03}{0.00071}\) To get a denominator of 7.1, we must take 0.00071 and move the decimal 4 places to the right. So, we'll multiply numerator and denominator by 10,000 When we do this, we get: \(\frac{300}{7.1}\)

B. \(\frac{0.03}{0.0071}\) To get a denominator of 7.1, we must take 0.0071 and move the decimal 3 places to the right. So, we'll multiply numerator and denominator by 1,000 When we do this, we get: \(\frac{30}{7.1}\)

C. \(\frac{0.03}{0.071}\) To get a denominator of 7.1, we must take 0.071 and move the decimal 2 places to the right. So, we'll multiply numerator and denominator by 100 When we do this, we get: \(\frac{3}{7.1}\)

D. \(\frac{0.03}{0.71}\) To get a denominator of 7.1, we must take 0.71 and move the decimal 1 place to the right. So, we'll multiply numerator and denominator by 10 When we do this, we get: \(\frac{0.3}{7.1}\)

E. \(\frac{0.03}{7.1}\) This already has a denominator of 7.1

Now that we have the same denominator, we can that \(\frac{0.03}{7.1}\) is the smallest fraction. Answer: E

Re: Of the following, which is least? [#permalink]

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22 Aug 2017, 23:05

Given that the demonimator is same value 71 in each case, the problem can be solved by considering 3/71 in each options and expressing them as power of 10.Going by that option E is the right choice.it is the least since the denominator is greater that the numerator.

Re: Of the following, which is least? [#permalink]

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22 Aug 2017, 23:54

All the numerators are the same. Hence the fraction with the largest denominator will be the smallest fraction. Option E has the largest denominator among all options.

Bunuel. Do you have any shortcut solution to share other than division?

I think that the fastest approach is given HERE. All the numerators are equal, so the smallest fraction will be the one with largest denominator (true for positive fractions).
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