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# Of the following, which is least?

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Re: Of the following, which is least? [#permalink]
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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. $$\frac{0.03}{7.1}$$

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)

Thus, E is the correct answer
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Re: Of the following, which is least? [#permalink]
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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. $$\frac{0.03}{7.1}$$

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.

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

Hence Option E is the answer.
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Re: Of the following, which is least? [#permalink]
Bunuel. Do you have any shortcut solution to share other than division?
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Re: Of the following, which is least? [#permalink]
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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Re: Of the following, which is least? [#permalink]
number with greatest denominator would be lowest. In given options, in option E denominator is greatest and whole number is smallest. So Answer is E
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Re: Of the following, which is least? [#permalink]
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The math here is this, as stated by the other posters:
1. If the numerators are the same, the fraction with the smallest denominator has the largest value. The fraction with the largest denominator has the smallest value.
2. If the denominators are the same, the fraction with the smallest numerator has the smallest value. The fraction with the largest numerator has the largest value.

If you "get" rule one, this is an easy question that takes you 25 seconds to solve - the GMAT is rewarding you for mastery of a logical relationship between values. So, learning this rule has clear rewards.
If you don't "get" rule one, for problems such as this plan to set the denominators equal to one another and compare numerators. This will take about 1:30 on this question, so still a very valid approach.

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Re: Of the following, which is least? [#permalink]
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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. $$\frac{0.03}{7.1}$$

All the numerators are the same. E has the largest denominator. So the least value will be E.

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Re: Of the following, which is least? [#permalink]
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. $$\frac{0.03}{7.1}$$

As you can see the bigger the denominator the lesser the fraction value and the lesser the numerator the lesser the fraction value. If you put one decimal in fraction format and make the multiplication format inverting the dividing fraction you will see that the fraction value decreases the lesser the zeros in front of the comma for the denominator and the more the zeros in front of the comma on the numerator. Thus E.
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Re: Of the following, which is least? [#permalink]
Does anyone have examples where the numerators might be different too? I wasted a lot of time on this one because I didn't look at the answer choices carefully enough, but looking back up...it's super easy.

Largest denominator here makes the fraction smallest.

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Re: Of the following, which is least? [#permalink]
Since all the Numerators are the same we can simply look at the denominators to find the answer. The option with the greatest denominator will be the least. Hence (E)
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Of the following, which is least? [#permalink]
Quick solution:

The same numerator - 0.03
The biggest denominator - 7.1

So, the least fraction is 0.03/7.1

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