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# Of the following, which is least?

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Manager
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Joined: 08 Jan 2016
Posts: 123
Location: Hong Kong
GMAT 1: 750 Q50 V41
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Of the following, which is least? [#permalink]

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26 May 2016, 20:59
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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. $$\frac{0.03}{7.1}$$
[Reveal] Spoiler: OA
Senior Manager
Joined: 18 Jan 2010
Posts: 257
Re: Of the following, which is least? [#permalink]

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26 May 2016, 21:12
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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

So E is the least.
Intern
Joined: 18 Sep 2016
Posts: 49
Re: Of the following, which is least? [#permalink]

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27 Sep 2016, 11:29
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)

Thus, E is the correct answer
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Re: Of the following, which is least? [#permalink]

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30 Nov 2016, 09:33
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Expert's post
Top Contributor
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 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

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Brent Hanneson – Founder of gmatprepnow.com

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Joined: 11 Sep 2015
Posts: 2001
Re: Of the following, which is least? [#permalink]

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30 Nov 2016, 09:42
Expert's post
Top Contributor
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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Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 15 Jan 2016
Posts: 3
Re: Of the following, which is least? [#permalink]

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22 Aug 2017, 22:05
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.
Manager
Status: Searching for something I've been searching..LOL
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Concentration: Healthcare, Operations
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Re: Of the following, which is least? [#permalink]

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22 Aug 2017, 22:54
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.

Hence Option E is the answer.
Intern
Joined: 10 Sep 2014
Posts: 19
Re: Of the following, which is least? [#permalink]

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11 Dec 2017, 08:47
Bunuel. Do you have any shortcut solution to share other than division?
Math Expert
Joined: 02 Sep 2009
Posts: 43381
Re: Of the following, which is least? [#permalink]

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11 Dec 2017, 21:33
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] 11 Dec 2017, 21:33
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