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# Which of the following fractions has the greatest value?

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Math Expert
Joined: 02 Sep 2009
Posts: 58458
Which of the following fractions has the greatest value?  [#permalink]

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23 Jan 2019, 00:43
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Difficulty:

15% (low)

Question Stats:

76% (01:00) correct 24% (00:52) wrong based on 36 sessions

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Which of the following fractions has the greatest value?

A $$\frac{3^2}{7^5*5^3}$$

B $$\frac{2^2}{7^5 * 5^3}$$

C $$\frac{3^3}{7^6 * 5^3}$$

D $$\frac{21}{7^5 * 5^3}$$

E $$\frac{3^2 * 2}{7^6 * 5^3}$$

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Re: Which of the following fractions has the greatest value?  [#permalink]

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23 Jan 2019, 10:24
IMO D

A $$\frac{3^2}{7^5*5^3}$$ = $$\frac{9}{7^5*5^3}$$

B $$\frac{2^2}{7^5 * 5^3}$$ = $$\frac{4}{7^5 * 5^3}$$

C $$\frac{3^3}{7^6 * 5^3}$$ = $$\frac{27}{7^6 * 5^3}$$

D $$\frac{21}{7^5 * 5^3}$$ = $$\frac{21}{7^5 * 5^3}$$

E $$\frac{3^2 * 2}{7^6 * 5^3}$$[/quote] = $$\frac{18}{7^6 * 5^3}$$[/quote]

Now if you can see we have two sets of fractions in which

$$\frac{21}{7^5 * 5^3}$$ & $$\frac{27}{7^6 * 5^3}$$

Out of which

$$\frac{21}{7^5 * 5^3}$$
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Joined: 22 May 2016
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Which of the following fractions has the greatest value?  [#permalink]

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23 Jan 2019, 11:19
Bunuel wrote:
Which of the following fractions has the greatest value?

A $$\frac{3^2}{7^5*5^3}$$

B $$\frac{2^2}{7^5 * 5^3}$$

C $$\frac{3^3}{7^6 * 5^3}$$

D $$\frac{21}{7^5 * 5^3}$$

E $$\frac{3^2 * 2}{7^6 * 5^3}$$

Use splits.

If all else is equal, a smaller denominator creates a fraction with greater value (more to the right on the number line).

$$\frac{1}{3}<\frac{1}{2}$$

All denominators in the options contain $$5^3$$

But C and E contain $$7^6$$, while the others contain $$7^5$$
-- $$7^6$$ is much greater than $$7^5$$.
-- We need a smaller denominator

Eliminate C and E

Now we have the same denominator, and its value does matter. The denominator could equal 100, or 1,000,000.

In fact, we can write the denominator as "100" for easy comparison.

We need the greatest numerator.

A greater numerator over the same denominator equals a fraction with greater value.
($$\frac{9}{10}>\frac{3}{10}$$)

Numerators:

A) $$3^2=9$$
$$\frac{9}{100}=0.09$$

B) $$2^2=4$$
$$\frac{4}{100}=0.04$$

D) $$3^3=27$$
$$\frac{27}{100}=0.27$$

D's numerator is the greatest, and thus the value of D's fraction is the greatest.

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Joined: 15 Feb 2018
Posts: 366
Re: Which of the following fractions has the greatest value?  [#permalink]

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23 Jan 2019, 22:09
Bunuel, I used cross multiplication to compare A and D. Is there a better method?
Re: Which of the following fractions has the greatest value?   [#permalink] 23 Jan 2019, 22:09
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