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23 Jan 2019, 00:43
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
80% (01:15) correct
20%
(01:18)
wrong
based on 222
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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 \(\frac{3^2 * 2}{7^6 * 5^3}\)
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 \(\frac{3^2 * 2}{7^6 * 5^3}\)
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
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Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
23 Jan 2019, 10:24
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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
\(\frac{21}{7^5 * 5^3}\)
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
\(\frac{21}{7^5 * 5^3}\)
23 Jan 2019, 11:19
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Bunuel
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.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 \(\frac{3^2 * 2}{7^6 * 5^3}\)
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.
Answer
