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Which of the following has the greatest value?

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

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New post 29 Aug 2017, 22:48
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Question Stats:

54% (01:34) correct 46% (01:32) wrong based on 260 sessions

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Which of the following has the greatest value?


A. \(\frac{1}{5^37^3}\)

B. \(\frac{6}{5^47^3}\)

C. \(\frac{45}{5^47^4}\)

D. \(\frac{180}{5^57^4}\)

E. \(\frac{900}{5^57^5}\)

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

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New post 29 Aug 2017, 23:21
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Bunuel wrote:
Which of the following has the greatest value?


A. \(\frac{1}{5^37^3}\)

B. \(\frac{6}{5^47^3}\)

C. \(\frac{45}{5^47^4}\)

D. \(\frac{180}{5^57^4}\)

E. \(\frac{900}{5^57^5}\)


A \(1/1 * 1/5^3*7^3\)
B \(6/5 * 1/5^3*7^3\)
C \(45/35 * 1/5^3*7^3\)
D \(180/175 * 1/5^3*7^3\)
E \(900/1225 * 1/5^3*7^3\)

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

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New post 30 Aug 2017, 16:03
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Bunuel wrote:
Which of the following has the greatest value?


A. \(\frac{1}{5^37^3}\)

B. \(\frac{6}{5^47^3}\)

C. \(\frac{45}{5^47^4}\)

D. \(\frac{180}{5^57^4}\)

E. \(\frac{900}{5^57^5}\)


Multiply all fractions by the least common multiple of all 5 denominators: (5^5)(7^5)

We get:
A) (5²)(7²)
B) (6)(5)(7²)
C) (45)(5)(7)
D) (180)(7)
E) 900

Now divide the answer choices by 5 to get:
A) (5)(7²)
B) (6)(7²)
C) (45)(7)
D) (36)(7)
E) 180

B is clearly bigger than A - ELIMINATE A
C is clearly bigger than D and E - ELIMINATE D and E

We're left with B and C
B) (6)(7²)
C) (45)(7)

Rewrite B as follows:
B) (6)(7²) = (6)(7)(7) = (42)(7)

Now we can see that C is greater.

Answer:

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

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New post 02 Sep 2017, 06:17
1
Bunuel wrote:
Which of the following has the greatest value?


A. \(\frac{1}{5^37^3}\)

B. \(\frac{6}{5^47^3}\)

C. \(\frac{45}{5^47^4}\)

D. \(\frac{180}{5^57^4}\)

E. \(\frac{900}{5^57^5}\)


We can create a common denominator of (5^5)(7^5) for each answer choice. The choice with the largest numerator will be the fraction with the greatest value:

A)

[1/(5^3)(7^3)][(5^2)(7^2)/(5^2)(7^2)]

Numerator = (5^2)(7^2) = 1225

B)

[6/(5^4)(7^3)][(5^1)(7^2)/(5^1)(7^2)]

Numerator = (6)(5^1)(7^2) = 1470

C)

[45/(5^4)(7^4)][(5^1)(7^1)/(5^1)(7^1)]

Numerator = (45)(5^1)(7^1) = 1575

D)

[180/(5^5)(7^4)][(7^1)/(7^1)]

Numerator = (180)(7^1) = 1260

E)

Numerator = 900

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

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New post 04 Oct 2018, 23:22
1
Bunuel wrote:
Which of the following has the greatest value?


A. \(\frac{1}{5^37^3}\)

B. \(\frac{6}{5^47^3}\)

C. \(\frac{45}{5^47^4}\)

D. \(\frac{180}{5^57^4}\)

E. \(\frac{900}{5^57^5}\)


Use the number properties we know:

Whenever we multiply a positive number by another number greater than 1, the number increases. Whenever we multiply it by a number less than 1, the number decreases.
e.g.

2 * (1/2) = 1 (multiplying by 1/2, decreases 2 to 1)

(1/3) * 2 = (2/3) (multiplying by 2 increases 1/3 to 2/3)

A. \(\frac{1}{5^37^3}\)

B. \(\frac{6}{5^47^3}\)

\(= \frac{6}{5} * (A)\) so this is greater than option (A). Eliminate (A)

C. \(\frac{45}{5^47^4}\)

\(= \frac{7.5}{7} * (B)\) so this is greater than option (B). Eliminate (B)

D. \(\frac{180}{5^57^4}\)

\(= \frac{4}{5} * (C)\) so this is less than option (C). Eliminate (D)

E. \(\frac{900}{5^57^5}\)

\(= \frac{20}{35} * (C)\) so this is less than option (C). Eliminate (E)

Answer (C)
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Re: Which of the following has the greatest value? &nbs [#permalink] 04 Oct 2018, 23:22
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