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# Which of the following has the greatest value?

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Math Expert
Joined: 02 Sep 2009
Posts: 43803
Which of the following has the greatest value? [#permalink]

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29 Aug 2017, 22:48
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Difficulty:

95% (hard)

Question Stats:

45% (01:38) correct 55% (01:31) wrong based on 153 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. $$\frac{900}{5^57^5}$$
[Reveal] Spoiler: OA

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

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29 Aug 2017, 23:21
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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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.

[Reveal] Spoiler:
C

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

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02 Sep 2017, 06:17
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

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Re: Which of the following has the greatest value?   [#permalink] 02 Sep 2017, 06:17
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