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Rank these three quantities from least to greatest.

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Joined: 02 Sep 2009
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Rank these three quantities from least to greatest.  [#permalink]

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New post 23 Oct 2018, 04:09
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:28) correct 40% (01:45) wrong based on 139 sessions

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Re: Rank these three quantities from least to greatest.  [#permalink]

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New post 23 Oct 2018, 04:34
Bunuel wrote:
Consider these three quantities:

Ⅰ. \(\frac{49!}{48!}\)

Ⅱ. \(\frac{49!}{(7!)^2}\)

Ⅲ. \(\frac{49!}{(42!)(7!)}\)

Rank these three quantities from least to greatest.


A. I, II, III
B. I, III, II
C. II, I, III
D. II, III, I
E. III, I, II



Ⅰ. \(\frac{49!}{48!} = \frac{49*48!}{48!} = 49\)

Ⅱ. \(\frac{49!}{(7!)^2} = 7*8*47*23*3*11*43*42!/7!\)

Ⅲ. \(\frac{49!}{(42!)(7!)} = \frac{49*48*47*46*45*44*43*42!}{42!7!}= 7*8*47*23*3*11*43\)

From the above expressions it clear that II is largest and I is smallest

Answer: Option B
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Rank these three quantities from least to greatest.  [#permalink]

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New post 18 Jan 2019, 16:08
Just by canceling 7! we can reach to the answer:

Ⅰ. \(\frac{49!}{48!} = \frac{49*48!}{48!} = 49\)

Ⅱ. \(\frac{49!}{(7!)^2}\)

Ⅲ. \(\frac{49!}{(42!)(7!)}\)

Both Ⅱ and Ⅲ have at least one 7!.

Cancel one of them from each.

Hence, \(\frac{49!}{7!}\) > \(\frac{49!}{42!}\)

B
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Rank these three quantities from least to greatest.   [#permalink] 18 Jan 2019, 16:08
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