FDPs -- Help Evaluating Factorials

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laura003: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Feb 28, 2010 6:23 pm

by laura003 » Fri Apr 23, 2010 7:16 am

Hi All,

I'm a new poster -- but long-time reader -- of the BTG Forum looking for help on this question from a recent MGMAT CAT exam. I know the answer is D once you convert them all to a common denominator of 5(9!), but I'm struggling to understand why.

Could someone please offer up an explanation for why D is the correct choice? Specifically, the MGMAT CAT explanation says you should multiply answer choice D by 8 and 9 to get the common base -- and I don't understand why that 8 gets thrown in.

Thanks for your help!
Laura

Which of the following has the greatest value?
(A) 3/8!
(B) 6(4!)
5(9!)
(C) 4(3!)
9!
(D) 3
5(7!)
(E) 14
5(8!)

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Source: Beat The GMAT — Problem Solving | Fri Apr 23, 2010 7:16 am

akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Fri Apr 23, 2010 7:20 am

Answer choices are not in proper way.

Can you please arrange it?

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laura003: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Feb 28, 2010 6:23 pm

by laura003 » Fri Apr 23, 2010 7:23 am

Sorry about that. In the problem, MGMAT doesn't use the fraction bar on choices B, C, D, and E, it just has one number on top of the other w/o the bar in the middle, so I was trying to mimic that. For the purposes of clarity and legibility though, I'll add in the fraction bar on all the answer choices.

Which of the following has the greatest value?
(A) 3/8!
(B) 6(4!)/5(9!)
(C) 4(3!)/9!
(D) 3/5(7!)
(E) 14/5(8!)

Thanks!
Laura

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Fri Apr 23, 2010 7:27 am

(A) 3/8! = 135 / ( 5 * 9! )
(B) 6(4!)/5(9!) = 144 / ( 5 * 9! )
(C) 4(3!)/9! = 120 / ( 5 * 9! )
(D) 3/5(7!) = 216 / ( 5 * 9! )
(E) 14/5(8!) = 126 / ( 5 * 9! )

Hence D

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laura003: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Feb 28, 2010 6:23 pm

by laura003 » Fri Apr 23, 2010 7:32 am

Thanks for your quick reply. Why did you multiply by 8 on answer choice (D) to get 216/5(9!)?

I understand that you needed to multiply by 9 to get the 5(9!) denominator, but I'm not sure why the 8 was also necessary.

Thank you!

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Fri Apr 23, 2010 7:36 am

For comparison, it is better to compare in integer rather than fraction.

I made 5 * 9! at denominator.

All nominator become integer.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Apr 23, 2010 4:15 pm

laura003 wrote:Sorry about that. In the problem, MGMAT doesn't use the fraction bar on choices B, C, D, and E, it just has one number on top of the other w/o the bar in the middle, so I was trying to mimic that. For the purposes of clarity and legibility though, I'll add in the fraction bar on all the answer choices.

Which of the following has the greatest value?
(A) 3/8!
(B) 6(4!)/5(9!)
(C) 4(3!)/9!
(D) 3/5(7!)
(E) 14/5(8!)

Thanks!
Laura

Hi,

for (D), we're changing 7! to 9!.

Well, 9! = 9*8*7!

So, to get a denominator of 9!, we need to multiply the top and bottom of the fraction by 9*8:

3/5(7!) * (9*8)/(9*8)

= 3*9*8/5*(9*8*7!)

= 216 /5*(9!)

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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laura003: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Feb 28, 2010 6:23 pm

by laura003 » Sat Apr 24, 2010 5:28 am

Thank you both!

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govind_raj_76: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Apr 20, 2010 7:16 pm; Location: Newark, DE

by govind_raj_76 » Sat Apr 24, 2010 5:50 am

Akhilesh

How did u arrive at a common number ? Did u go by taking the max of dr 5(9!) in option B , made that a reference to change other options A,C,D and E ?

(A) 3/8! = 135 / ( 5 * 9! )
(B) 6(4!)/5(9!) = 144 / ( 5 * 9! )
(C) 4(3!)/9! = 120 / ( 5 * 9! )
(D) 3/5(7!) = 216 / ( 5 * 9! )
(E) 14/5(8!) = 126 / ( 5 * 9! )

Thanks,

Govind

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Sat Apr 24, 2010 5:59 am

Yes, we can say max of Denominators in this case.

But in general, if we have to compare fractional numbers, take the LCM of denominators and make the denominator common (LCM) so that we can compare Nominator only.

Usually, we should not play with the factional numbers as this is a time consuming.

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