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Which of the following fractions has the greatest value?

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Which of the following fractions has the greatest value? [#permalink] New post 05 Jan 2010, 19:40
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A
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48% (02:11) correct 52% (01:01) wrong based on 78 sessions
Which of the following fractions has the greatest value?

A. \frac {3}{8!}

B. \frac{6(4!)}{5(9!)}

C. \frac{4(3!)}{9!}

D. \frac{3}{5(7!)}

E. \frac{14}{5(8!)}
[Reveal] Spoiler: OA
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Re: math question [#permalink] New post 06 Jan 2010, 10:38
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a)\frac {3}{8!}

b) \frac{6(4!)}{5(9!)} = \frac{3.2}{8!}

c)\frac{4(3!)}{9!} = \frac{2.(6)}{8!}

d) \frac{3}{5(7!)} = \frac{4.8}{8!} < - - - Greatest fraction

e) \frac{14}{5(8!)}= \frac{2.8}{8!}
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Re: math question [#permalink] New post 06 Jan 2010, 10:55
Thanks Shalva! Could please explain your answer? I dont quite get it.
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Re: math question [#permalink] New post 06 Jan 2010, 11:07
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ppaulyni3 wrote:
Thanks Shalva! Could please explain your answer? I dont quite get it.



You should manipulate fractions in order to get them to some common denominator. Then the one with greatest numerator has the greatest value

The math here is quite simple.

9! = 8! * 9

To get 8! from 7! in answer (d) you should multiply both the numerator and denominator by 8 : 7! * 8 = 8!

These are the only points worth mentioning
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Re: math question [#permalink] New post 07 Jan 2010, 06:38
ppaulyni3 wrote:
Which of the following fractions has the greatest value?


a) [3][/8!]


b) [6(4!)][/5(9!)]


c) [4(3!)][/9!]

d) [3][/5(7!)]

e) [14][/5(8!)]


I'm having some difficulties solving this one. Can someone help me!


convert the fractions to some common factor

a)[3/8!]=k*(3/8)

b) [6(4!)][/5(9!)]=k*(4!/60)

c) [4(3!)][/9!]=k*{(4*3!)/72}

d) [3][/5(7!)]=k*(3/5)

e) [14][/5(8!)]=k*(14/40)


where k =(1/7!)
it is easy to solve it now..clearly D has the maximum value

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Re: Fraction factorial-mgmat [#permalink] New post 03 Mar 2010, 05:44
IMO D

Compare a and b

a = 3/8! and b = (6*4!)/5*9! = (16/15)* (3/8!)

=> b>a

now compare a and c

c = 4*3!/9! = (8/9)* (3/8!) => a<c
so among a b c b is greatest.

Now d = 3/(5*7!) = (3/8!) *8/5 so d>b

now e =14/(5*8!) multiple num and dem by 3

=> e = (14/15)* (3/8!)

Thus d is greatest.

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Re: Fraction factorial-mgmat [#permalink] New post 03 Mar 2010, 08:39
joyseychow wrote:
Which of the following fractions has the greatest value?

A. 3/8!
B. 6(4!) / 5(9!)
C. 4(3!) / 9!
D. 3 / 5(7!)
E. 14 / 5(8!)
Where do I start? I can't see any similarities to narrow the down the answer. :?
[Reveal] Spoiler:
OA is D.


Make denominator same and compare numerator.
Whichever numerator is large that fraction has greatest value.

Start with A & E
A = 15/5(8!) > E
then A & D
D= 24/5(8!) > A
Now compare B & C
c= 5!/5(9!) < B

Now B & D
D = (24 * 9)/5(9!) = 9(4!)/5(9!) > 6(4!) / 5(9!) hence D.
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Re: Fraction factorial-mgmat [#permalink] New post 03 Mar 2010, 11:30
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joyseychow wrote:
Which of the following fractions has the greatest value?

A. 3/8!

B. 6(4!) / 5(9!)

C. 4(3!) / 9!

D. 3 / 5(7!)

E. 14 / 5(8!)

Where do I start? I can't see any similarities to narrow the down the answer. :?


My Approach:

Check the lowest denominator u could take common. It's 7!

A = 3/8 * 1/7!
B = 2/5 * 1/7!
C = 1/3 * 1/7!
D = 3/5 * 1/7!
E = 7/20 * 1/7! [corrected this!]

Now compare - 3/8, 2/5, 1/3, 3/5, 7/20. Largest is 3/5... Hence D

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Last edited by jeeteshsingh on 19 Apr 2010, 10:38, edited 2 times in total.
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Re: Fraction factorial-mgmat [#permalink] New post 05 Mar 2010, 21:54
jeeteshsingh wrote:
joyseychow wrote:
Which of the following fractions has the greatest value?

A. 3/8!

B. 6(4!) / 5(9!)

C. 4(3!) / 9!

D. 3 / 5(7!)

E. 14 / 5(8!)

Where do I start? I can't see any similarities to narrow the down the answer. :?


My Approach:

Check the lowest denominator u could take common. It's 7!

A = 3/8 * 1/7!
B = 2/5 * 1/7!
C = 1/3 * 1/7!
D = 3/5 * 1/7!
E = 1/20 * 1/7!

Now compare - 3/8, 2/5, 1/3, 3/5, 1/20. Largest is 3/5... Hence D



jeeteshsingh ,
your approach was very smart and simple!
i found i was calculating value of each and every option.. which was very time consuming..
Kudos to u for this.. :cool

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Re: Fraction factorial-mgmat [#permalink] New post 18 Apr 2010, 13:33
Joseph

Which of the following fractions has the greatest value?

A. 3/8!
B. 6(4!) / 5(9!)
C. 4(3!) / 9!
D. 3 / 5(7!)
E. 14 / 5(8!)


Check the lowest denominator u could take common. It's 7!

A = 3/8 * 1/7!
B = 2/5 * 1/7!
C = 1/3 * 1/7!
D = 3/5 * 1/7!
E = 1/20 * 1/7!


How did you convert the second fraction (as well as the 3rd and the 4th and the 5th) for example how did 6(4!)/5(9!) became 2/5???
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Re: Fraction factorial-mgmat [#permalink] New post 19 Apr 2010, 10:41
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Almontas33 wrote:
Joseph

Which of the following fractions has the greatest value?

A. 3/8!
B. 6(4!) / 5(9!)
C. 4(3!) / 9!
D. 3 / 5(7!)
E. 14 / 5(8!)


Check the lowest denominator u could take common. It's 7!

A = 3/8 * 1/7!
B = 2/5 * 1/7!
C = 1/3 * 1/7!
D = 3/5 * 1/7!
E = 1/20 * 1/7!


How did you convert the second fraction (as well as the 3rd and the 4th and the 5th) for example how did 6(4!)/5(9!) became 2/5???


I haven't converted anything. I have reduced the fractions after taking out 7! common in the denominator.

E.g.: \frac{6(4!)}{5(9!)}=\frac{6*24}{5*9*8*7!}=\frac{2}{5*7!}
Similarly the others..... Hope this helps.

By the way I corrected the E value in my post too. Please have a look again!

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Re: Fraction factorial-mgmat [#permalink] New post 03 Jan 2014, 06:04
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Re: Fraction factorial-mgmat   [#permalink] 03 Jan 2014, 06:04
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