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# Fraction factorial-mgmat

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Fraction factorial-mgmat [#permalink]  03 Mar 2010, 05:23
00:00

Difficulty:

5% (low)

Question Stats:

77% (01:49) correct 22% (01:11) wrong based on 9 sessions
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.
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Re: Fraction factorial-mgmat [#permalink]  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]  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.

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]  03 Mar 2010, 11:30
1
KUDOS
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]  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..
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Re: Fraction factorial-mgmat [#permalink]  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]  19 Apr 2010, 00:54
great explanations !
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Re: Fraction factorial-mgmat [#permalink]  19 Apr 2010, 10:41
3
KUDOS
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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JT...........
If u like my post..... payback in Kudos!!

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~~Better Burn Out... Than Fade Away~~

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Posts: 26
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Kudos [?]: 1 [0], given: 3

Re: Fraction factorial-mgmat [#permalink]  19 Apr 2010, 15:30
wonderful response.....lots of kudos!
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Re: Fraction factorial-mgmat [#permalink]  25 Apr 2010, 03:37
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 = 7/20 * 1/7! [corrected this!]

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

excellent ... kudos +1
Re: Fraction factorial-mgmat   [#permalink] 25 Apr 2010, 03:37
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