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# Which of the following fractions has the greatest value?

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Intern
Joined: 06 Dec 2009
Posts: 3
Which of the following fractions has the greatest value?  [#permalink]

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05 Jan 2010, 19:40
4
14
00:00

Difficulty:

65% (hard)

Question Stats:

66% (02:15) correct 34% (02:14) wrong based on 512 sessions

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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. $$\frac{14}{5(8!)}$$
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Re: math question  [#permalink]

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06 Jan 2010, 10:38
3
3
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) $$\frac{14}{5(8!)}= \frac{2.8}{8!}$$
##### General Discussion
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Re: math question  [#permalink]

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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]

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06 Jan 2010, 11:07
2
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]

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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]

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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]

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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.
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]

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Updated on: 19 Apr 2010, 10:38
3
2
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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Originally posted by jeeteshsingh on 03 Mar 2010, 11:30.
Last edited by jeeteshsingh on 19 Apr 2010, 10:38, edited 2 times in total.
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Re: Fraction factorial-mgmat  [#permalink]

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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]

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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]

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19 Apr 2010, 10:41
3
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: Which of the following fractions has the greatest value?  [#permalink]

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11 Nov 2016, 12:03
What we can do here is we can make 8! as the common denominator and then compare the fractions w.r.t their numerators.
numerators after making 8! as the common denominator =>
3
3.2
2.something
4.something
2.8

Clearly D will the greatest fraction.
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Re: Which of the following fractions has the greatest value?  [#permalink]

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# Which of the following fractions has the greatest value?

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