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# Which of the following fractions has the greatest value?

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Intern
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Which of the following fractions has the greatest value? [#permalink]

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05 Jan 2010, 20:40
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Question Stats:

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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. $$\frac{14}{5(8!)}$$
[Reveal] Spoiler: OA
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06 Jan 2010, 11:38
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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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06 Jan 2010, 11:55
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06 Jan 2010, 12:07
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ppaulyni3 wrote:

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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07 Jan 2010, 07:38
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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03 Mar 2010, 06:44
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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03 Mar 2010, 09:39
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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03 Mar 2010, 12:30
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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, 11:38, edited 2 times in total.
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05 Mar 2010, 22:54
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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18 Apr 2010, 14:33
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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19 Apr 2010, 11:41
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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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03 Jan 2014, 07:04
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Re: Which of the following fractions has the greatest value? [#permalink]

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19 Mar 2015, 15:29
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Re: Which of the following fractions has the greatest value? [#permalink]

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09 May 2016, 07:51
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Re: Which of the following fractions has the greatest value? [#permalink]

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11 Nov 2016, 13:03
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] 11 Nov 2016, 13:03
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