approach in factorials

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approach in factorials

by alltimeacheiver » Mon Apr 18, 2011 9:33 pm
Which of the following fractions has the greatest value?
3/8!


6(4!)/5(9!)


4(3!)/9!


3/5(7!)



14/5(8!)

I solved this question by a small approch that inorder to have gratest value of fractions, we need to have smallest number in numerator and denominator needs to be highest so I clicked an option while scanning all the case, the option d. But still looking fr an small approach to sove factorial terms
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by Anurag@Gurome » Mon Apr 18, 2011 9:42 pm
alltimeacheiver wrote:Which of the following fractions has the greatest value?
3/8!


6(4!)/5(9!)


4(3!)/9!


3/5(7!)



14/5(8!)

I solved this question by a small approch that inorder to have gratest value of fractions, we need to have smallest number in numerator and denominator needs to be highest so I clicked an option while scanning all the case, the option d. But still looking fr an small approach to sove factorial terms
Another approach: Let's make the denominators equal.

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

So, 216/5*9! has the greatest value.

The correct answer is D.
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