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# If k is a positive integer, then k is defined as the product of all t

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Re: If k is a positive integer, then k is defined as the product of all t [#permalink]
Top Contributor
IIMC wrote:
GMATPrepNow wrote:
vikasp99 wrote:
If k is a positive integer, then k@ is defined as the product of all the fractions of the form 1/S, where S is a positive integer not greater than k. What is the value of 5@/4@?

A. 1/5

B. 4/5

C. 1

D. 5/4

E. 5

5@/4@ = (1/1)(1/2)(1/3)(1/4)(1/5)/(1/1)(1/2)(1/3)(1/4)
= 1/5

Cheers,
Brent

**Hi, It said S can be less than or equal to K, so for @5 the value of S could be 1,2,3,4 or 5 and for @4 the value of S could be 1,2,3,4...so while calculating @5/@4 with value of S as 4 for @5 and similarly S=4 for @4 the answer would be 1...So there is lots of ambiguity in this question.

But the questions say "....all the fractions of the form 1/S"

Cheers,
Brent
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Re: If k is a positive integer, then k is defined as the product of all t [#permalink]
Asked: If k is a positive integer, then kis defined as the product of all the fractions of the form 1/S, where S is a positive integer not greater than k. What is the value of 5@/4@?

5@ = 1/1 * 1/2 * 1/3 * 1/4 * 1/5 = 1/5!
4@ = 1/1 * 1/2 * 1/3 * 1/4 = 1/4!
5@/4@ = 4!/5! = 1/5

IMO A
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Re: If k is a positive integer, then k is defined as the product of all t [#permalink]
Top Contributor
Given that k[b]is defined as the product of all the fractions of the form 1/S, where S is a positive integer not greater than k and we need to find the value of 5@/4@[/b]

Lets start by finding the value of 5@

5@ = the product of all the fractions of the form 1/S, where S is a positive integer not greater than 5. => 1 ≤ S ≤ 5
=> 5@ = $$\frac{1}{1} * \frac{1}{2} * \frac{1}{3} * \frac{1}{4} * \frac{1}{5}$$

Similarly, 4@ = $$\frac{1}{1} * \frac{1}{2} * \frac{1}{3} * \frac{1}{4}$$

=> 5@/4@ = ($$\frac{1}{1} * \frac{1}{2} * \frac{1}{3} * \frac{1}{4} * \frac{1}{5}$$) / ($$\frac{1}{1} * \frac{1}{2} * \frac{1}{3} * \frac{1}{4}$$)

All terms will cancel out except $$\frac{1}{5}$$