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# For any integer k greater than 1, the symbol k* denotes the

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Manager
Joined: 28 Aug 2010
Posts: 149
For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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Updated on: 17 Apr 2012, 21:18
2
13
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:16) correct 30% (01:33) wrong based on 370 sessions

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For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/4* ?

A. 5
B. 5/4
C. 4/5
D. 1/4
E. 1/5

Originally posted by ajit257 on 06 Dec 2010, 18:36.
Last edited by Bunuel on 17 Apr 2012, 21:18, edited 1 time in total.
Edited the question
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Joined: 02 Sep 2009
Posts: 59561
For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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07 Dec 2010, 02:52
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ajit257 wrote:
For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form t1, where t is an integer between 1 and k, inclusive. What is the value of *4/*5?
A. 5
B. 5/4
C. 4/5
D. 1/4
E. 1/5

ajit257 please check the questions when posting.

Original questions is:

For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/4* ?

A. 5
B. 5/4
C. 4/5
D. 1/4
E. 1/5

As k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive then $$5*=\frac{1}{1}*\frac{1}{2}*\frac{1}{3}*\frac{1}{4}*\frac{1}{5}=\frac{1}{5!}$$ and $$4*=\frac{1}{1}*\frac{1}{2}*\frac{1}{3}*\frac{1}{4}=\frac{1}{4!}$$ --> $$\frac{5*}{4*}=\frac{4!}{5!}=\frac{1}{5}$$.

##### General Discussion
Manager
Joined: 13 Jul 2010
Posts: 100
Re: For any integer k greater than 1  [#permalink]

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06 Dec 2010, 20:47
I initially picked C, but read the question more carefully.

For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form t1, where t is an integer between 1 and k, inclusive.

so given these definitions *4/*5 = 4!/5! or 4*3*2*1/5*4*3*2*1 which gives you 1/5, option E.
Manager
Joined: 13 Jul 2010
Posts: 100
Re: For any integer k greater than 1  [#permalink]

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07 Dec 2010, 17:50
Great catch Bunuel, and I got the answer right even though i the question was incorrectly stated. Got lucky I guess.
Manager
Joined: 28 Aug 2010
Posts: 149
Re: For any integer k greater than 1  [#permalink]

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08 Dec 2010, 05:29
apologies for that ..thanks
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Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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03 Apr 2015, 11:22
Hi All,

When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.

Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.

Based on this definition....

IF....
K = 2
K* = (1/1)(1/2) = 1/2

IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6

Etc.

We're asked to find the value of 5*/4*

Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....

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

Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'

4* = (1/1)(1/2)(1/3)(1/4)

We're looking for the value of:

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

Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:

1/5

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Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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20 Nov 2019, 15:39
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Re: For any integer k greater than 1, the symbol k* denotes the   [#permalink] 20 Nov 2019, 15:39
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