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

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06 Dec 2010, 18:36

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68% (00:52) correct
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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* ?

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.

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 \(4*=\frac{1}{1}*\frac{1}{2}*\frac{1}{3}*\frac{1}{4}=\frac{1}{4!}\) --> \(\frac{5*}{4*}=\frac{4!}{5!}=\frac{1}{5}\).

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

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09 Jan 2014, 11:02

Hello from the GMAT Club BumpBot!

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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, 01:19

Hello from the GMAT Club BumpBot!

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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:

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

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06 Sep 2016, 21:17

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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18 Sep 2017, 18:33

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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