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

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

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New post Updated on: 17 Apr 2012, 21:18
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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.
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For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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

Answer: E.
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Re: For any integer k greater than 1  [#permalink]

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New post 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.
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New post 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.
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New post 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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New post 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

Final Answer:

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

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New post 09 Dec 2019, 07:20
Bunuel wrote:
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 \(4*=\frac{1}{1}*\frac{1}{2}*\frac{1}{3}*\frac{1}{4}=\frac{1}{4!}\) --> \(\frac{5*}{4*}=\frac{4!}{5!}=\frac{1}{5}\).

Answer: E.



Hi Bunuel,

Please clarify me below doubt,

How can you sure that the value of t is 5, it can be 1 or 2 or 3 or 4 or 5. As it is mentioned t is an integer between 1 and k, inclusive.

Please help

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

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New post 09 Dec 2019, 17:17
Hi a12bansal,

In this prompt, "T" is not a value that we're trying to solve for - it's a variable that helps to define how we are supposed to do a calculating using the Symbol involved. Based on what we are told, we can calculate the value of 5*/4* (re: the numerator and denominator of the question).

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)

Looking at these two products, can you spot the parts that 'cancel out...?'

The (1/5) in the numerator is all that's left, meaning that the end value of the calculation is (1/5)/1 = 1/5. This does NOT mean that T = 5.

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

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New post 09 Dec 2019, 22:05
EMPOWERgmatRichC wrote:
Hi a12bansal,

In this prompt, "T" is not a value that we're trying to solve for - it's a variable that helps to define how we are supposed to do a calculating using the Symbol involved. Based on what we are told, we can calculate the value of 5*/4* (re: the numerator and denominator of the question).

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)

Looking at these two products, can you spot the parts that 'cancel out...?'

The (1/5) in the numerator is all that's left, meaning that the end value of the calculation is (1/5)/1 = 1/5. This does NOT mean that T = 5.

GMAT assassins aren't born, they're made,
Rich



Thanks a lot :) EMPOWERgmatRichC
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Re: For any integer k greater than 1, the symbol k* denotes the   [#permalink] 09 Dec 2019, 22:05
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