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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: 146
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
14
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:16) correct 31% (01:30) wrong based on 413 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: 60515
For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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07 Dec 2010, 02:52
2
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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 $$4*=\frac{1}{1}*\frac{1}{2}*\frac{1}{3}*\frac{1}{4}=\frac{1}{4!}$$ --> $$\frac{5*}{4*}=\frac{4!}{5!}=\frac{1}{5}$$.

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Manager
Joined: 13 Jul 2010
Posts: 99
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: 99
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: 146
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

GMAT assassins aren't born, they're made,
Rich
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Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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

Hi Bunuel,

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.

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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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.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Joined: 13 Dec 2018
Posts: 26
Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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