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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # 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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14 00:00

Difficulty:   25% (medium)

Question Stats: 69% (01:16) correct 31% (01:30) wrong based on 412 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
Math Expert V
Joined: 02 Sep 2009
Posts: 60480
For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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9
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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##### General Discussion
Manager  Joined: 13 Jul 2010
Posts: 99
Re: For any integer k greater than 1  [#permalink]

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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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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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apologies for that ..thanks
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
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Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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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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Intern  B
Joined: 13 Dec 2018
Posts: 26
Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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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.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
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Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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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
_________________
Intern  B
Joined: 13 Dec 2018
Posts: 26
Re: For any integer k greater than 1, the symbol k* denotes the  [#permalink]

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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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