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ajit257
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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.
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apologies for that ..thanks
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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

Final Answer:
GMAT assassins aren't born, they're made,
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Bunuel
ajit257
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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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
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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


Thanks a lot :) EMPOWERgmatRichC
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Bunuel
ajit257
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 are:

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.

How did you decide that 1 & K were both inclusive to the range, I interpreted as both are not part of the range hence my answer is different
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AmandeepSingh0796
Bunuel
ajit257
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 are:

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.

How did you decide that 1 & K were both inclusive to the range, I interpreted as both are not part of the range hence my answer is different


The stem says that both 1 and k are inclusive. Check the highlighted part above. Hope it helps.
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Ans: 1/5.

I think the key to the question is in understanding the questions i.e. the K* part.

Possible mistake to avoid: I initially jumped into question with solving mindset only to find that perhaps I need moment of reflection to solve it rather efficiently.
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