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S is the set of all fractions

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S is the set of all fractions [#permalink] New post 14 May 2018, 14:05
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S is the set of all fractions of the form \(\frac{n}{n+1}\), where n is a positive integer less than 20.

Quantity A
Quantity B
The product of all the fractions that are in S
\(\frac{1}{20}\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: S is the set of all fractions [#permalink] New post 15 May 2018, 06:28
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From the given expression,
1st fraction = \(1/2\)
2nd fraction = \(2/3\)
3rd fraction = \(3/4\)

Here we can observe a \(pattern\)
the numerator begins with 1 and ultimately will end in 19
the denominator begins with 2 and ultimately will end in 20

when we multiply all the fractions our end product will be \(\frac{1*2*3*4*5.........19}{2*3*4*5.......20}\)At this point we can cancel off all the numerators except 1 with all the denominators except 20 finally reducing the term to \(1/20\)
option c
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Re: S is the set of all fractions [#permalink] New post 01 Oct 2019, 09:25
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Expert's post
Carcass wrote:
S is the set of all fractions of the form \(\frac{n}{n+1}\), where n is a positive integer less than 20.

Quantity A
Quantity B
The product of all the fractions that are in S
\(\frac{1}{20}\)



Let's get a better idea of what Set S looks like.
We're told that n can have any integer value from 1 to 19 inclusive.

When n = 1, the corresponding fraction is \(\frac{1}{1+1}=\frac{1}{2}\)

When n = 2, the corresponding fraction is \(\frac{2}{2+1}=\frac{2}{3}\)

When n = 3, the corresponding fraction is \(\frac{3}{3+1}=\frac{3}{4}\)
.
.
.
.
.
When n = 18, the corresponding fraction is \(\frac{18}{18+1}=\frac{18}{19}\)

When n = 19, the corresponding fraction is \(\frac{19}{19+1}=\frac{19}{20}\)

So, Quantity B \(= (\frac{1}{2})(\frac{2}{3})(\frac{3}{4})(\frac{4}{5})......(\frac{17}{18})(\frac{18}{19})(\frac{19}{20})\)

\(=\frac{(1)(2)(3)(4)(5)....(17)(18)(19)}{(2)(3)(4)(5)....(17)(18)(19)(20)}\)

\(=\frac{1}{20}\)


We get:
QUANTITY A: \(\frac{1}{20}\)

QUANTITY B: \(\frac{1}{20}\)

Answer: C

Cheers,
Brent
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Re: S is the set of all fractions [#permalink] New post 24 Dec 2019, 06:14
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A -> (1/2) (2/3) (3/4) .....(19/20)
Cancelling the denominator of the term with the numerator of next term
= 1/20

A = B

Hence, C is the Answer.
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Re: S is the set of all fractions [#permalink] New post 26 Dec 2019, 20:41
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When n = 1 the fraction is \(\frac{1}{2}\).
Now, A says product of all the fractions that are in S.
It means \(\frac{1}{2}*\frac{2}{3}*.....\frac{19}{20}\) Since N is less than 20.
The denominator and numerator will cancel out and we will be left with \(\frac{1}{20}\)

Hence, C
Carcass wrote:
S is the set of all fractions of the form \(\frac{n}{n+1}\), where n is a positive integer less than 20.

Quantity A
Quantity B
The product of all the fractions that are in S
\(\frac{1}{20}\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Re: S is the set of all fractions   [#permalink] 26 Dec 2019, 20:41
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