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(1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?

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Math Revolution GMAT Instructor
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(1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 16 Oct 2018, 23:41
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (00:54) correct 14% (01:13) wrong based on 37 sessions

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[Math Revolution GMAT math practice question]

\((1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?\)

\(A. \frac{1}{10}\)
\(B. \frac{9}{10}\)
\(C. \frac{9}{100}\)
\(D. \frac{1}{100}\)
\(E. \frac{9}{50}\)

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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 16 Oct 2018, 23:49
1
The question can be reduced to \(\frac{9}{10}*\frac{10}{11}*\frac{11}{12}\).....\(\frac{98}{99}*\frac{99}{100}\).

All the terms will be canceled except 9/100.

C is the answer.
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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 17 Oct 2018, 00:17
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\((1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?\)

\(A. \frac{1}{10}\)
\(B. \frac{9}{10}\)
\(C. \frac{9}{100}\)
\(D. \frac{1}{100}\)
\(E. \frac{9}{50}\)



So we are asked to find
(1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100})

=9/10 * 10/11* 11/12 *...will go on till 99/100
= 9/10 * 10/11* 11/12 *...will go on till99/100
=9/100


Press Kudos if helps!!
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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 17 Oct 2018, 00:18
MathRevolution wrote:
[Math Revolution GMAT math practice question]


\(A. \frac{1}{10}\)
\(B. \frac{9}{10}\)
\(C. \frac{9}{100}\)
\(D. \frac{1}{100}\)
\(E. \frac{9}{50}\)



So we are asked to find
\((1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?\)


=9/10 * 10/11* 11/12 *...will go on till 99/100
= 9/10 * 10/11* 11/12 *...will go on till99/100
=9/100


Press Kudos if helps!!
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(1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 17 Oct 2018, 00:24
1
Product will yield the following:

9/10 * 10/11 * 11/12 * ... * 99/100

So, for the numerator we have: 99!/8!

and for the denominator we have: 100!/9!

numerator/denominator = (99!/8!)/(100!/9!) = (99!*9!)/(100!*8!)

simplifying we get 9/100

ANSWER C
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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 17 Oct 2018, 00:28
MarcoAD wrote:
Product will yield the following:

9/10 * 10/11 * 11/12 * ... * 99/100

So, for the numerator we have: 99!/8!

and for the denominator we have: 100!/9!

numerator/denominator = (99!/8!)/(100!/9!) = (99!*9!)/(100!*8!)

simplifying we get 9/100

ANSWER C


This is a nice approach..
Imagining in terms of factorial ..Makes life simpler :)
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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 17 Oct 2018, 18:09
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\((1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) =?\)

\(A. \frac{1}{10}\)
\(B. \frac{9}{10}\)
\(C. \frac{9}{100}\)
\(D. \frac{1}{100}\)
\(E. \frac{9}{50}\)


Starting with the first 4 factors we have:

(1-1/10)(1-1/11)(1-1/12)(1 - 1/13)

(9/10)(10/11)(11/12)(12/13) = 9/13

So we see only the first numerator and last denominator remain; thus, the product is 9/100.

Answer: C
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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?  [#permalink]

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New post 19 Oct 2018, 00:05
=>

\((1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100}) = (\frac{9}{10})(\frac{10}{11})(\frac{11}{12})…(\frac{99}{100}) = \frac{9}{100}.\)
Therefore, C is the answer.
Answer: C
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Re: (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? &nbs [#permalink] 19 Oct 2018, 00:05
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