[Math Revolution GMAT math practice question]
(1-1/10)(1-1/11)(1-1/12)...(1-1/100) =?
A. 1/10
B. 9/10
C. 9/100
D. 1/100
E. 9/50
(1-1/10)(1-1/11)(1-1/12)…(1-1/100) =?
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- Max@Math Revolution
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(1-1/10)(1-1/11)(1-1/12)...(1-1/99)(1-1/100)Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
(1-1/10)(1-1/11)(1-1/12)...(1-1/100) =?
A. 1/10
B. 9/10
C. 9/100
D. 1/100
E. 9/50
= (9/10)(10/11)(11/12)....(98/99)(99/100).
The values in blue all cancel out, leaving only the values in red:
9/100.
The correct answer is C.
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- fskilnik@GMATH
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\[? = \left( {1 - \frac{1}{{10}}} \right)\left( {1 - \frac{1}{{11}}} \right)\left( {1 - \frac{1}{{12}}} \right) \ldots \left( {1 - \frac{1}{{100}}} \right)\]Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
(1-1/10)(1-1/11)(1-1/12)...(1-1/100) =?
A. 1/10
B. 9/10
C. 9/100
D. 1/100
E. 9/50
Just look for a PATTERN:
\[1 - \frac{1}{{\boxed{10}}} = \frac{9}{{\boxed{10}}}\,\,\]
\[\left( {1 - \frac{1}{{10}}} \right)\left( {1 - \frac{1}{{\boxed{11}}}} \right) = \frac{9}{{10}} \cdot \frac{{10}}{{11}} = \frac{9}{{\boxed{11}}}\]
\[\left( {1 - \frac{1}{{10}}} \right)\left( {1 - \frac{1}{{11}}} \right)\left( {1 - \frac{1}{{\boxed{12}}}} \right) = \frac{9}{{10}} \cdot \frac{{10}}{{11}} \cdot \frac{{11}}{{12}} = \frac{9}{{\boxed{12}}}\,\,\]
\[\left( {1 - \frac{1}{{10}}} \right)\left( {1 - \frac{1}{{11}}} \right)\left( {1 - \frac{1}{{12}}} \right)\left( {1 - \frac{1}{{\boxed{13}}}} \right) = \frac{9}{{10}} \cdot \frac{{10}}{{11}} \cdot \frac{{11}}{{12}} \cdot \frac{{12}}{{13}} = \frac{9}{{\boxed{13}}}\]
\[ \ldots \]
\[? = \left( {1 - \frac{1}{{10}}} \right)\left( {1 - \frac{1}{{11}}} \right)\left( {1 - \frac{1}{{12}}} \right) \ldots \left( {1 - \frac{1}{{\boxed{100}}}} \right) = \frac{9}{{\boxed{100}}}\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Starting with the first 4 factors we have:Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
(1-1/10)(1-1/11)(1-1/12)...(1-1/100) =?
A. 1/10
B. 9/10
C. 9/100
D. 1/100
E. 9/50
(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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- Max@Math Revolution
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=>
(1-1/10)(1-1/11)(1-1/12)...(1-1/100) = (9/10)(10/11)(11/12)...(99/100) = 9/100.
Therefore, C is the answer.
Answer: C
(1-1/10)(1-1/11)(1-1/12)...(1-1/100) = (9/10)(10/11)(11/12)...(99/100) = 9/100.
Therefore, C is the answer.
Answer: C
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