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M06-01
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Bunuel
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M06-01 [#permalink] New post  15 Sep 2014, 23:26
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\(\frac{15^{11} - 15^{10}}{14} = ?\)

A. \(\frac{1}{14}\)
B. \(\frac{15}{14}\)
C. \(\frac{15^{10}}{14}\)
D. \(15^{10}\)
E. 1
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Re: M06-01 [#permalink] New post  25 Sep 2019, 09:34
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\(\frac{15^1^1 - 15^1^0}{14}\)

\(\frac{15^1^0(15-1)}{14}\)

\(\frac{15^1^0(14)}{14}\)

\(15^1^0\)

The correct answer is answer choice D.


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Bunuel
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Re M06-01 [#permalink] New post  15 Sep 2014, 23:26
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\(\frac{15^{11} - 15^{10}}{14} = ?\)

A. \(\frac{1}{14}\)
B. \(\frac{15}{14}\)
C. \(\frac{15^{10}}{14}\)
D. \(15^{10}\)
E. 1

Factor out \(15^{10}\): \(15^{10} * \frac{(15 - 1)}{14} = 15^{10}\).

Answer: D
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Bunuel
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Re: M06-01 [#permalink] New post  19 Mar 2021, 13:15
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inlotr wrote:
Why is 15\(11\) - 15\(10\) = 15\(10\)* (15-1)? Why is there a -1?



\(15^{11}-15^{10}=15*15^{10}-1*15^{10}=15^{10}(15-1)=15^{10}*14\).
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Re: M06-01 [#permalink] New post  16 Jun 2020, 06:35
\(\frac{15^{11} - 15^{10}}{14} = ?\)

A. \(\frac{1}{14}\)
B. \(\frac{15}{14}\)
C. \(\frac{15^{10}}{14}\)
D. \(15^{10}\) --> correct: \(\frac{15^{11} - 15^{10}}{14} = 15^{10}*\frac{15 - 1}{14} = 15^{10}\)
E. 1
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NITI2021
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Re: M06-01 [#permalink] New post  08 Mar 2021, 20:44
Answer is option D.
We can take 15^10 outside and then 14 in numerator and denominator will get cancelled finally giving the answer as 15^10.
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inlotr
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Re: M06-01 [#permalink] New post  19 Mar 2021, 13:09
Why is 15\(11\) - 15\(10\) = 15\(10\)* (15-1)? Why is there a -1?
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Re: M06-01 [#permalink]
19 Mar 2021, 13:09
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