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Demetri has trouble spelling the word “banana.” Whenever he tries to

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Demetri has trouble spelling the word “banana.” Whenever he tries to [#permalink]

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New post 06 Mar 2017, 04:35
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54% (01:01) correct 46% (01:02) wrong based on 59 sessions

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Demetri has trouble spelling the word “banana.” Whenever he tries to spell the word, he writes the letters “ba,” then writes “na” one or more times, then stops. Every time Demetri writes the letters “na” there is a 60% chance that he will write the letters “na” again (otherwise he stops). When Demetri tries to spell the word “banana,” what percent of the time does Demetri spell “banana” correctly?

A. 14.4%
B. 24%
C. 36%
D. 40%
E. 60%
[Reveal] Spoiler: OA

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Re: Demetri has trouble spelling the word “banana.” Whenever he tries to [#permalink]

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Demetria has to spell twice "na" to say banana correctly

Then there is 100% that we will write the first "na"
Then 60 % to write the second one
Then now, he has 40% to stop writing (100-60)

100% * 60% * 40% = 24% Answer B
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Demetri has trouble spelling the word “banana.” Whenever he tries to [#permalink]

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New post 20 Mar 2017, 18:45
Bunuel wrote:
Demetri has trouble spelling the word “banana.” Whenever he tries to spell the word, he writes the letters “ba,” then writes “na” one or more times, then stops. Every time Demetri writes the letters “na” there is a 60% chance that he will write the letters “na” again (otherwise he stops). When Demetri tries to spell the word “banana,” what percent of the time does Demetri spell “banana” correctly?

A. 14.4%
B. 24%
C. 36%
D. 40%
E. 60%


OFFICIAL SOLUTION

In order for Demetri to spell "banana" correctly, he must write the letters "ba" (it is given that he will do so), and then write the letters "na" (it is also given that he will do this at least the first time), and then write the letters "na" again (this happens 60% of the time), and then not write the letters "na" again (this happens 100%−60%=40% of the time).

Thus, since "and" means "multiply," Demetri spells "banana" correctly 60%∗40%=24% of the time. This is B.
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Demetri has trouble spelling the word “banana.” Whenever he tries to   [#permalink] 20 Mar 2017, 18:45
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