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A market survey showed that 76 percent of the visitors at a certain re

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A market survey showed that 76 percent of the visitors at a certain re  [#permalink]

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New post 09 Jul 2018, 06:11
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A
B
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E

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Question Stats:

78% (02:07) correct 22% (02:21) wrong based on 86 sessions

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A market survey showed that 76 percent of the visitors at a certain resort came from Pacific or southwestern states. Of these, (2/3) were from California, and 87 percent of the Californians were from southern California. Approximately what percent of the visitors at the resort were from southern California?

(A) 40%
(B) 45%
(C) 50%
(D) 55%
(E) 65%

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Re: A market survey showed that 76 percent of the visitors at a certain re  [#permalink]

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New post 09 Jul 2018, 06:18

Solution



Given:
    • A market survey showed that 76 percent of the visitors at a certain resort came from Pacific or southwestern states
    • Of these, \(\frac{2}{3}\) were from California, and 87 percent of the Californians were from southern California

To find:
    • The approximate percent of the visitors at the resort who were from southern California

Approach and Working:
If we assume the total visitors to be 100,
    • Visitors from Pacific or southwestern states = 76% of 100 = 76
    • Visitors from California = \(76 * \frac{2}{3} = 50\)(approx.)
    • Visitors from Southern California = 87% of 50 = 43.5 = approximately 45

Hence, the correct answer is option B.

Answer: B
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Re: A market survey showed that 76 percent of the visitors at a certain re  [#permalink]

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New post 09 Jul 2018, 06:44
Bunuel wrote:
A market survey showed that 76 percent of the visitors at a certain resort came from Pacific or southwestern states. Of these, (2/3) were from California, and 87 percent of the Californians were from southern California. Approximately what percent of the visitors at the resort were from southern California?

(A) 40%
(B) 45%
(C) 50%
(D) 55%
(E) 65%

Let the total population be 100

So, 76 visitors came from Pacific or southwestern states

Out of the 76 visitors 50.67 ( ie 2/3 of 76) visitors came from California

Again out of those 50.67 visitors 44.08 (87% of 50.67) visitors came from southern California.

So, We have Approximately 45 % visitors who came from southern California, Answer must be (B)
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Re: A market survey showed that 76 percent of the visitors at a certain re  [#permalink]

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New post 11 Jul 2018, 17:21
76% = 3/4(+)
87% = 7/8

Now
3/4 * 2/3 * 7/8 = 14/32 = 7/16
7/16 = 43% (+)
Then B.

Suggestion work in fractions is quicker.
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Re: A market survey showed that 76 percent of the visitors at a certain re   [#permalink] 11 Jul 2018, 17:21
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