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

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Math Expert
Joined: 02 Sep 2009
Posts: 48037
A market survey showed that 76 percent of the visitors at a certain re  [#permalink]

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09 Jul 2018, 06:11
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:49) correct 23% (02:17) wrong based on 62 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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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.

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

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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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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.
Peace out.
Re: A market survey showed that 76 percent of the visitors at a certain re &nbs [#permalink] 11 Jul 2018, 17:21
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