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A company conducted a survey about its two brands

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by canbtg » Wed Oct 23, 2013 1:10 am
A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x - 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?

A. 46
B. 80
C. 90
D. 100
E. 200

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by mevicks » Wed Oct 23, 2013 1:32 am
canbtg wrote:A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x - 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?

A. 46
B. 80
C. 90
D. 100
E. 200

OAD
Given: 23% people liked "something", hated "something" etc.. As the number of people has to be a positive integer 23% of the minimum no people should also be an integer.

Quickly check the answer choices for divisibility by the prime no 23:

Starting with D:
(23/100)100 = 23 = INTEGER .. Lets keep this, and check the next lower value
(23/100)90 = NONINTEGER
(23/100)80 = NONINTEGER
(23/100)46 = NONINTEGER

Answer D

Don't know if this is an optimum approach but it worked :)
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by theCodeToGMAT » Wed Oct 23, 2013 2:16 am
mevicks wrote:
Don't know if this is an optimum approach but it worked :)
For this question it is an optimum approach :) .. as we have prime number as numerator & 100 as denominator.
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