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30 Jun 2019, 22:15
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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95% (01:13) correct
5%
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In a certain apartment building, exactly \(\frac{1}{3}\) of the apartments have two bedrooms and exactly \(\frac{1}{7}\) of the two-bedroom apartments are front apartments. Which of the following could be the total number of apartments in the building?
(A) 42
(B) 50
(C) 51
(D) 56
(E) 57
(A) 42
(B) 50
(C) 51
(D) 56
(E) 57
30 Jun 2019, 22:25
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Bunuel
Let us assume total apartment = x
Then \(\frac{x}{3}\) apartments are 2 bedroom apartments and \(\frac{x}{3}*\frac{1}{7}=\frac{x}{21}\) apartments are front apartments . Since front apartments must be positive integers => \(\frac{x}{21}\) must be positive integer.
=> x = 21k where k is a positive integer
Only choice (A) 42 satisfies this condition
Therefore A is correct.
30 Jun 2019, 22:49
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3 and 7 must be the factors of the total number of apartments, on checking options we can say option A is the only one which meets our requirement .
Hence , answer is A
Hence , answer is A
