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02 Jul 2013, 23:23
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A
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Difficulty:
45%
(medium)
Question Stats:
73% (02:54) correct
27%
(03:14)
wrong
based on 601
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In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 50
(B) 70
(C) 100
(D) 105
(E) 140
(A) 50
(B) 70
(C) 100
(D) 105
(E) 140
02 Jul 2013, 23:31
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In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 50
(B) 70
(C) 100
(D) 105
(E) 140
Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).
Rented one-bedroom units are 1/5 of all one-bedroom: 1/5*{All one bedroom} = 40 --> {All one-bedroom} = 200.
{All two-bedroom} = 490 - 200 = 290.
Two-bedroom not rented = 290 - 240 = 50.
Answer: A.
(A) 50
(B) 70
(C) 100
(D) 105
(E) 140
Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).
Rented one-bedroom units are 1/5 of all one-bedroom: 1/5*{All one bedroom} = 40 --> {All one-bedroom} = 200.
{All two-bedroom} = 490 - 200 = 290.
Two-bedroom not rented = 290 - 240 = 50.
Answer: A.
General Discussion
02 Jul 2013, 23:38
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vtran
Out of every 7 units, 4 are rented. Thus, out of 490 units, \(4*\frac{490}{7}\) will be rented \(\to 280\). Total no of not rented bedrooms = (490-280)= 210 units.
Let the total no of 1 bedroom units be 5x.The total rented apartments include x units of 1 bedroom and 6x units of 2 bedrooms \(\to 7x\) = \(280 \to x\)= 40. Thus, the total no of 1 bedroom units = 5*40 = 200.
Total not rented 1 bedroom units = (200-40)=160
The no of 2 bedroom units not rented = 210-160= 50 units.
A.
