Official Solution: A survey was conducted among the tenants of the Arconia building about their support for two propositions, X and Y. The ratio of the number of tenants who support proposition X to the number who support both X and Y is 3 to 2. The ratio of the number of tenants who support proposition Y to the number who support both propositions is twice that ratio. What is the ratio of the number of tenants who support only proposition X to the number who support only proposition Y? A. 1:4
B. 1:3
C. 1:2
D. 3:1
E. 4:1
The ratio of the number of tenants who support proposition X to the number who support both X and Y is 3 to 2:
X : (both X and Y) = 3 : 2
The ratio of the number of tenants who support proposition Y to the number who support both propositions is twice that ratio, so its numeric value is 2 * (3/2) = 6/2. Therefore:
Y : (both X and Y) = 6 : 2
Adjust the first two ratios, 3 : 2 and 6 : 2, so that the “both X and Y” term is 4, matching the third ratio:
X : (both X and Y) = 6 : 4
Y : (both X and Y) = 12 : 4
In this case, assuming X = 6, Y = 12, and (both X and Y) = 4, we get:
(Only X) = 6 - 4 = 2
(Only Y) = 12 - 4 = 8
Therefore, the ratio of those is 2 : 8 = 1 : 4.
Answer: A