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12 Jan 2026, 06:09
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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
A. 1:4
B. 1:3
C. 1:2
D. 3:1
E. 4:1
12 Jan 2026, 06:09
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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
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
13 Jan 2026, 12:16
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We should approach this problem by Vienns Diagram. Say A is only X B is both X and Y, C is only Y. So X (xonly+both) = A+B, likewise Y (yonly + both) = B+C. We are given (A+B)/B=3/2 and (B+C)/B=3 We are to find A/C? A/B+1=1.5 and B/C+1=3. A/B=0.5, B/C=2. Hence A/C=1/4. Thanks
