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Difficulty:
85%
(hard)
Question Stats:
59% (02:19) correct
41%
(02:40)
wrong
based on 295
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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. The ratio of the number of tenants who support neither proposition to the number who support both propositions is half the first 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
M46-05
A. 1 : 4
B. 1 : 3
C. 1 : 2
D. 3 : 1
E. 4 : 1
M46-05
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16 Dec 2025, 10:00
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Bunuel
GMAT Club Official Explanation:
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.
General Discussion
16 Dec 2025, 09:17
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Let x, y, b and n denote supporting X, Y, both and neither
x/b = 3/2
y/b = 3
n/b = 3/4
Taking the denominator as 4 as common for all these, we get
x:y:b:n = 6:12:4:3
We can also assume x = 6k, y=12k, etc, but since we are solving for ratio, we can ignore it as k will cancel out.
x only = x - b => 6 - 4 = 2
y only = y - b =>> 12 - 4 = 8
x only/y only = 2/8 = 1/4
x/b = 3/2
y/b = 3
n/b = 3/4
Taking the denominator as 4 as common for all these, we get
x:y:b:n = 6:12:4:3
We can also assume x = 6k, y=12k, etc, but since we are solving for ratio, we can ignore it as k will cancel out.
x only = x - b => 6 - 4 = 2
y only = y - b =>> 12 - 4 = 8
x only/y only = 2/8 = 1/4
Bunuel
