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12 Days of Christmas GMAT Competition 2025 - Day 2: A survey was

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msignatius

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16 Dec 2025, 23:26

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In questions like these, I tend to get confused between 'doubling' and 'halving' the ratio, so I am not too confident about my answer. Yet, here goes my explanation:

Arconia's residents are deciding between two propositions - X and Y.

For every 3 people who support X, there are 2 people who support both X and Y.

For every 3 people who support Y, the number of people who support both X and Y is twice the 3:2 ratio of X to X & Y. I interpret that as (could be wrong) 3:1, which is for every 3 people who support X, there is one who support both X and Y. This doubles the relationship from 1.5:1 to 3:1.

Moving on - the ratio of those who support neither proposition to those who support both is half the first ratio, that is half of 3:2. In the same vein as above, I would take that as 3:4.

Now, we must compare those who support only X to those who support only Y. As we're given the comparison between those who support X and those who support both X and Y (and the corresponding comparison for Y with X & Y). We know there are 3 X supporters for every two X & Y supporters, and 3 Y supporters for every X & Y supporter. So, the only Xs are double of the only Ys, making the answer 1:2.

Bunuel

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

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SSWTtoKellogg

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16 Dec 2025, 23:32

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Writing all the ratios and then making it equivalent ratio, for example, making both proposition same in all ratios using multiples, we will get:

only X : only Y = 2n : 8n = 1:4 (A)

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16 Dec 2025, 23:33

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Given 1 : X /X+Y = 3/2
Given 2 : Y/X+Y = 6 /2 (Twice of First )
Ratio of neither to both is half of first ratio ;
Niether = 3/4 x 2 = 1.5
Required ratio = Ratio of Tenants who support only X to Only Y ;
Only X = X - Both = 3-2 =1
Only Y = Y - both = 6-2 =4
Ans is 1:4

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16 Dec 2025, 23:54

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Bunuel

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Given,

X/(X+Y) = 3/2
let (X+Y) = B,
=> X/B = 3/2
=> X = 3B/2 ---------------- Eq 1

Similarly,
=> Y/B = 3/1
=> Y = 3B ------------------- Eq 2

Also,
=> Neither/B = 3/4
let Neither = N,
=> N = 3B/4

What we need, X(only)/Y(only)

We know X(only) = X - B
Y(only) = Y - B

From Eq 1, Eq 2

X(only) = X - B = 3B/2 - B = B/2
Y(only) = Y - B = 3B - B = 2B

=> X(only)/Y(only) = (B/2)/2B = 1/4

Therefore, answer A) 1 : 4

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17 Dec 2025, 00:35

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Based on the stem,

X : X&Y = 3 : 2

Y : X&Y = 2(3 : 2) = 6 : 2

(X&Y)' : X&Y = 0.5 (3 : 2) = 1.5 : 2

With X&Y's proportion common for all, it should be easy to simplify the problem

Considering x as the constant for proportions,

X = 3x, Y = 6x, (X&Y)' = 1.5x, X&Y = 2x (Based on the ratios)

Therefore, only X = X - X&Y = 3x-2x = 1x

only Y = Y - X&Y = 6x-2x = 4x

=> Only X : Only Y = 1x : 4x = 1 : 4

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17 Dec 2025, 01:49

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X:B = 3:2, Y:B = 3:1

Only X = X - B = 3B/2 - B = B/2
Only Y = Y - B = 3B - B = 2B

Only X / Only Y = (B/2)/(2B) = 1/4

Answer A

Bunuel

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17 Dec 2025, 02:39

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The ratio of the number of tenants who support X to the number who support both is 3 to 2: (All X)/(Both) = 3/2
The ratio of the number of tenants who support Y to the number who support both is twice that ratio: (All Y)/(Both) = 2*3/2 = 3/1
The ratio of the number of tenants who support neither to the number who support both is half the first ratio: (Neither)/(Both) = 1/2*3/2 = 3/4

Hence, we have the ratio All X : All Y : Both : Neither = 6:12:4:3
Lets call there are 6a tenants for All X, 12a for All Y and 4a for Both X and Y.

The number of tenants support only X = 6a - 4a = 2a
The number of tenants support only Y = 12a - 4a = 8a
=> (Only X)/(Only Y) = 2a/8a = 1/4

Answer: A

Bunuel

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17 Dec 2025, 03:03

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Let the number of people supporting both be x. The number of people supporting only X is a and the number of people supporting Y is b.

Then based on the question =>

People supporting X / people supporting both => a+x /x =3/2 => a => x/2
People supporting Y/people supporting both => b+x/x = 6/2 (double) = > b = 2x

We do not need the next condition as these two should be enough.

Only X / Only Y = a/b = (x/2) / 2x = 1/4 => Correct Answer is A

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17 Dec 2025, 03:13

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Answer: A

X: (X+Y) = 3:2 or 6:4 (for the sake of simplicity)
Y: (X+Y) = 6:2 or 12:4
Neither : (X+Y) = 3:4

Thus, assuming both X&Y =4,
Supporters of only X = 6-4 = 2
Supporters of only Y = 12-4 = 8

Ratio of supporters of only X : Supporters of only Y = 2:8 = 1:4

Bunuel

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hershehy

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17 Dec 2025, 03:58

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IMO A

let the number of ratios who support both x and y are k.

Given ratios

1. Rx/R(x+y)= 3/2; from this, total who supports X= 3/2k
2. Ry/R(x+y)= 6/2; from this total who supports Y=3k
3. Rn/R(x+y)= 3/4; who supports neither = 3/4k

for only supporters of x
Only X= Supports X- Supports Both= 3/2k - k= 1/2k

Only Y= Supports Y- Supports Both= 3k-k= 2k

Ratio of X/Y= 1/2K:2K= 1:4. Hence A is correct.

We can also solve this using tabular method, below

	Rx	R(not x)	total
Ry	4	8	12
R(not y)	2	3	5
total	6	11	17

Now we can see that only residents which supports X can be in multiple of 2 and only supports Y in multiples of 8, therefore the ration of X and Y is 1:4.

Bunuel

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17 Dec 2025, 04:04

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17 Dec 2025, 04:34

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Given

X/(X & Y) = 3/2 -- Eq (1)

Y/(X & Y) = 2*3/2 = 6/2 --> Eq (2)

(nX & nY)/(X & Y) = 1/2 * 3/2 = 3/4

To find
(Only X)/(Only Y) = [X - (X & Y)] / [Y - (X & Y)]

Replacing values of (X & Y) from Eq(1) and Eq(2)
= [X - 2X/3] / [Y - Y/3]

= [X/3]/[2Y/3]

=> [Only X]/[Only Y] = X/2Y --> Eq(3)

Dividing Eq(1) with Eq(2) we get
X/Y = [3/2]/3 = 1/2

Using this X/Y value in Eq (3) we get
=> X/2Y = 1/2 * X/Y = 1/2 * 1/2 = 1/4

Option A

Bunuel

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17 Dec 2025, 04:59

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Let the number of tenants who support both propositions be .

1) Use the first ratio to express

We’re told:

X : B = 3 : 2

X = 3*B/2

2) Use the second statement to express

“The ratio of Y to both is twice that ratio.”
The “first ratio” was 3/2 . Twice that is 3/2*2=3 . So:

Y : B = 3 : 1
Y = 3*B

3) Convert totals into “only” counts

People who support only X are those who support X minus those who support both:

Only X = X - B = 3B/2 - B = B/2

Similarly, Only Y = Y - B = 3B - B = 2B

4) Form the required ratio

X : Y = B/2: 2*B

1 : 4

Therefore the answer is option (A) 1:4

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17 Dec 2025, 06:08

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Question:

only x : only y =?

Gn.:
X:Both = 3:2
Y:Both = 6:2
Neither:Both = 3:4

Only x = X - both => 3 - 2 =>1
Only y = Y - both => 6 - 2 => 4

Answer: 1:4 (Option A)

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17 Dec 2025, 06:37

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This is a question of overlapping sets.
Fill the ratios in the grid and you will find the answer.

	x	not x
y	4x	12x
not y	6x	3x

only x/only y =6x/12x=1/2

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17 Dec 2025, 07:15

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Let the number of tenants who support both X and Y be C

Ratio of X to both X and Y is 3:2
=> X/C = 3/2
=> X = 3C/2

Ratio of Y to both X and Y is twice the initial ratio
=> Y/C = 3
=> Y = 3C

Ratio of neither to both X and Y is half the initial ratio
=> Neither/C = 3/4
=> Neither = 3C/4

Only X = X - Both = 3C/2 - C = C/2

Only Y = Y - Both = 3C - C = 2C

Only X : Only Y = (C / 2) / 2C
=> Only X : Only Y = 1 : 4

A: 1:4

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17 Dec 2025, 07:27

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Bunuel

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x/x+y = 3/2
y/x+y = 6/2

x : x+y : y = 3:2:6

only x: only y = (3-2)/(6-2) = 1/4 = 1:4

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17 Dec 2025, 07:29

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1:4

first i know we have venn diagram
total X is 3/2B
total y is 3b

then only x and y

0.5b 2b 2b

1/2 /2b = 1/4

Bunuel

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17 Dec 2025, 07:45

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Let the no.of tenants who supports both X and Y be 2
Given the ratio of x:both is 3:2, so the total no. supporting X will be 3 and those supporting only X will be 3-2 = 1
Now the Ratio of Y to both is twice the first ratio = 6:2
so the total no. of tenant supporting Y is 6 and those supporting only Y will be 6-2 = 4
therefore X:Y = 1:4

Bunuel

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haldersujoy

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17 Dec 2025, 08:15

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According to the problem,
X supporter : Both = 3:2 --> (i)
Y supporter : Both = 6:2 --> (ii)

Therefore,
form (i), Only X supporter = 3-2 = 1
form (ii), Only Y supporter = 6-2 = 4

=> Only X supporter : Only Y supporter = 1:4

OA: A

Bunuel

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