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GMAT Club Olympics 2025 (Day 4): In a company-wide vote between two

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Gg153

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04 Jul 2025, 04:25

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y = 70
Total votes = x + 70
x = 70 + 0.2(x + 70)
Solving for x,
x = 105, so y lost by 35 votes
Option C

Bunuel

In a company-wide vote between two project proposals, each employee voted for exactly one proposal. Proposal X received 20% of the total votes more than Proposal Y. If Proposal Y received 70 votes, by how many votes did it lose?

A. 14
B. 28
C. 35
D. 105
E. 140

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Edwin555

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Let votes for proposals X & Y be $x$ and $y$ respectively.
Since it is mentioned 20% of the total votes, we have to find 20% of $(x + 70)$

From the given information we have,
$x = 70 + (x + 70)*0.$2; $(x + 70)$ is the total number of votes
$x - 0.2x = 84$; $x = 105$

Now the question asks by how many votes did proposal Y lose. To find this,

$x - y = 105 - 70 = 35$

The correct option is Option C

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Proposal X received 20% more of the total votes than Proposal Y
Proposal Y received 70 votes

Let the
Total votes = T
Votes for Y be y = 70
Votes for X be x = y + 0.2T = 70 + 0.2T

We know,
x + y = T
70 + 0.2T + 70= T
=> T = 175

=> x = 70 + 0.2*175 = 105

Difference of votes between X and Y = 105 - 70 - 35

C. 35

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Option C is the correct answer.

Before answering the question lets understand the given information. So the question tells us at in a company wide voting for two projects each employee has taken part in this voting and every one has voted for only one of the two projects. Then it tells us that Project X received 20% more votes than Project Y, Finally tell us that Project Y received total 70 votes and then ask us about the vote difference between Project X & Project Y.

Lets solve for the answer now:

Lets take vote percentage of Project Y to be 'A' then for Project X it will be 'A+20'
so, Vote percent of Project Y + Vote percent of Project X = 100
A + A + 20 = 100
2A = 80
A = 40%
Vote percent of Project Y = 40%
Vote percent of Project X = 40 + 20 = 60%

Now we know that Project Y has 40% vote share and has received a total of 70 votes. So from here we can calculate the total number of votes casted by all the employees in the company. Lets take total number of votes to be 'V'.
So, Vote for Project Y = 70
40%*(V) = 70
(40/100)*(V) = 70
V = 70*(100/40)
V = 175

Now lets calculate Votes for Project X.

Votes for Project X = 60% of 175
=(60/100)*175
=105

Now the question asks us about the vote difference between the projects or by how many votes does Project Y lose
Vote Difference = Votes for Project X - Vote for Project Y
= 105 - 70
= 35 (Option C)

Bunuel

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SumnerSCB

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Bunuel

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My first instinct was to do x=1.2y and solve, however a key point is that x didn't just receive 20% more votes but 20% more of the total votes. so x = y +.2(x+y). that gives x = 1.5y so x = 105 which means proposal y lost by 35 votes. we go a step further to check and if 105 +70 = 175. 175*.2=35. so done C

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Proposal X received 20 % more than total. So, x=(X+Y)/5 +Y . Solving this you get x=105. Now the question asks that how much did y lose ? Y lost 35 to X. 105-70. Hence, C.

Bunuel

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X=Y+20
X+Y=100

2Y+20=100
Y=40%
X=60%

40 -> 60
70 -> VX

VX=70*60/40=105

VX-VY=105-70=35

Y lost by 35 votes

The right answer is C

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Bunuel

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Let total votes be V,
We know that (1) V = X + Y and (2) Y = 70.

Further, X received 20% of toal votes more than Y, hence:
X = (20% of V) + Y

Plugging into (1),
V = (20% of V + Y) + Y
= 20% of V + 2Y
2Y = V - 20% of V
2Y = 80% of V ...(3)

Plugging (2) into (3),
2(70) = 0.8V
140 = (4/5)V
V = (5/4)*140
V = 175

Again plugging into (1),
175 = X + 70
X = 105

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Total votes = x+y

x = 20% (x+y) + y
y = 70

Solving for x:
20% (x+70)+70 + 70 = x+70

20% x + 14 + 140 = x + 70

84 = 80% x

84 *[5][/4] = x

x = 105

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Assume X got a votes and Y got 70 votes and total is c
so a+70 = c
a-70 =0.2c
Add both equations you get 2a=1.2c
a=0.6 which translates to 60% meanig y = 40%
So if 40% = 70 then 20% = half of 70 which is 35
ANS C

Bunuel

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First we Find Value of X and Y in terms of percentage.
X = Y+20
X+Y=100
Y+Y+20=100
Y=40

Y received 70 votes
Therefore 70 votes= 40% of the votes.

(70/40)*60=X votes=105

Bunuel

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if the total votes is taken as x, then $\frac{x}{5} + 70 + 70 = x$. Solving this, we find that x = 175. but proposal Y lost by 20% of the total votes, which is 35, option C.

Bunuel

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First find the percentage of X and Y.

Proposal X + Proposal Y = 100
Proposal Y + 20 + Proposal Y = 100
2*Proposal Y = 80
Proposal Y = 40
Proposal X = 60

40% is 70 votes, so 100% is 100*70/40=175
60% is 175-70=105

So Proposal Y lost by 105-70=35 votes

Correct answer is C

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Translate words into algebraic equation: X = 0.2 (X+70) + 70
0.8X = 84 --> X = 105
The difference is 35 votes between X & Y

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Let Y got "y" votes => X = 0.2 + y
y=70
so the difference is 0.2*y = 0.2*70 = 14

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PX is 20% more than PY -> PX=60% and PY=40%

0.4x=70 -> x=70/0.4
0.6x=0.6*70/0.4=210/2=105

105-70=35

Proposal Y lost by 35 votes

Answer C

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Lets assume there are 100 people who voted, and N people voted for Y.
X + Y = 100

Hence, x won by 20 votes

So,
X = N + 20. & Y= N.
Putting value of X and Y in first equation: N + 20 + N = 100; N = 40.
But N according to question is 70 and we need to find value of 20
Using unitary method
if 70 is 40
then 20 is 35.

Hence option C

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Let T be the total votes,
Y + $\frac{T}{5}$ = X
Y + $\frac{T}{5}$ = (T-Y)
70 + $\frac{T}{5}$ = T-70
350+T = 5T-350
700= 4T
T= 175
So, X= 175-70= 105
Therefore, margin = 105-70= 35.

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Let total votes = n
Y = 70 votes
As per question : X = 70 + 20% of n -------- (1)

We also know total votes (n) = X + Y ----- (2)

Substituting (2) in (1)

X = 70 + (X + Y) / 5
X = (350 + X + Y) / 5
5X = 350 + X + Y

We know Y = 70

So, 4X = 350 + 70
X = 105

Total votes = 70 + 105 = 175 votes

So Y lost by 105 - 70 = 35 Votes

Bunuel

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Let T be the total number of votes.
Let X be the number of votes for Proposal X.
Let Y be the number of votes for Proposal Y.

We are given two pieces of information:

Each employee voted for exactly one proposal, so the total votes are the sum of votes for X and Y:
T = X + Y

Proposal X received 20% of the total votes more than Proposal Y. This can be written as:
X = Y + 0.20 * T

We are also given that Proposal Y received 70 votes:
Y = 70

Now, we can substitute Y = 70 into the first equation:
T = X + 70

And substitute Y = 70 into the second equation:
X = 70 + 0.20 * T

Now we have a system of two equations with two variables (X and T):

T = X + 70

X = 70 + 0.20 * T

Substitute the expression for X from equation (2) into equation (1):
T = (70 + 0.20 * T) + 70
T = 140 + 0.20 * T

Now, solve for T:
T - 0.20 * T = 140
0.80 * T = 140
T = 140 / 0.80
T = 140 / (8/10)
T = 140 * (10/8)
T = 1400 / 8
T = 175

So, the total number of votes (T) is 175.

Now that we have T, we can find X:
X = T - Y
X = 175 - 70
X = 105

Alternatively, using X = 70 + 0.20 * T:
X = 70 + 0.20 * 175
X = 70 + 35
X = 105

The question asks by how many votes did Proposal Y lose. This is the difference between the votes received by Proposal X and Proposal Y.
Difference = X - Y
Difference = 105 - 70
Difference = 35

Therefore, Proposal Y lost by 35 votes.

The final answer is 35