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

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Sketchitesh

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03 Jul 2025, 09:02

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Proposal Y received (Y Votes) : Y= 70
Proposal X received (X votes) : X= 20% (X+Y)+ 70 => X= 0.2* (X+70)+ 70
0.8X =84 => X = 105
X-Y = 105-70 = 35

C is the Answer

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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FruAdey

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Tricky wording.
the key is to noticing that 20% is not of Y's votes but of the total votes (T)
( wrong interpretation: X = y + y/5)
(correct interpretation : X = y + T/5) where T is total number of votes.

but since total number of votes take away y votes correspond to X votes ( x = T -y )

we can say that

T - y = y + T/5

T - 70 = 70 + T/5

4T = 700

T = 175

y loss = T -y ( 175 - 70)

which is 105 (D)

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Ok. This has a small trap. The wordings are important, X received 20% of the total votes more than proposal Y.
Lets assume total votes is M. and Y received 70.

So Total votes can be calculated by

M = 70(votes to Y) + (70 +0.2M) (Votes to X)

M = 140+0.2M
M = 140/0.8
M = 175.
X received 105, Y received 70. Excess X received than Y is 35. So Answer is (C).

Bunuel

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bebu24

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Let x be the votes of X and y be the votes of Y and T be total votes
It is given that:
x - y = 20% of T

If the total vote% is 100%, and since there is no overlap between x and y votes, we can say that:
X received 60% of T
Y received 40% of T

since 40% of T = 70, T = 175

Y lost = 175 - 70 = 105 votes

Bunuel

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justinioane

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03 Jul 2025, 09:06

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X = Y(1.2)

X = 70*1.2

X = 84

how many votes did it lose?

84 - 70 = 14

RBgmatPre

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03 Jul 2025, 09:13

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It's a fairly easy question. The only tricky bit is to understand - "X received 20% of the total votes more than Proposal Y"

Total votes = T

Suppose Y receives - y votes

Y = y

For X:
20% of total votes = 0.2 T
more than proposal Y = +y

X = 0.2T + y

Given information - Y received 70 votes -> y=70

T = x + y
T = 0.2T + 70 + 70
0.8T = 140
T = 175

y=70
x = 105

Difference = 35 votes | ANSWER - option C

Bunuel

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BeachStudy

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03 Jul 2025, 09:15

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Notes:
Company wide (everyone)
Proposal X got 20% more than Y
Y received 70 votes.
How many did it not get?

It has to be greater than 70 so its D or E

Lets check 105.
105+70 = 175 (total votes is potential x + y)
20%of 175 = 35 (x got 20% more so how much is 20% of total)
140 / 2 = 70 (remove 20% from total and you should get a 50/50 split. divide by 2 and it should get you 70, or y)

This is correct no need to check 140

Answer: D

Bunuel

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03 Jul 2025, 09:16

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Let the total number of employees = total number of votes = T
Proposal Y received 70 votes.
Proposal X received 70 + 20% of T.
Since each employee voted for exactly one proposal, votes of Y + votes of x = total votes.

70 + 70 + 0.2T = T
T = 175

votes of X = 105
Thus Y lost by 105 - 70 = 35 votes.
Answer is option C.

Bunuel

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03 Jul 2025, 09:18

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should be 35

Lets assume total to be t. The equation is

t = 70+70+1/5(t)
4/5(t)=140
t=175

(1/5)t=35.This is the extra votes

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03 Jul 2025, 09:20

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Lets us say
X= the number of votes received by propsal X
Y= the number of votes received by propsal X
T= the total number of votes

We know that
Y=70
Equation 1(E1) :X+Y=T --> X+70=T
Equation 2 (E2) :X=Y+0.2T --> X=70+0.2T
We solve the two equations :
E1 : X=T-70 and E2 : X=0.2T+70
E1-E2 : (T-0.2T)-(70+70)=0 --->T=175
We can deduce that X=105
The Y lost by 105-70 = 35 votes

Bunuel

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Let total votes be 100v and the difference between X and Y is 20% of 100v = 20v

Thus, 80v is equally divided between Project X and Y i.e. 40v each

Project Y =40v=70 votes
Project X= 40v + 20v = 70 + 35 = 105 votes
Difference is 35 votes

Fastest way: Project Y =40v=70 votes and difference=20v=Half of 70=35

Answer: C. 35 votes

Harika2024

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03 Jul 2025, 09:33

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given conditions,
x = y + 0.2 *(x+y)
y = 70
subsitite y = 70 in above equation
on simplifying,
x = 70 + 0.2x + 0.2 * 70
x = 70 + 0.2x + 14
0.8x = 84
x = 105
now lets find difference between x and y, i.e., = 105 - 70 = 35

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03 Jul 2025, 09:35

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If X received 20% more votes than Y, then the ratio of X to Y is 60:40

{ x=y+20, x+y=100
2y+20=100, so y=40 and x=60 }

We can simplify the ratio of X to Y as 3:2
So if Y=70, we can write:
$\frac{X}{Y}$= $\frac{X}{70}$= $\frac{3}{2}$
So X= $\frac{3*70}{2}$=105
The question asks for the difference in the votes, so:
X-Y = 105-70 = 35

Option C is correct.

Bunuel

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Bunuel

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Votes for X=Votes for Y+20% of total => X = 70+0.2*(70 + X) => X = 105 => Final answer: 105 - 70 = 35

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Let total votes be T.
Proposal Y =70 votes
Proposal X got 20% of total, more than Y
X=Y+0.20T

And everyone votes for exactly one proposal,So: X+Y=T

Y+0.20T+Y=T
2Y=0.80T
2*70=0.80T
T=175

Hence,
X=175-70=105 votes
The margin by which Y lose: 105-70 = 35

C)35

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03 Jul 2025, 09:39

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X = 70 + 20% x (X+Y)
X = 105

Answer: X - Y = 105 - 70 = 35
Answer: C

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03 Jul 2025, 09:41

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Ans (C)
Total votes recived by X= A
Total votes recived by Y= B

A+B= Total Votes cast (T)

A = 20% T + B

B = 70

20%T + 70 + 70 = T

140= T- T/5

140=4T/5

700/4=T

T= 175

X= 105
B= 70

Thus, 105-70=35 (C)

Bunuel

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x= y(1+20%)
x= 70 (120%)
x= 84

x-y=84-70

Bunuel

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Bunuel

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Number of votes received by proposal X = x

Number of votes received by proposal Y = y

x - y = 20/100 (x + y)

5x - 5y = x + y

4x = 6y

x/y = 6/4

x = 3/2 * 70

x = 105

Difference = 105 - 70 = 35

Option C

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Let No of votes to Proposal X be $X$
And No of votes to Proposal Y is given $70$
Let Total no of votes be $T$

Decoding one sentence at a time.

"In a company-wide vote between two project proposals, each employee voted for exactly one proposal."
Meaning $X+70 = T$ ...... (1)

Proposal X received $20$% of the total votes more than Proposal Y.
Meaning, $X-70 = \frac{20}{100}*T = \frac{T}{5 }$........(2)

Removing $X$, we subtract (2) from (1)

$140=\frac{4T}{5}$
$T=35*5$

$X-Y = 35$

Answer C

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