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

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Bunuel

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45% (01:34) wrong

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Bunuel

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Bunuel

GMAT Club Official Explanation:

Notice that we are given: "Proposal X received 20% of the total votes more than Proposal Y"

Let the total number of votes be t. Then Proposal X received 0.2t more votes than Proposal Y. Since Proposal Y received 70 votes, Proposal X received 70 + 0.2t.

We also know that the total number of votes is the sum of the votes for X and Y:

(70 + 0.2t) + 70 = t
t = 175

Proposal Y lost by 0.2t = 0.2 * 175 = 35 votes.

Answer: C.

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Let total be x

Proposal X received 0.2x more than Proposal Y

Given company-wide vote between two project proposals, this means Proposal X = 0.6x and Proposal Y = 0.4x
0.4x = 70

Proposal Y lost by 0.2x
0.4x = 70
0.2x = 35

Answer 35

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D.

X received 20% more, so X-Y=20%of total. Thus, Y received 40%of total.

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As per the question, Y =70 and X=Y+20%(X+Y)

Now on solving the equation and putting the value of Y = 70

X= 70+0.2*70+0.2X which will give the X=105 so, Y lost by 105-70 which is 35

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If Proposal X received 20% more votes than Y and the sum total of vote percentages between x and Y amount to 100%, then X would have received 60% votes and Y 40% of the votes.

Y would have lost 60% of the votes and also 70 votes equal 40% of total votes. Therefore, it follows that, 60% of the votes will be (70*60)/40 = 105

Therefore, Option D

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Let total votes be T
So Y = 70
then X = 70 + 0.2T
X+Y= 140 +0.2T
T = 140 + 0.2T
0.8T = 140
T = 175
Now Y = 70 so X= 175-70 = 105
So X won by 35 votes. that means Y lost by 35 votes.

Hence Ans C

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Let Proposal Y got 'a' votes
Proposal X will get 20% more , that is 1.2a

Now, a=70
Y got 70 votes

1.2a=84
X got 84 votes

difference =84-70=14

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Information given:
- Every employee votes for exactly one of two proposals (X and Y)
- Proposal X received 20% of total votes more than Proposal Y
- Proposal Y got 70 votes

Question:
- By how many votes did proposal Y lose?

Solution:
- Total votes = T, Y votes = 70, so X votes = ?
- X = Y + 0.2T
- T = X + Y = (70 + 0.2T) + 70
- T = 140 + 0.2T, 0.8T = 140, T = 175
- So, total amount of votes is 175
- X = 70 + 0.2 * 175 = 105
- Difference: X - Y = 105 - 70 = 35

Answer: C, 35

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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?

Let us assume that Proposal X got x votes and Proposal Y got y votes.

x = 1.2y
y = 70

x = 1.2*y = 1.2*70 = 84

Y lost by number of votes = x - y = 84 - 70 = 14

IMO A

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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?

Total = T = X + Y;

Given X = 20% of T + Y = 0.2T + Y;

T = 0.2T + Y + Y;
0.8T = 2Y;
T = 2.5Y = X + Y;
X = 1.5Y;
Y = 70;
X = 105;

X - Y = 35; Y Lose by 35 Votes;

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Bunuel

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total no of votes be = T
votes for Y = 70
Votes for X = 70 + 0.2T

Equation- total votes = X+Y

T = 70+70+0.2T
0.8T=140
T= 175
X votes = 70+0.2*175= 105
Difference between X and Y votes = X-Y = 105 - 70 =35 (Option C)

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Let's say Y gets 'a' votes.
So, X gets (1 + 0.2)a.
If a = 70,
then X = 84.
84 - 70 = 14.

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x + y = total, we are looking for the difference between x and y.

x / (t) = 120% x (70 / (70 + x))
x = 84

x - y = 84 - 70 = 14

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given votes of y is 70
votes of x will be
70 *.20 ; 14
70+14 ; 84 votes are of X
so Y lost by 84-70 ; 14 votes
OPTION A

Bunuel

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Bunuel

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X+Y=100%
But X=Y+20%
Substitute X With Y in the equation
We have Y+0.2+Y=1
2Y=0.8
Y=0.4=70 implies 1=70*10/4=175, hence lost by 105 votes

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Votes received by Proposal Y = 70 Votes

Proposal X received 20 % more votes than Proposal Y = 70*1.2= 84

So Proposal Y lost by 84-70 Votes i.e. 14 Votes

Correct answer is A.

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Y got 70 votes
The difference in votes between X and Y is 20% of the Total votes (say T)

So acc to the question we can say that the votes received by X will be 70 + 20% of T
So, we can make the following equation:
70+20% of T +70=T
140=T-T/5
4T/5=140=>T=35*5=175 Votes.
Votes received by X=105, Y=70.
Y lost by 105-70=35 votes (Option C)

Bunuel

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Proposal X received 20% of total votes more than Proposal Y. It means proposal Y received 40% votes and X received 60%.
Lets assume, Total votes = x.

20% more than 70 votes is:

40% of x = 70
40/100 × x = 70
x = 175

20% of total votes = 20/100 ×175=35

The number of votes Proposal Y lost by is: 35

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