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

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Natansha

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Suppose Y received a votes, then X received 6/5a votes

X/Y = 6/5

we have Y votes given as 70
X/70 = 6/5
X = 84 votes, Y = 70 votes
Hence, Y lost by 84-70 = 14 votes

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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?
Y=70
Total Votes= x+y = x+70
x=0.20(Total Value)+ y
x=0.20(x+70)+70
x=0.20x+14+70
x-0.2x=84
0.8x=84
x=84/0.8=105

Y lost by (x-y) votes= (105-70=35)

C

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Let
x=votes for proposal x
y=votes for proposal y = 70
total votes=x+y = x+70
According to the question
x=0.2(x+70) + 70
and then calculate to get x=105.
So y project lost how many votes =105-70=35votes.

So the answer is C.

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To Find: what is the vote difference between X and Y?
Votes for X= Votes for Y+20% of Votes for Y
Votes for X - Votes for Y = 20% of Votes for Y
Votes for X - Votes for Y = 70 (0.2)
Votes for X - Votes for Y = 14
(A) 14 votes

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Let x be the number of votes proposal X received, and y be the number of votes proposal Y received:

x = y + 0.2 * (x+y)
0.8x = 1.2y
x = 1.5y = 1.5 * (70)
x = 105

y lost by 105-70 votes = 35

Bunuel

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Tricky one -

Total votes - V
X received - Y + .2V
Hence,
Y + Y + .2V = V

V = 175

Therefore Y lost by 35 votes. C

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x = 20%(x+y) + y
=> x = (1/5)x + (1/5)*70 + 70
=> (4/5)x = 14+ 70 =84
=> x = 84/(4/5) =105

The number of votes Y lost: 105-70=35

Answer: C

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total vote =x
70+0.2x+70=x
x=175

vote lost=175-70=105
Ans D

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Total Votes = X+ Y
Also, X= 20% of (X+Y) + Y
Simplified, X=1.5Y

Also Given, Y = 70, therefore X= 105 and the difference in vote = 105-70 = 35 ... and that's our answer

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Let's say total votes = T
votes received by Y=a
votes received by X=1.2a
given: a=70
Total votes = Votes received by X + Votes received by Y
T=1.2a+a
substituting a=70
we get, T=154
So , X=84 and Y=70
Y lost by 14 votes

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Bunuel

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Let T eb the total number of votes.

asked: by how much Y lost OR the value of 20% of T

T = X + Y ....Eq1
X = Y + 20% of T ...Eq2
Therefore we can solve it by putting the value of X from Eq2 in Eq1 => Y + 20% of T + Y = T
which is 2*Y = 80% of T
Since Y = 70 then T = 140 * (5/4)
0.2T = 0.2*(140 *(5/4))
And hence the value of 20% of T = 35 Option C

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Total votes = T
Since Y got 70 votes, we know:
Votes for X=70+0.20T Now use the fact that all votes went to either X or Y, so:
Votes for X+ Votes for Y= T
140 + 0.20 T = T => T =175. So X =105 & Y =70, thus X-Y = 35 is answer.

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Let’s say total number of votes = T
Then:

Votes for Y = 70
Votes for X = Y's votes + 20% of total votes
Votes for X = 70 + 0.2T

Since total votes = X + Y:
T=70+(70+0.2T)
=>T=140+0.2T
=>T−0.2T=140
=>0.8T=140
=>T =1400/8 = 175

Now:

Total votes = 175
Y = 70
So X = 175 – 70 = 105
Difference (how many votes did Y lose by):105−70=35 (C)

[hr]
Difference (how many votes did Y lose by):
105−70=35105 - 70 = \boxed{35}105−70=35

Bunuel

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Bunuel

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Total votes to X = X = xT, where T is the total votes cast. Now as stated Y = yT where Y is the total votes for proposal Y.

As per the statement x= 0.2+y and Y = 70. Due to percentage x+y = 1.
0.2+2y = 1 i.e. y=0.4

Using this in above equation, 70 = 0.4T
and X = (0.2 + 0.4)(70/0.4)
X= 105

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X=0.2T+y,
Y=70 votes (given)
T=X+Y (Substituting the values)
T=0.2T+70+70 (bringing similar variables together)
T-0.2T=140
0.8T=140
T=1400/8=175
Since X is 20% of Total more than Y, it means X won by that much only and we have T=175
Hence, 20% of 175=35, answer is c

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Total votes = T
Y received = 70
X received = T - 70

According to the equation:

T-70 = 70 + (20/100*T)

solving we get T = (140*100)/80

we need to find 20/100*T

Which is the from above two equation 35.

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Bunuel

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Given in the Question

1. Each employee voted for exactly one of the two proposals => No employee left out, and no employee voted for both proposals
2. Proposal X received 20% more votes than proposal Y => Proposal X received 60% votes and Proposal Y received 40% votes.
3. Total Number of Votes received by Proposal Y = 70.

Asked in Question

By how many votes did proposal Y lose, or proposal X receive how many more votes than proposal Y

Solution

Since, proposal Y received 70 votes that is 40% of the total votes cast
=> Total votes received by proposal X (ie 60% of the votes) = [70][/40] * 60 = 105 votes
Therefore, by how many votes did proposal Y lose = Votes cast for proposal X - Votes cast for proposal Y = 105 - 70 = 35 Votes

Option C is the answer.

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Let total votes = T
And let the votes received by Y = Y and
And let the votes received by X = X
Now, X+Y=T - equation 1
and from the question, X-Y=0.2T - equation 2
Adding equation 1 and equation 2
2X=1.2T, simplyfying gives X=0.6T
Also, given in the question that Y received 70 votes, putting this value in quation 1, we get 0.6T + 70 = T, simplyfying this gives us,
70=0.4T, therefore, T=70/0.4, T=175, Y received 70 votes, therefore, X received 105 votes.
Difference between X and Y = 105-70= 35 votes.
Answer is 35 votes.

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Let total votes be V,
we have, Proposal X + Proposal Y = Total Votes
As per question,
Proposal X = Proposal Y + 20%V ---(1)
also given, Proposal Y = 70
So, Proposal X= V-70
solving (1), we get
Total votes (V) = 175
Proposal X= 105
Thus, proposal Y lose will be 105 votes (total votes - vote received)

Answer choice (D)

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Let X has got x votes

As per question,
x = 0.2*(x+70)+70
=> x = 105

So X won by 105-70 = 35 votes

Option C is correct

Bunuel

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