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

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yasshita

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So basically we can form 2 equations here, and then solve for T-

1. For X -> 0.2T + 70
For Y -> 70
2. T= no. of votes for X + no. of votes for Y
T= X+Y
T= (0.2T + 70) + 70
3. On solving for T we get T= 35

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Bunuel

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Let the votes for each proposal are x, y

So fro the given data we know that x = 0.2(x+y)+y. So x=1.5y. . We know that y=70, x=105. So it lost by 35 votes,

Hence IMO C

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70 x 1.20 (20% as a multiplier) = 84.
84-70= 14

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Total votes = v
Votes to Y = 70
Votes to X =(20% of v)+70
0.2v +70+70 = v
140 = 0.8v
v = 140/0.8 =175

Votes to X = 0.2*175 + 70 =105 (option D)

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Trap was 20% of y or Total!
Had to assume the total to be t and then solve.
When questions seems to be this easy, re-read!

Bunuel

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Given:

Proposal Y got 70 votes
Proposal X got 20% of all the votes cast MORE than Proposal Y
Everyone voted for one proposal or the other

"20% of the total votes more" means. It's not 20% more than Y's votes - it's 20% of ALL votes cast as an extra amount.
So let the total number of votes "T", then:

Proposal X got: 70 + (20% of T)
Proposal Y got: 70

Since these two proposals got ALL the votes:
X + Y = T
70 + (70 + 20% of T) = T
140 + 0.20T = T
140 = T - 0.20T
140 = 0.80T
T = 175 total votes

Now we can find how many votes each proposal actually got:

Proposal X: 70 + (20% of 175) = 70 + 35 = 105 votes
Proposal Y: 70 votes

So Proposal Y lost by: 105 - 70 = 35 votes
The answer is C. 35.

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Let project X receive X votes.
Total votes = 70 + X

Given in ques (crucial part) - X = Y + 0.2 (total votes)
X = 70 + 0.2 (70+X)
Solving we get X = 105

By how many votes did Y lose? 105 - 70 = 35 (C)

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What's asked: Difference of votes between X and Y

What can be calculated from provided info: Total votes = X + Y. | X = Y + 0.2 x Total -> X = Y + 0.2 x (X + Y) | Y = 70

Calculus development: X = Y + 0.2X + 0.2Y -> X = 70 + 0.2X + 14 -> 0.8X = 84 -> X = 105
*Mental math tip: It may be hard to calculate 84/0.8, but there is a nice trick: 84/0.8 = 80/0.8 + 4/0.8 -> 80/0.8 = 100 and 4/0.8 = 5

Final answer: X got 105 votes and Y got 70 votes -> Difference = 35 (C)

-------------------
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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The question tells us that X has 20% more of the total votes than Y. Furthermore we know that each vote was given either X or Y, therefore we know that X has to be 60% of the total votes while Y will be the remaining 40% of the votes. This is the case because we votes for X and Y together have to be 100%. Now we can calculate X being 60/40 * Y = 1.5 * 70 = 105. Answer D.

Regards,
Lucas

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Say total number of votes $= v$
Votes for proposal X $= x$
Votes for porposal Y $= 70 = y$
Proposal X received 20% of the total votes more than Proposal Y -> $x = y +\frac{20}{100}v$ -------(1)

We know $x+y = v$ (because each employee voted for exactly one of the two proposals)\
$x+70 = v$
$x = v-70$ (Plug this into Eq.1)

$v-70=y+\frac{20}{100}v$
$v=175$

Then, $x = v-y = 175-70 = 105$

Then proposal Y lost by $x-y = 105-70 = 35$ votes

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Bunuel

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X received 20% more of total
X=Y+20%
X+Y=100%
X=60%
Y=40%

Y=70=40%
therefore, 20%=35 by this many votes Y lose X

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Bunuel

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Proposal X received X votes, and proposal Y received Y votes.
(1) X + Y = 100%
(2) X = Y + 20%
=> Y = 40% and X=60%.
If Y=70 votes => X=105 votes.
=> They lost 35 votes.

ANSWER: (C)

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Given proposal X recieves 20% more votes than proposal Y

i.e x= (1+1/5)Y
x= 6y/5
Given y=70, So X= (6*70)/5 =84

So Y loses by 84-70 =14 votes

Bunuel

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Total = X% + (X%+20%)
100% = 2X% + 20%
80% = 2X%

X = 40%
X = 40% = 70
X + 20% = 60%

Since 40% = 70, we have 60% = 40% + 20% = 70 + 70/2 = 105

De difference of votes will be 105 - 70 = 35.

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We are given that in a company-wide vote, Proposal X received 20% more votes than Proposal Y, and that Proposal Y received 70 votes. We are tasked with determining by how many votes Proposal Y lost.
Let the number of votes for Proposal Y be yyy and the number of votes for Proposal X be xxx.
From the problem, we know the following:

Proposal Y received 70 votes, so y=70y = 70y=70.
Proposal X received 20% more votes than Proposal Y, so x=1.2×yx = 1.2 \times yx=1.2×y.

Substituting the value of yyy:
x=1.2×70=84x = 1.2 \times 70 = 84x=1.2×70=84
Thus, Proposal X received 84 votes.
Now, to find by how many votes Proposal Y lost, we subtract the number of votes for Proposal Y from the number of votes for Proposal X:
Votes by which Proposal Y lost=x−y=84−70=14\text{Votes by which Proposal Y lost} = x - y = 84 - 70 = 14Votes by which Proposal Y lost=x−y=84−70=14
Therefore, Proposal Y lost by 14\boxed{14}14 votes.
The correct answer is A. 14.

Bunuel

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Let
Total number of votes = T
Number of votes for proposalX = X
Number of votes for proposalY = Y

Given :
1)T = X + Y-----1
2)Proposal X recieved 20% of total votes more than proposal Y
==> X = Y + 0.2T------2
3) Y= 70-----3

On Solving 1,2,3

==> T= 175, X= 105

Difference between the votes for proposal X and proposal Y
==> X-Y = 105-75 = 35

Correct option C

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Bunuel

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We know, that X + Y = Total.
Total = X = (X + Total * 0.2) + Y
Therefore: Total = 70 + 70 + Total*0.2, as the question indicate, that X must be 20% of the total votes more.
E.g. with 100, it would be 20 more.

Now, with target bruteforce: 140+35 =175*0,2 = 35.
That agreets with the formula created before of: Total = 70 + 70 + Total*0.2

That means: C is sufficient.

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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?

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

X has 20% more of the total votes. So 80% of the total votes is divided equally among X and Y

=> X = 60% of the total amount of votes and Y = 40% of the total amount of votes

40% of the total votes = 70 votes => 70 = 4/10 => 175 total votes

175 - 70 votes (Y) = 105 votes for X

X - Y = 105- 70 = 35

Y lost by 35 votes.

Answer C

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Let,
Total votes = t
Vote received by Proposal x = x
Vote received by Proposal y = y

t=x+y

Given, x=0.2t+y
=> t= 0.2t+y+y
=> t-0.2t = 2y
=> 0.8t=140 (y=70)
t= 175

x= 175-70 = 105
Asked: By how many votes did Y lost?

We need the difference between the total votes received by x and vote received by y = 105-70 = 35

Option C

Bunuel

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Let total votes = V
Votes for proposal y = 70
Votes for proposal x = 0.2V+70

0.2V +70 +70 = V

140= .8V
V = 175
y lost by 175-70 = 105 votes

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