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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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X - 0.2(X-Y) = Y

X - 0.2X + 0.2Y = Y

0.8X = 1.2Y

2X = 3Y

X = 3/2 * Y

X = 3/2 * 70

X = 105

X - Y = 105 - 70 = 35

Option C
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Let X be the votes for Proposal X and Y be the votes for Proposal Y. We know Y = 70.

The phrase "X received 20% of the total votes more than Y" means X = Y + (0.20 * Total Votes).

The total votes are X + Y, or X + 70. So, we can write the equation: X = 70 + 0.20 * (X + 70).

Solving this gives us X = 70 + 0.2X + 14, which simplifies to 0.8X = 84. Therefore, X = 105.

The question asks for the difference between the votes for X and Y. The difference is 105 - 70 = 35.

Proposal Y lost by 35 votes. The correct answer is C. 35.

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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for the GMAT Club Olympics Competition

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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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As per the Give Equation i.e X received 20% of the total votes more than Proposal Y forms as:

X = 20%(X+Y) +Y
X=0.2X+1.2 Y
X= 1.5Y

Now Y given as 70

X= 105

Hence X-Y -105-70=35 (Ans)
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Let X be the number of votes for Proposal X and Y be the number of votes for Proposal Y. Let T be the total number of votes.

We are given that Y = 70.

The total number of votes is T = X + Y.

The main condition is that Proposal X received 20% of the total votes more than Proposal Y. This translates to the equation:
X = Y + (0.20 * T)

Substitute and solve for X:
Now, substitute the known values and expressions into the main equation:

X = 70 + 0.2 * (X + 70)

X = 70 + 0.2X + 14

X = 84 + 0.2X

0.8X = 84

X = 84 / 0.8

X = 105

So, Proposal X received 105 votes.

Find the difference:
The number of votes by which Proposal Y lost is the difference between the votes for X and the votes for Y.

Loss Margin = X - Y

Loss Margin = 105 - 70

Loss Margin = 35
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Votes for Y=70
Proposal X received:
Votes for X = 70 + 0.2T
Also, since there are only two proposals :
Votes for X + Votes for Y = T
Substitute:
(70+0.2T)+70=T
140+0.2T=T
140=T−0.2T=0.8T
T=140/0.8=175

Difference=105−70=35
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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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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Given that:

There are 2 project proposals - X and Y. Thus, total proposals = (X+Y)

And each voted in EXCATLY one proposal , so there is NO overlapping.

Proposal X = 20%( Total votes) + Y

X = (1/5)* (X+Y) + Y

If Y = 70. Then X = (1/5)* (X+70) + 70

X = (X/5) + 14+70

4X/5 = 84

X = 105

Y= 70.

Y lost by 105-70 = 35 votes

Option C
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x=20%(x+y)+y
y=70 (given)
x=1/5*(x+70)+70
x=105

Y lost by 105-70 i.e. 35 votes
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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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Total votes = Proposal X + Proposal Y

\(T=X+Y\)

\(X=Y+0.2*T=Y+0.2(X+Y)\)

\(X=Y+0.2X+0.2Y\)

\(0.8X=1.2Y\)

\(\frac{X}{Y}=\frac{1.2}{0.8}=\frac{3}{2}\)

\(Y=70\), \(X=\frac{3*70}{2}=105\)

\(X-Y=105-70=35\)

\(Y\) lost by \(35\) votes

Answer: C
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Total vote = 70/(100-20)/2))x100 = 175
Votes Y lost = Vote of X - Vote Y = ((100+20)/2 - (100-20)/2)x175/100= 35
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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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Topics- Disjoint "events" (Event X&Y=0); Percents
Rephrase question- How far is X from Y?
Strategy- Algebra, Visualization
  • To visualize, you can draw two non-overlapping circles within a box that totals 100%
    • "Circle X" = (Y% + 20%)
    • "Circle Y" = Y%
    • "T" = Total = 100%

  1. Find T
  • X% + Y% = 100%
(Y+20%) + (Y%) = (100%)
Y = 40%
  • Y = (40%/100%) = (70 votes)/(T votes)
T = 175 votes
2. Find (X-Y)
  • X = (T) - (Y) = (175) - (70)
    X = 105
  • (X-Y) = (105) - (70) = 35

Answer: C
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Let Total votes be x,
votes received by Y = 70
votes received by X = 20% of total + (Votes received by Y) --> 0.2x + 70

By how many votes Y lost = ( 0.2x + 70 ) - 70 = 0.2x

Total votes x needs to be equal 140+0.2x (Votes of Y + Votes of X)
0.8x = 140,
diving by 4 on both sides, gives 0.2x = 35 (this is the required 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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

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C. 35

X% + Y% = 100%
(Y%+20%) + Y% = 100%
Y% = 40%
X%= 60%

70/40*60=105
105-70=35

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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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Ans: A

Each employee voted for exactly one proposal.
Proposal X received 20% of the total votes more than Proposal Y. = x = (1+20/100)y
If Proposal Y received 70 votes then = x = 1.2 * 70 = 84 votes.
by how many votes did it (Y) lose? 84-70 = 14 votes (answer)
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Given the number of votes of Y is 70
And vote of x is 20% more than vote percent of Y
Hence if total vote is 't'
x is 0.6 t and y is 0.4t

Hence 0.4 t = 70 ==> t=135
Hence x = 105
X lead by 35 votes Option C
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Let's say there were a total of "m" votes received across projects

X received 20% of the total votes more than Y,

we can say, X = Y +0.2m (equation 1)

Now, we are also told that, Y=70

We can infer that if Y=70, and there are a total of "m" votes, X = m-70

Substituting these 2 values in equation 1, we get,

m=70 = 70 + 0.2m

Solving for m, we get, m=175

So, X = 105 and Y = 70

Question is, by how many votes did Y lose, or in other words, X had how many more votes than Y

X-Y = 105 - 70 = 35

Answer C.
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Proposal X is 20% more than Y
Then X= 1.2Y
X = 1.2*70 = 84

The difference between x and y is 14. Ans A
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IMO C

Proposal Y= 70 votes
Proposal X= x votes

Total votes = (x+70)

x- 70 = 20/100 (x+70)
Therefore, x= 105

Proposal Y lost by 105 -70= 35 votes

Hence Answer C
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