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605-655 (Medium)|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 23:31
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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Column A

( 240 * 1/2 ) = ( 200 * 2/5 ) + 40 * x

120 = 80 + 40 x

x = 40/40 = 1

Column B

200 * 2/5 = 2 ( 40 * y)

2 * 40 = 2 * 40 * y

y = 1

Therefore

x = 1
y = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 23:46
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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Total electrical output for Strategy 1
0.5kWH *240 square meters = 120kWH

Strategy 2 - 200 square meters's electrical output
0.4kWH * 200 = 80kWH

To result some total electrical output, the electrical output for the remaining 40 square meters is:
120kWH - 80kWH = 40kWH

Calculate x
x kWH * 40 square meters = 40 kWH
x = 1

---------------------------------------------------------

Twice of additional output from 40 square meter setup:
40 kWH *2 = 80kWH

Calculate y
y kWH * 200 square meters = 80kWH
y = 0.4

Therefore x = 1, y = 0.4
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 23:50
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
x y
0.1
0.4
0.5
0.8
1

240*0.5=200*0.4+40x
x=1

200*0.4=2(40y)
y=1

Ans 1,1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 00:08
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1) the same!--> 240*0.5=200*0.4+x*40-->120-80=40x->40=40x->x=1
2) 0.4*200=2*40*y-->20*4=2*40y->y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 00:11
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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For Strategy 1, the entire 240 square meters operate at 0.5 kWh per square meter, resulting in a total electrical output of 240×0.5=120 kWh.

For Strategy 2, 200 square meters operate at 0.4 kWh per square meter, yielding an output of 200×0.4=80 kWh.
The remaining 40 square meters operate at x kWh per square meter, producing 40x kWh.
The total output for Strategy 2 is 80+40x kWh

To find x such that the strategies have the same total output, equate the total outputs:
120=80+40x
Solving gives x=1

For the value of y such that the output from the 200 square meters is twice the output from the 40 square meters, set:
200×0.4=2×(40×y)
This simplifies to 80=80y, giving y=1

The values are x=1 and y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 00:33
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Strategy 1: total electrical output = 120 kW
Strategy 2 : 200 square meters = 80kW and the remaining 40 square meters = x kW

x the value of x at which the two strategies result in the same total electrical output
the differential 40 kW can be produced at a rate of 1kWH per square meter

y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup
Hence the output produced by the remaining 40 square meters should be 40 kW (80/2) that can be produced at a rate of 1kWH per square meter

Hence, for both the answer is 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 00:39
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From the first set-up, we get \(240*0.5=120 kWH\)
From the second one, we get: \(200*0.4=80 kWH\) PLUS \(40*n kWH\)

  • To find x: \(80 + 40n = 120, 40n=40, n=1=x\)
  • To find y: \(80kWH=2*40n => 40n=40, n=1=y\)

Therefore, the answers are identical and x=y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 00:52
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Therefore for strategy 1 total = 240*0.5 = 120

Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. For this 200 * 0.4= 80 we find the value x so that these two strategy be provide same electrical output so we know that strategy 1 provide 120 electrical output from 240 square meter and from strategy 2 we know that from the 200 square meter area we got 80 electrical output and remaining 40 has to multiply by x to get the value of 120 so 80+40x = 120
40x= 120-80
40x=40
x=1 so x is 1 By putting the value of x in strategy 2 we get the same electrical output as strategy 1


select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. 200 sq meter has the output of 80 which is twice of 40(40*2=80) and we need to find y which by multiplying with 40 which gives us the answer as 40 so the only answer to this is 1 by putting the value 1 in y we get 40 so the twice of 40 is 80

so our answers are x =1 and y= 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 01:04
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Hi everyone :)

straightforward. many words but we can keep it simple.

Option 1: 240 - 0.5kWH - 120kWH total
Option 2: 200 - 0.4kWH - 80kWH + 40 - xkWH

Now we are asked 2 question:
"x"- same total kWH? 120-80=40 thus: 40*x=40? x=1
"y" - half of 200 (80kWH) = 40 thus: 80/2=40*y y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 01:07
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Strategy 1: entire 240 square meters * electrical output 0.5kWH per square meter
Total output = 240 * .05 kWH

Strategy 2: 200 square meters * 0.4kWH per square meter + 40 square meters * x kWH per square meter
200*0.4 + 40 * y kWH

For x the two strategies result in the same total electrical output
240 * .05 kWH = 200*0.4 + 40 * x kWH
120 = 80 + 40x
x = 1

For y: Output from the 200 square meters setup = output from the 40 square meters setup.
200*0.4 = 2(40 * y)
80 = 80 y
y = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 01:42
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Mission 1: x =? so that A and B result in the same total electrical output.
Strategy A:
240 sq meters, high-efficiency solar panel setup producing 0.5 kWH/sq meter
=> Total production = 240 * 0.5 = 120 kWH

Strategy B:
240 sq meters, with:
* 200 sq meters, each producing 0.4kWH
* 40 sq mater, each producing x kWH
=> Total production = 200 * 0.4 + 40 * x = 80 + 40x
=> To be equal production as strategy A: 80 + 40x = 120 => x = 1
=> E

Mission 2: y =? so that output from the 200 sq meters is exactly twice the additional output from the 40 sq meters setup
* Total Production for 200 sq meter setup = 200 * 04 = 80 kWH
* Total Production for 40 sq meter setup = 40y
As per the mission, 80 = 2*40y => 80 = 80y => y = 1
=> E
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 01:48
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Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter.

Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter.

Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Question

Select for x the value of x at which the two strategies result in the same total electrical output

Select for y the value at which the output from the 200 square meters setup


the total output from strategy 1

240*0.5=120

Strategy 2

200*0.4+40*x


120= 80+40x

40x= 40

x=1


Y

to solve for Y we remember that strategy 2 has 2 phases

Phase 1 is 200sqm @ 0.4KWH

Phase 2 is 40sqm @ y kwh


Y is such that Phase 1= 2*phase 2

Phase 1 = 80

80= 2(40y)

80= 80Y

Y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 01:56
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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for x we have: 240*0.5= 200*0.4+40x ==> x=1

for y we can write : 200*0.4=2*40*y ==> y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 02:04
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Strategy 1 -

240 * 0.5 = 120kWH per square meter

Strategy 2 -

200 * 0.4 + 40 * x

(80 + 40x)kWH per square meter

For first column,

(80 + 40x) = 120

x = 1

For second column,

80 = 2(40*y)

y = 1

Therefore,

x=1
y=1
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 02:14
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To solve this question, calculate the energy accumulated from Strategy 1:

240*0.5 Kwh=120 Kwh

For the energy from Strategy 2 to be equal to the energy generated from Strategy 1,
120=0.4*200+40*x
40=40x
x=1

For the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup,

0.4*200=40*2*y
80=80*y
y=1

Hence the values of x & y both come out to be 1
x=1
y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 02:17
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Ans. value of x in both scenario = 1

Strategy 1:
Area = 240 sq. meter
Electrical output per sq. meter = 0.5 kWH
Total electrical output = 240*0.5 = 120 kWH

Strategy 2:
Area1 = 200 sq. meter
Electrical output per sq. meter for area1 = 0.4 kWH
Total electrical output for area1= 200*0.4 = 80 kWH

Area2 = 240 sq. meter
Electrical output per sq. meter for area2 = x kWH
Total electrical output for area2= 40*x = 40x kWH

Total electrical output= Electrical output for area1 + Electrical output for area2 = 80+40x


Now in Scenario 1(select for x), it is said that the electrical power in both strategies is same
So, 80+40x=120
=> 40x=40
=>x=1

In Scenario 2(select for y), it is mentioned that the energy in Area1 of strategy 2 is twice the energy in Area2 of strategy 2
So, 40x=80/2
=> x = 1

Therefore in both scenarios(value for x and y), the solution is 1
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 04:14
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In Strategy 1:
240*0.5=120 kWh

In Strategy 2:
200*0.4+40*x=80+40x kWh

120=80+40x
x=1

80=2*40y=80y
y=1

Answers x=1, y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 04:30
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i) 240 * 0.5 = 200 * 0.4 + 40 * x
120 = 80 + 40x
x = 1

ii) y * 200 * 0.4 = 2 * 40
y = 1

x = 1 & y = 1
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 05:27
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In TPA questions its always better to form a strategy first before solving. Well this is a detail bulky question.

The stem tells us that;

  • A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from
  • Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter
  • Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter
  • and the remaining 40 square meters with an output of x kWH per square meter
  • Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

And we have to select values for;
  • x at which the two strategies result in the same total electrical output
  • y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup

Let's tabulate the data to better read it;

STRATEGY ASTRATEGY B
240*0.5200*0.440*x
1208040x

For same total electrical output;

120=80+40x
40=40x
x=1

When the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup,
80=2*40y
80=80y
y=1

Hence we can fill the respective options here.
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 20 Dec 2024, 06:01
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  1. For same output, I believe it should be:
    (240)(0.5) = (200)(0.4) + (40)(x),
    Solving for x we get x+1.
  2. For out of 200 m = twice output of 40 m. It should be :
    (200)(0.4) = (2)(40)(y),
    Solving for y, we get y=1.

    Hence , answer is 1 for both x & y.
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A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of x kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.

Select for x the value of x at which the two strategies result in the same total electrical output, and select for y the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.
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