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605-655 Level|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 11:05
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Strategy 1

Area used = 240 square meter
Electrical op = 0.5 kWH per square meter

Total electrical op = 240*0.5 = 120kWH

Strategy 2

Area used = 200 square meter and 40 square meter (in parts)
Electrical op = 0.4 kWH per square meter for 200 square meter and x kWH per square meter for 40 square meter

Total electrical op = 200*0.4 + 40*x = 80 + 40*x kWH

Same total electrical op for both strategies

120 = 80 + 40*x
x = 1

x = 1

Op from 200 setup = Twice the op from 40 setup

80 = 2 * (40*x)
x = 1

y = 1

Answer = 1,1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 11:22
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Condition 1: Equal total electrical output
  • Strategy 1: 240 sq.m * 0.5 kWh = 120 kWh
  • Strategy 2:
    • 200 sq.m * 0.4 kWh = 80 kWh
    • 40 sq.m * x kWh = 40x kWh
      For total output to be equal:
      80 + 40x = 120
      Solving:
      40x = 40 → x = 1
Condition 2: Output from 200 sq.m is twice the additional output from 40 sq.m
  • We know x = 1, so the output from 40 sq.m is 40 kWh and from 200 sq.m is 80 kWh.
    At y = 0.4, we have the desired condition.

Final Answer: x = 1 and y = 0.4
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 11:38
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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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Strategy 1:
Energy = 240*0.5 = 120kWH

Strategy 2:
Energy = 200*0.4 + 40*x = (80+40x)kWH

Case 1:
Strategy 1 energy = Strategy 2 energy
120 = 80+40x
=> x=1

Case 2:
80 = 2*40y
=> y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 11:46
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1. Using the full 240 sq meters with 0.5 kWh per square meter:
Output1 = 240*1/2 =120 120kWh
Output2 = (200*0.4) + (40*x) -> 80 + 40x

Output 1 = Output 2, Thus 80 + 4x = 120 -> x = 1

2. 200 sq meters is 2x additional output from 40 sqd meters.

200*0.4 =80 kWh, and the additional output from 40 sad meters is 40x

80 = 2(40x) -> x = 0.4, which we denominated as y.

Thus y=0.4 and x=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 11:56
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strategy 1:
0.5kWh * 240
120KWh

strategy 2:
0.4KWh * 200 + xKWh * 40
80KWh + 40x

to product equal power in both strategies

80 + 40x = 120
x = 1

to produce half the power in the 40x of the 80KWh in strategy2

x must be 1.
1/2(80KWh) = 40x
x = 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 19 Dec 2024, 12:13
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Strategy 1
Output = 240 × 0.5 = 120

Strategy 2
Output = (200 × 0.4) + (40 × x)

Scenario 1
120 = (200 × 0.4) + (40 × x)
120 = 80 + 40x
40x = 40
x = 1

Scenario 2
From Strategy 2, 200 × 0.4 = 80

80 = 2 × (40 × y)
80 = 80y
y = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 12:21
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From the question, we can calculate that under Strategy 1, the total electrical output = 0.5*240 = 120 KWH

Under strategy 2, for the 200 square meter area, the total electrical output = 0.4*200 = 80 KWH

The first column/question asks us to calculate the value of x that would result in same total electrical output. Therefore, x*40 = Total output from A - output from B for the 200 square meters >> x*40 = (120-80) >> x = 1

Note that the 200 square meter area is giving a total output of 80 KWH and for x = 1 , the 40 square meter area is giving a total output of 40 KWH. Hence, the electrical output from the 200 square meter area is twice that from the 40 square meter area, which is what the second part of the question is asking for. Hence, 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 19 Dec 2024, 12:36
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0.5*240 = 200*0.4 + 40x
x=1

200*0.4= 2*40y
y=1


Answer 1 & 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 12:44
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Quote:
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.
Show more

Total output by using strategy 1= 240*0.5=120 kWH

Output from the 200 m2 part in strategy 2= 200*0.4=80 kWH
Output required from the 40 m2 stretch to match the output from strategy 1= 40 kWH\
Value of x = 40/40 = 1 kWH

Value of x at which the output from 200 m2 is exactly double of that from 40 m2= 1 kWH as 80 = 1/2(40)

Therefore Answer (1), (1)
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 14:31
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Strategy 1, 0.5*240 = 120 kWh
[color=#2a2a2a][color=#0f0f0f]Strategy 2, 200*0,4 + 40x

if both outputs are identical then, 80 + 40x = 120 --> x = 1 kWh

if 80 is double the energy output from 40y then --> 80y + 40y = 120 --> 120y = 120 --> y= 1.
Correct solutions are x = 1 & y = 1[/color][/color]
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 14:58
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Bunuel
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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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x = 1 y = 1

240 x .5kwh = 120
200 x .4kwh = 80
40(x) = 40 x = 1
left is 120, and right is 120 so X = 1

200(.4) = 80 and 40(1) = 40
so Y = 1 again.
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 18:15
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strategy 1: 240x0.5 = 120
strategy 2: 200x0.4 + 40x = 80 + 40x

120 = 80 + 40x
x = 1

80 = 2*40y
y = 1

x = 1 and y = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 18:33
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1) 120=80+40x
x=1


2) 80=2(80-40y)
=> y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 19:30
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1. Complete 240 Sq. M. => 0.5*240 = 120
2. 200 + 40 sq. M. => 0.4*200 + x * 40 = 80 + 40x

Now for First Statement Equal Power, So 40x should produce 40, so x=1

For Second 80 = 2*40x; x=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 20:26
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output of 240 strategy = 240 x 0.5 = 120
Output of alternative strategy = 200 x 0.4 + 40X = 80 + 40X

Solve for x scenario:
120 = 80 + 40X
X = 1

Solve for y scenario:
80 = 2 x 40X
X = 1

Answer: x = y = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 21:25
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Hello,
strategy 1
total output =240*0.5=120KWH
strategy 2
total output =200*0.4=80KWH
40*x=120-80
so both output to be same x value has to been 1 as we need additional 40KWH

Then Y value has to be 0.4 so that is gets exactly double output of additional requirement
so X=1 and Y=0.4
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 22:47
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Strategy 1:
Area = 240 square meters
Electrical output = 0.5kWH per square meter
Total Electrical output = 240*0.5 = 120 kWH

Strategy 2:

Setup 1:
Area = 200 square meters
Electrical output = 0.4kWH per square meter
Total Electrical output = 200*0.4 = 80 kWH

Setup 2:
Area = 40 square meters
Electrical output = x kWH per square meter
Total Electrical output = 40*x = 40x kWH

Q: Select for x the value of x at which the two strategies result in the same total electrical output
This will be true when x = 1
120 kWH = 80 kWH + 40(1) kWH

So, x = 1

Q: 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
This will be true when x = 0.5
80 kWH = 2[40(0.5)] kWH
80 kWH = 2*20 kWH
80 kWH = 40 kWH

So, y = 0.5
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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 19 Dec 2024, 22:48
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Hi All,

Given:

S1: 240 sq meters for 0.5 kWH per sqm output .

Therefore total output = 240 x 0.5

S2: 200 sq meter for 0.4 kWH per sqm output + 40 sq m for x kWH output

Solving for X:

the value for x for both the stratergies have same output

250 x 0.5 = 200 x 0.4 + 40(x)

Solving the equation we get

x=1

Solving for Y:

the value for 200 sq m sheet is twice the output from 40 sq m

200 x 0.4 = 2 x 40(y)

solving this y=1



Ans x=1,y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 23:08
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Explanation:

We have two strategies for installing solar panels on 240 square meters:
  1. Strategy 1:
    • Use all 240 sqm with an efficiency of 0.5 kWH/sqm.
    • Total Output: 240 × 0.5 = 120 kWH.
  2. Strategy 2:
    • Use 200 sqm with an efficiency of 0.4 kWH/sqm.
    • Use the remaining 40 sqm with an efficiency of x kWH/sqm.
    • Total Output: 200 × 0.4 + 40 × x = 80 + 40x kWH.
Part 1: Finding xxx for Equal Total Output
We want both strategies to produce the same total electricity:
80 + 40x = 120
40x = 40 ⟹ x = 1
So, x = 1 kWH/sqm.

Part 2: Finding y Where 200 sqm Output is Twice the 40 sqm Output
Here, y represents the efficiency for the 40 sqm setup.
  • Output from 200 sqm: 200 × 0.4 = 80 kWH.
  • Output from 40 sqm: 40 × y kWH.
We want the 200 sqm output to be twice the 40 sqm output:
80 = 2 × (40y)
80 = 80y ⟹ y = 1
So, y = 1 kWH/sqm.
Final Selections:
  • x = 1
  • y = 1

Answer:
  • x = 1
  • y = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 23:28
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x and y both = 1

Strategy 1 = 240(0.5) = 120 kWH
Strategy 2 = 200(0.4) + 40x = 80 + 40x kWH

x: Strategy 1 = Strategy 2 --> 120 = 80 + 40x --> x = x = 1
y: 80 = 2y --> y = 40 = 40x --> x = y = 1
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