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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 09:00
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12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


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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
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:00
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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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GMAT Club's Official Explanation:



Let’s first calculate the total electrical output for both strategies and solve for the given conditions.

Strategy 1
The total output from Strategy 1 using the entire 240 square meters at 0.5 kWH per square meter:
240 × 0.5 = 120 kWH

Strategy 2
1. The output from the 200 square meters at 0.4 kWH per square meter:
200 × 0.4 = 80 kWH

2. The output from the remaining 40 square meters at x kWH per square meter:
40x kWH

The total output from Strategy 2 is:
80 + 40x kWH

Solving for x in the First Column
To make the total output of both strategies equal:
120 = 80 + 40x
40 = 40x → x = 1.0

Solving for y in the Second Column
We want the output from the 200 square meters setup (80 kWH) to be twice the output from the 40 square meters setup at y kWH per square meter:
80 = 2 × (40y)
80 = 80y → y = 1.0

Answer
- Same total electrical output: 1.0
- 200 sq. m. setup provides double the output: 1.0
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 09:39
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Here, electrical output = (Electric output/ square metre) * Area

First Case:

EO(Strategy 1)= EO(Strategy 2)

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

Similarly:

200*0.4=2(40*y)
y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 09:42
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StrategyAreaOutput per square meterTotal output
12400.5120
2200 and 400.4 and x200*0.4 + 40x = 80 + 40x

Equal output

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

Output from 200 is twice that of 40

80 = 2*(40x)
x = 1

Hence, answer for both the columns is (1, 1)
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Electric Output(EO) for Str-1 is 120kwh(240*0.5kwh)
EO for Str-2 is 200*0.4 =80kwh + 40*x
for it to be equal x should be 1
for 80kwh =2(40*x)kwh, x should be 1
So 1,1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 09:50
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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.
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Given:
  • Strategy 1: Total output = 0.5 kWH/m2×240 m2=120 kWH0.5 \, \text{kWH/m}^2 \times 240 \, \text{m}^2 = 120 \, \text{kWH}.
  • Strategy 2:
    • 200 m2 setup: Output = 0.4 kWH/m2×200=80 kWH0.4 \, \text{kWH/m}^2 \times 200 = 80 \, \text{kWH}.
    • 40 m2 setup: Output = x kWH/m2×40=40xx \, \text{kWH/m}^2 \times 40 = 40x.
    • Total output = 80+40x80 + 40x.
Conditions:
  1. To find xx:
    Set total output of Strategy 2 equal to Strategy 1:
    80+40x=12080 + 40x = 120
    Solve for xx:
    40x=40⇒x=1.40x = 40 \quad \Rightarrow \quad x = 1.
  2. To find yy:
    Output from the 200 m2 setup should be twice the output from the 40 m2 setup:
    0.4×200=2×(40y).0.4 \times 200 = 2 \times (40y).
    Solve for yy:
    80=80y⇒y=0.4.80 = 80y \quad \Rightarrow \quad y = 0.4.
[hr]
Selections:
  • x = 1
  • y = 0.4
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 09:52
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Strategy 1:
• Uses the entire 240 square meters.
• Electrical output per square meter: 0.5 kWH.
Total electrical output for Strategy 1:Output1=240×0.5=120 kWHOutput1=240×0.5=120 kWH

Strategy 2:
• Splits the area into two setups: 200 square meters and 40 square meters.
• Electrical output for the 200 square meters: 0.4 kWH per square meter.
• Electrical output for the remaining 40 square meters: xx kWH per square meter.

Total electrical output for Strategy 2:
Output2=(200×0.4)+(40×x)
Output2=(200×0.4)+(40×x)
Output2=80+40x
Output2=80+40x
To find the value of x that makes the total electrical output of both strategies equal:
Output1=Output2
120=80+40x
120−80=40x
40=40x
x=1
So, the value of x which the two strategies result in the same total electrical output is 1.

Additional Condition for y: we don't need the do calcuation as it satsfies the above condition

So, the value of y at which the output from the 200 square meters setup is exactly twice the additional output from the 40 square meters setup is 1.
Selections:
• x=1
• y=1
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[/quote]
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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.
Show more

Strategy 1: Total output = 240 * 0.5 = 120 kWH
Strategy 2:
Total output = 200 * 0.4 + 40 * x
For both strategies to have the same output: 200 * 0.4 + 40 * x = 120
80 + 40x = 120
40x = 40
x = 1
For the 200 sq m setup to have twice the output of the 40 sq m setup:
200 * 0.4 = 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, 10:07
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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.

Strategy 1: -
Area = 240 square meters
Electrical output = .5 KWH per square meters = 240*.5 = 120 KWH

Strategy 2: -
Area 1 = 200 square meters
Electrical output = .4 KWH per square meter = .4*200 = 80 KWH
Area 2 = 40 square meters
Electrical output = x KWH per square meter = x*40 = 40x KWH
Total Electrical output = 80 + 40x KWH

Select for x the value of x at which the two strategies result in the same total electrical output
120 = 80 + 40x
x = 1 KWH per square meter

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.
80 = 2*40y = 80y
y = 1 KWH per square meter

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.

xy
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:23
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240 square meters, 2 strategies can be followed

1. Single Panel with 0.5Kwh, total Output on 240 square meters = 120KWH

2. 2 Panels (1st 200 square meter with 0.4KWH and 40 square meter with xkwh)
Total Output = 80+40x KWH

Now
Select for x the value of x at which the two strategies result in the same total electrical output,
80+40x = 120
X = 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.

80 = 2*40X
X = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:25
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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.
Show more

For x (same output from both strategies):
  • Strategy 1 output:
  • 240×0.5=120
  • Strategy 2 output: 200×0.4+40×x=80+40x
    Set 80+40x=120, solve for x: 40x=40 Answer for x: 1
For y (200 sq. meters output twice 40 sq. meters output):
  • Set 200×0.4=2×(40×y)
  • Solve: 80=80y
    Answer for y: 1
Final Answer: 1,1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:26
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Total power from Strategy 1 = 240 * 0.5 = 120KWH
Total power from Strategy 2 = 200 * 0.4 + 40 * x = 80 + 40x

given, 80 + 40x = 120 => x = 1KWH

For y, we need to choose a y such that 200 * 0.4 = 2 * 40 * y => y = 1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:32
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Strategy 1 = 240 * 0.5 = 120kwh
Strategy 2 = 200 * 0.4 = 80
40 * x = 40x

120 = 80 + 40x
x = 1

For y
the value at which 80 = 2 * 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, 10:34
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To find x:
Strategy 1 = Strategy 2
--> 240 x 0.5 = 200 x 0.4 + 40 x (x)
-->120 =80 + 40x
--> x = 1

To find y:
200 x 0.4 = 2 x 40 x y
--> 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, 10:40
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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.
Show more
Strategy 1: 240 * 0.5 = 120 kWH
Strategy 2: 200 * 0.4 + 40 * x = 80 + 40*x kWH

Question 1: 120 = 80 + 40x => x =1
Question 2: 80 = 2(40y) => y = 1
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1) Total output = 240 * 0.5 = 120 kWH

2) Total output = (80 + 40x) kWH

For x:
=> 120 = 80 + 40x
=> x = 1

For y:
=> 80 = 2 * 40x
=> x = 1

Answer: (1, 1)
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:43
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Strategy 1:
  • Area: 240 m2
  • Efficiency: 0.5 kWh/m2
  • Output: 240×0.5=120 kWh
Strategy 2:
  • 200 m2 at 0.4 kWh/m2 and 40 m2 at x kWh/m2.
  • Output: (200×0.4)+40x
    =80+40x
To find x:
80+40x=120
⇒x=1

To find y: For 200 m2 output to be twice that of 40 m2:
80=2×40x
⇒x=1.

Final Answer:
  • x=1
  • y=1
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:47
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Ans for both x and y =1
I'll say though I feel under confident about marking the same option for both the columns. I did double check my solutions :)

Solving for x:

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

Solving for y:

200*0.4 = 2*(40*y)
=> y= 1
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A_Nishith
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:54
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Step 1: Determine the value of x for which the two strategies result in the same total electrical output.

Strategy 1:
The total electrical output for Strategy 1 is calculated by multiplying the area by the efficiency per square meter:

Output for Strategy 1=240×0.5=120kWh

Strategy 2:
Strategy 2 divides the area into two setups:

200 square meters with an output of 0.4 kWh per square meter, yielding:

Output for 200 square meters=200×0.4=80kWh

40 square meters with an output of x kWh per square meter, yielding:
Output for 40 square meters=40x
The total electrical output for Strategy 2 is:
Total Output for Strategy 2=80+40x

To make the total outputs equal for both strategies, we set the outputs equal:
120=80+40x

Solving for x:
120−80=40x⇒40=40x⇒x=1

So, the value of x that makes the two strategies result in the same output is 1

Step 2: Determine the value of y such that the output from the 200 square meters setup is exactly twice the additional output from the 40 square meters setup.

From Strategy 2, we have:

Output from the 200 square meters setup: 80kWh
Output from the 40 square meters setup: 40x kWh

We need to find x such that:

80=2×(40x)

Solving for x:
80=80x⇒x=1

Thus, for x=1, the output from the 200 square meters setup is exactly twice the output from the 40 square meters setup.

Therefore, the value of y is 1​

Final Answer:
x=1
y=1
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MKeerthu
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12 Days of Christmas GMAT Competition - Day 4: A solar energy project 19 Dec 2024, 10:54
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the answer is 1 and 0.4.

To calculate x -> 240 * 0.5 = 120

we need to find which will give 120 when multiplied 200*0.4 = 80 and the remaining 40 is obtained by 40* 1 = 40 . so x=1

To find y, Output from 200 m2
=2×(Output from 40m2)
80= 2*40y = 0.4
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