12 Days of Christmas GMAT Competition - Day 4: A solar energy project

Strategy	Area	Output per square meter	Total output
1	240	0.5	120
2	200 and 40	0.4 and x	200*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)

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

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.

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Selections:

• x = 1
• y = 0.4

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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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

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.

x	y
1	1

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

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

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

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

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

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

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)

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
  

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

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

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