Question

The total annual generation (GWh) is:

• A. \(20{,}500\)
• B. \(21{,}500\)
• C. \(22{,}000\)
• D. \(22{,}500\)
• A. \(42.5%\)
• B. \(43.8%\)
• C. \(44.3%\)
• D. \(45.0%\)
• A. Q1
• B. Q2
• C. Q3
• D. Q4
• A. \(975\)
• B. \(1{,}000\)
• C. \(1{,}015\)
• D. \(1{,}030\)
• A. \(13:15\)
• B. \(65:76\)
• C. \(5:6\)
• D. \(26:31\)
• A. Q1
• B. Q2
• C. Q3
• D. Q4

Answer 1

The Correct Option is C

Step 1: The four quarterly totals are 5,000, 5,500, 5,500, and 6,000, which average out to \((5{,}000+5{,}500+5{,}500+6{,}000)/4=5{,}500\) GWh per quarter.
Step 2: Multiply this average by the four quarters in the year, since the annual total is just four quarters added together.
\[ \boxed{5{,}500 \times 4 = 22{,}000 \text{ GWh}} \]

Answer 2

Since the four quarterly totals sit close together, around 5,000 to 6,000 GWh, dividing each option by 4 and comparing to that range is a quick check.

1. 20,500: Divided by four quarters, this gives an average of 5,125 GWh, lower than every individual quarter except Q1, which does not fit a set of totals that peak at 6,000.
2. 21,500: This averages to 5,375 GWh per quarter, still below three of the four actual quarterly totals.
3. 22,000: This averages to exactly 5,500 GWh per quarter, right in the middle of the actual range of 5,000 to 6,000, and matching the two middle quarters (Q2 and Q3) precisely.
4. 22,500: This averages to 5,625 GWh per quarter, higher than three of the four actual quarterly totals, which is too high given only one quarter reaches 6,000.

An average of 5,500 GWh per quarter fits the actual spread of quarterly totals best, giving an annual figure of 22,000 GWh.

So the correct answer is 22,000.

Answer 3

Step 1: Find each renewable source's own share of the 22,000 GWh annual total: Hydro = \(3{,}800/22{,}000\approx17.3\%\), Solar = \(3{,}400/22{,}000\approx15.5\%\), Wind = \(2{,}550/22{,}000\approx11.6\%\).
Step 2: Add the three individual shares together, since the combined renewable share is just these three percentages summed.
\[ \boxed{17.3\%+15.5\%+11.6\%\approx44.3\%} \]

Answer 4

Since the annual renewable share has to sit somewhere between the lowest and highest quarterly shares, checking each option against that range is a useful filter.

1. 42.5%: This sits below the shares of three of the four quarters (Q2 at about 43.6%, Q3 at about 45.5%, Q4 at 47.5%), which would need Q1's much lower 40% share to pull the annual figure down sharply, but Q1 is not large enough relative to the other quarters to drag the average this low.
2. 43.8%: Closer to the middle of the range but still slightly below where the actual weighted mix of quarterly totals lands.
3. 44.3%: This falls between Q2's roughly 43.6% and Q3's roughly 45.5%, consistent with an annual figure that blends all four quarters, weighted more toward the larger Q4 total, which carries the highest individual share.
4. 45.0%: This is close to Q3's individual share alone, too high to represent a blend that includes Q1's much lower 40% share.

Weighing all four quarters, with extra pull from Q4's larger total and higher share, settles the annual figure at 44.3%.

So the correct answer is 44.3%.

Answer 5

Step 1: Wind's own share of each quarter's total keeps rising: \(400/5{,}000=8\%\) in Q1, \(600/5{,}500\approx10.9\%\) in Q2, \(700/5{,}500\approx12.7\%\) in Q3, and \(850/6{,}000\approx14.2\%\) in Q4.
Step 2: Since Wind's share climbs every quarter without dropping back, and Hydro and Solar's shares in Q4 are also at or near their yearly highs, Q4 is positioned to have the strongest combined renewable share.
Step 3: Confirming with the full renewable total for Q4, \(1{,}100+900+850=2{,}850\) out of 6,000, gives 47.5%, the highest of all four quarters.
\[ \boxed{\text{Q4}} \]

Answer 6

Rounding each quarter's renewable share to the nearest whole number and ranking them side by side settles this quickly.

1. Q1: \(2{,}000\) out of \(5{,}000\) rounds to 40%, the lowest of the four quarters.
2. Q2: \(2{,}400\) out of \(5{,}500\) rounds to about 44%, an improvement over Q1 but still behind the second half of the year.
3. Q3: \(2{,}500\) out of \(5{,}500\) rounds to about 45%, ahead of both Q1 and Q2.
4. Q4: \(2{,}850\) out of \(6{,}000\) rounds to about 48%, clearly ahead of the other three quarters even after rounding smooths out the small differences between them.

Ranked from lowest to highest, the four quarters run Q1, Q2, Q3, Q4 in increasing order of renewable share, putting Q4 at the top.

So the correct answer is Q4.

Answer 7

Step 1: The 10% coal cut equals \(10\%\) of \(2{,}300=230\) GWh, and this amount is removed from Coal and injected into Solar and Wind combined.
Step 2: As a share of Q4's total generation, 230 GWh out of 6,000 is about \(3.83\%\); splitting this evenly means Solar and Wind each pick up about \(1.92\%\) of Q4's total.
Step 3: Apply that \(1.92\%\) of 6,000, which is 115 GWh, to Solar's original 900 GWh figure.
\[ \boxed{900+115=1{,}015 \text{ GWh}} \]

Answer 8

Since Wind gains the same amount as Solar under an equal split, each Solar option implies a specific Wind value too, which can be checked for consistency.

1. 975: This implies Wind also rises to \(850+75=925\), but the two gains combined would total \(150\), not the required \(230\) GWh cut from Coal, so this option breaks the equal-split condition.
2. 1,000: This implies Wind rises to \(850+100=950\), a combined gain of \(200\) GWh, still short of the full \(230\) GWh that has to move out of Coal.
3. 1,015: This implies Wind rises to \(850+115=965\), a combined gain of \(230\) GWh, exactly matching the full amount cut from Coal.
4. 1,030: This implies Wind rises to \(850+130=980\), a combined gain of \(260\) GWh, more than the \(230\) GWh actually available from the coal cut.

Only the 1,015 figure keeps Solar's and Wind's combined gain equal to the full 230 GWh taken from Coal, split evenly between them.

So the correct answer is 1,015.

Answer 9

Step 1: Pair Q1 with Q3 and Q2 with Q4 for each source: Gas = \((800+900)+(700+850)=1{,}700+1{,}550=3{,}250\); Hydro = \((900+800)+(1{,}000+1{,}100)=1{,}700+2{,}100=3{,}800\).
Step 2: Both totals share a common factor of 50, since \(3{,}250=65\times50\) and \(3{,}800=76\times50\).
Step 3: Divide both by 50 to reach 65 and 76; checking prime factors, \(65=5\times13\) and \(76=4\times19\), confirms they share no further common factor.
\[ \boxed{65:76} \]

Answer 10

Each ratio option implies a specific percentage that Gas represents of Hydro; comparing that implied percentage to the actual \(3{,}250/3{,}800\) figure sorts out the options.

1. 13:15: This implies Gas is about \(86.7\%\) of Hydro, slightly higher than the actual \(3{,}250/3{,}800\approx85.5\%\).
2. 65:76: This implies Gas is about \(85.5\%\) of Hydro, matching the actual figure of \(3{,}250/3{,}800\approx85.5\%\) closely.
3. 5:6: This implies Gas is about \(83.3\%\) of Hydro, noticeably lower than the actual \(85.5\%\).
4. 26:31: This implies Gas is about \(83.9\%\) of Hydro, also below the actual figure.

Comparing implied percentages, only 65:76 lines up with the true Gas-to-Hydro relationship of about 85.5%.

So the correct answer is 65:76.

Answer 11

Step 1: List the four values.
The renewable share for each quarter is Q1 = \(40\%\), Q2 = \(43.6\%\), Q3 = \(45.5\%\), Q4 = \(47.5\%\).

Step 2: Find the gap from the highest quarter.
Q4 has the highest share at \(47.5\%\). Subtracting each quarter's share from this value gives the size of the gap: Q1 is \(47.5 - 40 = 7.5\) points behind, Q2 is \(47.5 - 43.6 = 3.9\) points behind, and Q3 is \(47.5 - 45.5 = 2\) points behind.

Step 3: Pick the largest gap.
The quarter with the biggest gap from the top value is also the quarter with the smallest share, since a bigger drop from the maximum means a lower starting number. Q1's gap of \(7.5\) points is larger than Q2's or Q3's.
\[ \boxed{\text{Q1}} \]

Answer 12

This question tests whether we can correctly identify the minimum value in a short list of percentages. Let's assess each quarter as a candidate for the lowest share.

1. Q1: Expressed as a ratio of Q1 to Q4, \(40/47.5 \approx 0.84\), meaning Q1's renewable share is only about 84% of Q4's, the smallest ratio among the four quarters.
2. Q2: The ratio here is \(43.6/47.5 \approx 0.92\), noticeably closer to Q4 than Q1 is, so Q2's share is not the smallest.
3. Q3: The ratio works out to \(45.5/47.5 \approx 0.96\), even closer to Q4, confirming Q3 sits above both Q1 and Q2.
4. Q4: By definition its ratio to itself is \(1\), the reference point and the largest share of the year, not the smallest.

Since Q1 produces the smallest ratio relative to the year's peak quarter, it is the quarter with the lowest renewable percentage share.

The correct answer is Q1.