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

Quarterly totals are: \[ \text{Q1} = 5{,}000,\quad \text{Q2} = 5{,}500,\quad \text{Q3} = 5{,}500,\quad \text{Q4} = 6{,}000. \] Annual total \[ = 5{,}000 + 5{,}500 + 5{,}500 + 6{,}000 = 22{,}000\ \text{GWh}. \]

Answer 2

Add across sources for the year instead of across quarters. Coal: \(2,200+2,400+2,100+2,300 = 9,000\). Gas: \(800+700+900+850 = 3,250\). Hydro: \(900+1,000+800+1,100 = 3,800\). Solar: \(700+800+1,000+900 = 3,400\). Wind: \(400+600+700+850 = 2,550\). Summing these five annual totals, \(9,000+3,250+3,800+3,400+2,550 = 22,000\ \text{GWh}\), the same grand total reached by summing the four quarters.

Answer 3

Summing by source across the year, rather than by quarter, gives a second total that each option can be checked against.

1. 20,500: Adding the five annual source totals, Coal 9,000, Gas 3,250, Hydro 3,800, Solar 3,400, and Wind 2,550, gives 22,000, which is 1,500 more than this option, so it is too low.
2. 21,500: Still 500 short of the source-wise total of 22,000.
3. 22,000: This matches the sum of the five annual source totals exactly, \(9{,}000+3{,}250+3{,}800+3{,}400+2{,}550=22{,}000\).
4. 22,500: This overshoots the source-wise total by 500.

Adding up generation source by source across the whole year confirms the same 22,000 GWh reached by adding the four quarterly totals.

So the correct answer is 22,000.

Answer 4

Renewables by quarter: \[ \text{Q1: } 900+700+400 = 2{,}000, \] \[ \text{Q2: } 1{,}000+800+600 = 2{,}400, \] \[ \text{Q3: } 800+1{,}000+700 = 2{,}500, \] \[ \text{Q4: } 1{,}100+900+850 = 2{,}850. \] Total renewables \(= 2{,}000+2{,}400+2{,}500+2{,}850 = 9{,}750\ \text{GWh}.\) Annual total \(=22{,}000\ \text{GWh}\). \[ \text{Renewable share} = \frac{9{,}750}{22{,}000}\times 100 \approx 44.3%. \]

Answer 5

Instead of adding Hydro, Solar and Wind every quarter, find the non-renewable (Coal + Gas) total first: Q1 = \(2,200+800=3,000\); Q2 = \(2,400+700=3,100\); Q3 = \(2,100+900=3,000\); Q4 = \(2,300+850=3,150\). Annual non-renewable = \(3,000+3,100+3,000+3,150 = 12,250\ \text{GWh}\). Since the annual total is \(22,000\ \text{GWh}\), renewables must be \(22,000 - 12,250 = 9,750\ \text{GWh}\), giving the same \(9,750/22,000 \times 100 \approx 44.3\%\) share.

Answer 6

With total renewable generation already known to be 9,750 GWh out of 22,000 GWh annual generation, each option can be tested by multiplying it back against 22,000.

1. 42.5%: \(42.5\%\) of \(22{,}000=9{,}350\), short of the actual 9,750 GWh renewable figure.
2. 43.8%: \(43.8\%\) of \(22{,}000=9{,}636\), still below 9,750.
3. 44.3%: \(44.3\%\) of \(22{,}000=9{,}746\), matching the actual 9,750 GWh renewable total closely, the small gap being rounding in the percentage.
4. 45.0%: \(45\%\) of \(22{,}000=9{,}900\), overshooting the actual renewable total.

Only 44.3% reproduces the true renewable generation figure of 9,750 GWh when applied to the annual total.

So the correct answer is 44.3%.

Answer 7

Renewable share per quarter: \[ \text{Q1: } \frac{2{,}000}{5{,}000} = 40%, \quad \text{Q2: } \frac{2{,}400}{5{,}500} \approx 43.6%, \] \[ \text{Q3: } \frac{2{,}500}{5{,}500} \approx 45.5%, \quad \text{Q4: } \frac{2{,}850}{6{,}000} = 47.5%. \] Highest share is in \(\boxed{\text{Q4}}\).

Answer 8

Instead of computing each quarter's renewable percentage directly, look at the non-renewable (Coal + Gas) share, since a lower non-renewable share means a higher renewable share. As a fraction of that quarter's total: Q1 = \(3,000/5,000=60\%\), Q2 = \(3,100/5,500\approx56.4\%\), Q3 = \(3,000/5,500\approx54.5\%\), Q4 = \(3,150/6,000=52.5\%\). Q4 has the smallest non-renewable share, so it must carry the largest renewable share.

Answer 9

Comparing quarters pairwise by cross-multiplying their renewable fractions avoids converting every quarter to a decimal percentage up front.

1. Q1: Q1's renewable fraction is \(2{,}000/5{,}000\). Compared against Q4's \(2{,}850/6{,}000\) by cross-multiplying, \(2{,}000\times6{,}000=12{,}000{,}000\) versus \(2{,}850\times5{,}000=14{,}250{,}000\); since Q4's product is larger, Q1's share is smaller, ruling out Q1.
2. Q2: Q2's fraction is \(2{,}400/5{,}500\). Against Q4's \(2{,}850/6{,}000\), cross-multiplying gives \(2{,}400\times6{,}000=14{,}400{,}000\) versus \(2{,}850\times5{,}500=15{,}675{,}000\); Q4 again wins, so Q2 is not the highest.
3. Q3: Q3's fraction is \(2{,}500/5{,}500\). Against Q4, cross-multiplying gives \(2{,}500\times6{,}000=15{,}000{,}000\) versus \(2{,}850\times5{,}500=15{,}675{,}000\); Q4 still comes out ahead, so Q3 is not the highest either.
4. Q4: Having beaten Q1, Q2, and Q3 in every pairwise cross-multiplication check, Q4's renewable fraction is confirmed as the largest of the four.

Testing Q4 against each other quarter directly, without converting to percentages, confirms it has the highest renewable share.

So the correct answer is Q4.

Answer 10

Q4 Coal \(= 2{,}300\ \text{GWh}\). \(10%\) reduction \(= 230\ \text{GWh}\). This 230 GWh is shared equally by Solar and Wind: \[ \text{Extra for each} = 230/2 = 115\ \text{GWh}. \] Original Q4 Solar \(= 900\ \text{GWh}\). New Q4 Solar \(= 900 + 115 = 1{,}015\ \text{GWh}\).

Answer 11

Instead of computing the coal cut and directly adding half of it to Solar, use the fact that total Q4 generation is unchanged since the reduction is only redistributed, not lost. New Coal = \(2,300 - 230 = 2,070\), and Gas and Hydro don't change (\(850\) and \(1,100\)). So Solar and Wind together must now total \(6,000 - 2,070 - 850 - 1,100 = 1,980\), up from their old combined \(900+850=1,750\), a rise of \(230\ \text{GWh}\) split evenly between them. Adding half of that rise, \(115\), to Solar's original \(900\) gives the same \(1,015\ \text{GWh}\).

Answer 12

Since Solar and Wind gain the coal cut equally, and the coal cut itself is fixed at 230 GWh, each option can be tested by checking whether it implies exactly half of that cut being added to Solar's original 900 GWh.

1. 975: This is only 75 GWh more than Solar's original 900, but half of the 230 GWh coal cut is 115, so this option understates Solar's gain.
2. 1,000: This is 100 GWh more than 900, still short of the required 115 GWh gain.
3. 1,015: This is exactly 115 GWh more than Solar's original 900, matching half of the 230 GWh coal cut precisely.
4. 1,030: This would mean Solar gained 130 GWh, more than the 115 GWh it is actually entitled to under an equal split with Wind.

Half of the 230 GWh cut from Coal is 115 GWh, and adding that to Solar's original 900 GWh gives 1,015 GWh.

So the correct answer is 1,015.

Answer 13

Annual Gas: \[ 800 + 700 + 900 + 850 = 3{,}250\ \text{GWh}. \] Annual Hydro: \[ 900 + 1{,}000 + 800 + 1{,}100 = 3{,}800\ \text{GWh}. \] Ratio Gas : Hydro \[ = 3{,}250 : 3{,}800 = 3250:3800. \] Divide by \(50\): \[ = 65 : 76. \]

Answer 14

Rather than simplifying the raw totals directly, compute the decimal value of the ratio and check it against the options: Gas/Hydro = \(3,250/3,800 \approx 0.855\). As decimals, \(13:15 \approx 0.867\), \(65:76 \approx 0.855\), \(5:6 \approx 0.833\), and \(26:31 \approx 0.839\) — only \(65:76\) matches, confirming it without finding the greatest common divisor of \(3,250\) and \(3,800\).

Answer 15

With annual Gas at 3,250 GWh and annual Hydro at 3,800 GWh already established, each ratio option can be tested by cross-multiplying against these two figures.

1. 13:15: Cross-multiplying, \(13\times3{,}800=49{,}400\) and \(15\times3{,}250=48{,}750\). These do not match, so 13:15 is not the same ratio.
2. 65:76: Cross-multiplying, \(65\times3{,}800=2{,}47{,}000\) and \(76\times3{,}250=2{,}47{,}000\). These match exactly, confirming this ratio.
3. 5:6: Cross-multiplying, \(5\times3{,}800=19{,}000\) and \(6\times3{,}250=19{,}500\). These are close but not equal, so this simplified-looking ratio is not exact.
4. 26:31: Cross-multiplying, \(26\times3{,}800=98{,}800\) and \(31\times3{,}250=1{,}00{,}750\). These do not match either.

Only 65:76 survives the cross-multiplication check against the actual annual Gas and Hydro totals.

So the correct answer is 65:76.

Answer 16

From earlier calculations: \[ \text{Q1: } 40%,\quad \text{Q2: } \approx 43.6%,\quad \text{Q3: } \approx 45.5%,\quad \text{Q4: } 47.5%. \] The smallest share is in \(\boxed{\text{Q1}}\).

Answer 17

Instead of recomputing each quarter's share, simply rank the four figures directly: \(40\%, 43.6\%, 45.5\%, 47.5\%\). Arranging these in increasing order gives \(40\% < 43.6\% < 45.5\% < 47.5\%\), so the smallest value corresponds to Q1. Since every other quarter's share is strictly higher, Q1 is confirmed as the quarter with the lowest renewable percentage share.

Answer 18

This question asks which quarter recorded the smallest renewable-energy share among the four listed quarters. Let's look at each option against the computed quarterly shares.

1. Q1: The renewable share for this quarter works out to \(40\%\), the smallest of the four figures, since every later quarter shows a higher percentage than this one.
2. Q2: This quarter's share comes to about \(43.6\%\), which is higher than Q1's \(40\%\), so Q2 cannot be the lowest.
3. Q3: The share here rises further to about \(45.5\%\), continuing the upward pattern, so this option is also ruled out.
4. Q4: By the final quarter the share climbs to about \(47.5\%\), the highest of the year, so Q4 is the opposite of what the question asks for.

Comparing all four figures together, \(40\%\) is the smallest value on the list, so Q1 holds the lowest renewable percentage share.

So the correct answer is Q1.