# What If I Guessed on the SAT? and Other Questions

## Answering hypothetical questions with real calculations

### Reading Time: 4 minutes

Being a Stuyvesant student means breathing recycled eau de teenager air, deciding between running up stairs or braving crowded escalators, and wanting to throw in the towel on tests but never quite doing it. Sometimes, you get to wondering: am I really saving that much energy by avoiding the stairs? Does guessing on the SAT actually work for anyone? Could school air be useful? I figured it was time to put pen to paper (and finger to calculator) and find out.

1: What if we captured the carbon dioxide released by the Stuyvesant student body?

A person releases around 0.11 cubic meters of carbon dioxide per hour. Given the 3,344 students at Stuyvesant, 367.8 cubic meters of carbon dioxide are released into the building every hour. The air is kept breathable and circulating with windows and mechanical ventilation systems in accordance with building codes. If those ventilation systems were retrofitted with adsorbent filters, to which carbon dioxide would bind, they would be able to collect the gas and allow for its repurposing. Swedish company Climeworks is doing just that on a larger scale by capturing carbon dioxide in the open air. The captured gas is then dissolved in water and pumped underground. There, it reacts with basaltic rock to form carbonate minerals. It is predicted that if usage of carbon capture and storage technology became more widespread, it might be possible to offset climate change.

In one academic year at Stuyvesant, assuming every student is in the building for seven hours and maximum efficiency of filtration methods are utilized, 463,428 cubic meters of carbon dioxide could be captured. One ton of carbon dioxide is 556.2 cubic meters, meaning 833 tons of gas would be collected in total. The average American has a carbon footprint equivalent to 16 tons, so by collecting carbon dioxide at Stuyvesant over one year, 52 Americans’ damage to the environment is offset. Cars emit 4.6 tons of carbon dioxide annually, so one high school worth of carbon dioxide offsets 181 cars. Capturing carbon in offices and schools might be the key to the future.

2: What if I guessed on the SAT?

There are 141 multiple-choice questions (MCQs) with four answer choices each, and 13 grid-in questions on the SAT. If you were to guess on every MCQ and ace every grid-in, the chance of a 1600 is 1/4^141, or one in 7.7 x 1084. Good luck!

But, you’re a Stuyvesant student, so what if you took educated guesses instead? It is usually possible to narrow down the choices, so it may be more apt to guess between two possible answers. There are six ways to choose two answers out of four, three sets of which will contain the correct answer. The chance of choosing the right pair is one-third, and the chance of then choosing the right answer is one-half, so across the MCQs, the chance of a perfect score is one in 5.2 x 10109. The chances are actually lower than those of blind guessing.

However, if you always included the correct choice as one of the two possible ones, your chances of guessing to a perfect score improve to 1/2^141, or one in 2.8 x 1042.

To improve your chances, you might only guess on half of the multiple choice. Assuming the rest was correct and that your confidence in your educated guesses is 50 percent, that perfect score is one in 1.2 x 1021. Guessing on a third of the MCQ brings the chances up to one in 1.4 x 1014. Given the 3,344 students at Stuyvesant, if every student were to successfully narrow down 11 questions to two possible answer choices while getting the rest of the test correct, there would likely still only be one perfect score.

3: How much energy do I save by taking the Stuyvesant escalators instead of the stairs?

To answer this question, we need to know how much energy the average Stuyvesant student would burn if they were to always take the stairs. Judging by a few schedules from last year, most students are likely to have to go up 34 flights and down 32 flights of stairs on a no-gym school day. A healthy person should be able to climb four flights (60 stairs) per minute and descend about six flights (90 stairs) per minute, meaning a healthy Stuyvesant student spends about 14 minutes (8.5 ascending and 5.3 descending) on the stairs daily. The average 16-year-old male is 134 lbs, and the average 16-year-old female is 119 lbs, so without consideration of demographics, the average high school student is 127 lbs. Thus, this student will expend 62 calories a day on the Stuyvesant stairs, assuming a backpack weighing between one to 15 lbs.

However, this average student is not “saving” 62 calories by taking the escalator: standing burns energy, too! Standing on the escalator for about one minute per passing burns 12 calories, but counting the two flights up in the morning to get to the escalators, two flights down to the ground floor in the afternoon, and assuming four flights in either direction required by the odd and even floors, taking the escalators will still require an estimated maximum of 22 calories.

At 30 calories “saved” per day, what can you do? You can repurpose them to give your brain that extra boost when studying: a half-hour reading session requires 34 calories for someone at 125 lbs! Skipping the stairs for a week will “save” enough calories to fuel two hours of studying. Taking the escalators during midterms week isn’t laziness—it’s conservation. Or, use them towards building those abs: 70 sit-ups, perhaps?

Looking at it another way, skipping the stairs saves enough energy in joules to power a 60-watt light bulb for 34 minutes. Alternatively, taking the stairs all 180 days a school year expends the energy it takes to drive an electric car with a 25 kilowatt-hour engine 51 miles. After four years, the average Stuy student will burn enough calories on the stairs to drive that car 207 miles. But, the real question is: which option will get you to class on time more often? Knowledge is power!