# Tutor profile: Christine Q.

## Questions

### Subject: SAT

The coming decades will likely see more intense cluttering of jobs, innovation, and productivity in a smaller number of bigger cities and city-regions. Some regions could end up bloated beyond the capacity of their infrastructure, while others struggle, their promise sytmied by inadequate human or other resources. —Adapted from Richard Florida, the Great Reset Copy by Richard Florida. As used in line 55, “intense” most nearly means. A. emotional B. concentrated C. brilliant D. determined

Let’s first focus on a truth about the SAT, two answer choices that mean the same thing cancel each other out. On our first pass of the answer choices, before we even think about looking at the passage, can we eliminate any words that are the same? We can’t. What we do notice is that every answer choice agrees with a connotation of “intense”. The trap here is that students want to use their first idea of “intense” so that they can get to the next question. This question is not about the Test-Taker’s understanding of “intense”; it’s about Richard Florida’s understanding of “intense”. This question relies completely on the passage. Let’s look at the words around “intense” in the passage to figure out what clues we have that tell us what answer choice will work. We see: “coming decades will likely see more _____ cluttering of jobs, innovation, and productivity…” I really don’t see any clues in this sentence. I need these questions to be super obvious if I’m going to be answering them quickly and accurately. So I will move on to the next sentence: “…regions could end up bloated beyond the capacity”. There is my key phrase for intense: “bloated beyond the capacity”. My answer choice has to match that very literal phrase. Always count on the SAT being very literal. Answer choices A, C, and D do not literally describe “bloated beyond the capacity”, answer choice C does. Yay! We found our answer. To double check, we can always sub it in to the text: “The coming decades will likely see more “concentrated" cluttering of jobs, innovation, and productivity in a smaller number of bigger cities and city-regions. Some regions could end up bloated beyond the capacity of their infrastructure…” That is a double confirm!

### Subject: Geometry

Draw a circle with center O and diameter AC. Line segment OA = 5 ft. Line segment OD reaches from the point O, at the center of the circle to point D at the edge of the circle and has a length of 5 ft. Line segment OB, also reaches from center O to the point B at the edge of the circle. Line BD is not a diameter of circle O, it is a chord of circle O. Chord BD is perpendicular to Diameter AC. Chord BD forms the third side of triangle OBD. Point E is the midpoint of line BD. Point E is collinear to points O and C (lies on line OC). Line segment EC has a length of 2. What is the length of BD?

This is a really fun question, because the key to geometry is always looking for circles and right triangles. Every shape we will deal with in Geometry includes circles and triangles—yes, including quadrilaterals, they are made up of triangles! We were given some very helpful measurements. The description is so specific that we must draw it out. The directions are so abundant, that we will have certainty that there are no mistakes. First let’s review some terms: Diameter: A line that spans the greatest width of a circle, it passes through the center of the circle. It is comprised of two radii. D = 2r. Radius: The distance from the center of a circle to the edge of the circle. Chord: Any line that connects one point on the edge of a circle to another point on the edge of a circle. A chord cannot cross through the circle center. A chord will never be longer than a diameter. Perpendicular Lines: Two lines that meet each other at a ninety degree angle. Now that we are clear with the vocabulary, let’s solve this question. 1. First: Let’s add any lengths that we can determine based on the givens in the problem. A radius is the distance from the center of a circle to the edge of the circle. We were not given the length of OB, but, based on the other givens OB must equal 5 because OB is a radius, just like OA and OD. This same radius situation applies to OC; it too must equal 5. 2. Now that we know that OC equals 5 and we know that EC equals 2, we know that OE = 3. 3. We have two legs of right triangles OED and OEB. We will use the Pythagorean theorem to find the length of ED. Since we are missing one of the legs of the right triangle, but we have the hypotenuse, we use the following equation: 3^2 + x^2 = 5^2 = 9 + x^2 = 25. 4. Solve for x using SADMEP, the opposite of PEMDAS. Subtract 9 from both sides of the equation to get: x^2 = 25 - 9, so x^2 = 16. 5. Let’s find the square root of both sides, of x^2 and of 16, to finish solving for x. x = 4 and x = -4. 6. Since this is a geometric shape, sides with a negative length are impossible. This means that x must be 4. Line ED = 4. 7. Line ED = Line EB because E is the given midpoint of line BD. 8. Therefore, the length of BD = 8.

### Subject: ACT

Number 57 from ACT Math Test: Two numbers have a product of -48 and a sum of 0. What is the lesser of the 2 numbers? A. -4 rad 3 B. -3 rad 2 C. -2 rad 3 D. 0 E. 3

This is a really fun example of an ACT Math question that might stump a student. We always work from the position of looking at what answers we can eliminate; we look for what is wrong instead of wasting time trying to find the right answer. We also notice that the question gave us really valuable information: one of the two numbers in our product and sum! We can approach this two ways: Algebraically: xy = -48 x + y = 0, and then we can use Algebra to solve (have fun with that!) OR Strategically! -begin with the low hanging fruit: D. cannot be the answer because the product (result of multiplication of any two numbers) of zero and any number is zero, so the product cannot equal -48 thus breaking one of the requirements of the question E. cannot be the answer because 3 x -12 = -48: yay, the first requirement is met BUT the second requirement is not met: 3 + -12 is not equal to 0. Sum is the result of adding two numbers. Now we have to deal with the radicals. The trick of radicals is making sure that the other number you work with also includes the same radicand because we have to get to a sum of zero! Additionally, the ACT has to offer questions that can be solved quickly, so the numbers we have to choose from to test and find our answers will always be pretty obvious. Let's look at what that means with the question: I'll begin with C. and I'm going to use the number opposite -2 rad 3 because it will easily get me to 0: -2 rad 3 + 2 rad 3 = 0, awesome, 2nd requirement is met. Now let's test the first requirement: (-2 rad 3)(2 rad 3), does this equal -48? (-2)(2)(rad 3)(rad 3) = (-4)(3) = -12, okay, that's too low. Well this was the lowest of our three radicals, so now let's go to the highest of the three radicals: Answer choice A. If this doesn't work, the answer will be B. Here we go: -4 rad 3 + 4 rad 3 = 0, (-4 rad 3)(4 rad 3) = (-4)(4)(rad 3)(rad 3) = (-16)(3) = -48, yay we made it! Key Takeaways: -always look to eliminate the non-answers instead of wasting time trying to "solve" a question/“find” the answer -notice when a question gives the answer: "What is the lesser of the 2 numbers?". If the test asks this question, then it is providing the answer. It is telling us A. is the answer, B. is the answer, etc, so use the answers! -choose the easy actions to find the answers: notice that, when we reached the radicals: A. B. C., we immediately found the numbers that would give the sum of 0. Then, once we found the number, we could take the more difficult action of using that number to find the right product. -always look for easy!

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