Quant Strategy Flashcards

Question

What do I want to consider when I see this question with variables in the question and fractions in the answers?

Answer 1

Use Smart #'s: * Don't be fooled by the trickiness of the question * Is states If the committee selects y/x % of the black-and-white films * This means that whatever you calculate y/x to be, you will then use that value as a %

Answer 2

1. You know you want to simplify 2. If the exponent is too large to simplify remember that you can always breakdown a number to its factors * e.g. 12⁴ = (3⁴⁾(4⁴) you can now simplify

Answer 3

Remember that the greatest possible remainder for any number divided by 2 is 1 * With that in mind, you can back into whether or not the variables included in the question are even or odd * With the even / odd identifications you can answer the question This question is is an odds and evens question in disguise.

Answer 4

Pythagorean Theorum states that in a right triangle a² + b² = c² * In order to determine if one a triangle is right, we would have to konw the value of all three sides, to see if in fact * a² + b² = c²

Answer 5

When drawing on a coordinate plane, the distance between points, is between points, no from zero!

Answer 6

Fractions and % tell me that I want to use SMART NUMBERS * The question tells you the % each person makes of the co-workers salary * Set the highest paid employee's salary to 100, then identify other correlating salaries accordingly

Answer 7

Whats the slope of the line! * Rise over run (y/x) * Find the slope, and calculate the answer choices to see what has the same slope

Answer 8

We're given then value of n, it = 10¹⁰ (*i.e. 10 billion)* * If n = 10¹⁰ then nⁿ = 10^{10 (with this exponent 10 being raised to the 10 10th's as well)} * 10 to the 10th power raised to 10 to the 10th power = 10^d * Eliminate bases and you have 10\*10¹⁰ = d or 10¹¹ = d

Answer 9

What is the question asking? * Question asks for the minimal value of the f(x) In order to answer we need to know what the function of x is * Statement 1 tells us the value of (fx) for just on value of x. We have no idea about the other possible values * Statement 2 identifies the equation for the function. With the equation, we can calculate what the minimal value of x would be.

Answer 10

1. Remember that that questions says k is a positive integer. * This means it could be any positive integer 2. Based on the answer choices we can use smart numbers to solve 3. It's also possible that there's no remainder, as shown in answer (A) 4. Whenever you see a variable to the third - that variable (e.g. (k³- k) remember that this simplifies to three consecutive integers k(k²-1) = k(k+1)(k-1) * Rearrange to (k-1),k,(k+1) * This represents three consecutive integers 5. Then not that you have (k+2) also in the equation, so you now have 4 consecutive integers to (k-1),k,(k+1),(k+2). Meaning we have the product of 4 consecutive integers 4! * 4! = 24 (which is divisible by 6) * So the product must be divisible by 6 as well

Answer 11

The question is showing a value for k in a range -26 \< k \< 24 * Answer choices negative so this is probably testing something negative * If thats the range, draw out the first few numbers on each side of k * Notice that the number cancel out, except for the bookend of the negative range (-25 and -24) sum of those two is -49!!

Answer 12

* Redraw the described image * You know that the angle opposite the length of the ladder must be 90^º * If it's 90 and the other angle is 60, the remaining angle must be 30 to total 180 * This is a specifal triangle 30: 60: 90 which has the following length ratio x : x√3 : 2x * With that ratio you can solve for the other leg lengths because you know the length of the hypotenuse 70

Answer 13

* Redraw the line * If a negative value of a number on a line is = to another value on the line, then those 2 #'s are equi-distance from 0 * Statement 1: q = -s * If S were 1 then -1 (s) = q. Both equal distance to 0 * If r is to the right of q and before s then it is closer to 0

Answer 14

1. Make sure when you're working through this problem you copy the statements approrprately to your paper! * 1) x + y \> 0 * 2) y^x \< 0 2. You have to test cases for both statements completely independent of each other, as in all DS questions

Answer 15

Simplify where I can. * Remember exponents with multiple variables are equal to the base raised to each variable individually * *e.g. 2^x-2 = 2^x\* 2^-2* * Once you have a like base you can factor out to solve

Answer 16

1. Remember Geometry formulas * Area of a circle = πr² * Diameter of a circle = 2r * Circumference of a circle = πd or 2πr * Area of a circle = s² 2. With the formulas in mind, you can back the amount of wire used for the circle out of 40, and identify the wire used for the square as the remainder

Answer 17

1. Looking at the answer choices if R = 0, then you know xy must = -1 (SUFFICIENT) 2. The second statement doesn't give you anything. NOT SUFFICIENT

Answer 18

1. The question is asking for the cost of milligrams, while the price has been giving in kg 2. Convert the kg price to mg and multiply by the quantity * $500/Kg and 600/mg in one pill. * 1kg = 10⁶mg (500/10⁶) \* 600 = Cost per mg * Remember that you can convert the 500 to decimals, by counting the exponent # * 10⁶ has 6 decimal places. * 500. = 0.000500 * 0.0005 \* 600 = .3 Remember when multiplying by decimals that you want to calculate the number of decimals in the both numbers and apply that to the final product

Answer 19

Don't be scared of a function question. Understand it and figure out how to solve * The question is asking which of the functions listed in the answers would allow for the functions mentioned to work Plug each of the functions into the two functions to see if they work

Answer 20

What is the quesiton asking for? * How many ounces of concentrate are required to make 200 6 ounce cups of OJ? What's been given? * Ration of concentrate to water 1 : 3 * Ounces in a can of concentrate 12 * # of cups 200, number of ounces 6 How to solve * How many total ounces will we need? 200 \* 6 = 1,200 ounces * Plug this into the ratio table you've made * OJ = 1 : Water = 3 : Total = 4 * 1,200 is the total, which gives you a multipler of 300 * Apply the multipler to the OJ and water ratios * OJ = 300 (1 \* 300) and Water = 900 (3 \* 300) * How many 12 ounce cans of concentrate go into a 300 ounces? * 300/12 = 25

Answer 21

Special Product 2: (a+b)(a-b) = a^2 - b^2

Answer 22

1. Understand: t_n=t_n−1−3 means that each term is 3 less than the previous term. 2. Plan if t₁= 23 and it's asking for n when t_n = -4, then we're solving for n when you've moved from 23 to -4 * 23 - (-4) = 27 * 27 / 3 = 9 3. So you've moved 9 spaces from t₁. 1 + 9 = 10 * So the correct answer is 10

Answer 23

A growth percentage won't start from 0, unless explicitly stated * If you have a 20% growth after the first quarter, then you need to identify the basis, to calculate the growth between Q1 and Q2 Use 100 as your base to easily calculate

Answer 24

Read carefully! * Understand: Chance of selecting a student under 25 * Plan: * 48% M, 52% W; 40% M & 20% women \> 25 * Use Smart numbers 100 Base * Solve: * 48 M and 52 W * 1-40% = 60% M \< 25 * 1-20% = 80% W \< 25 * 60% \* 48 = 28.8 M \< 25 * 80% \* 52 = 41.6 W \< 25 * 29 + 42 = 71 students under 25 * 71/100 = 70% answer B

Answer 25

If you have multiple items being compared in the ratio: * Find the constant variable comparison * Build a multi-layer ratio table with all variables * Normalize the constant and correlating ratios * This allows you to solve for the unknow multipler

Answer 26

Remember that variables can be either positive or negative. You have to test cases to be sure 1. Statement 1: * If the sum of x & y \< 20, what are the possible values for x? * x = 25, y = -6 | X IS NOT UNDER 20 * x = 19, y = 1 | X IS UNDER 20 * Due to the different answers NOT SUFFICIENT 2. Statement 2: * Y is less than 20 * y = 19, x = 1 | X IS UNDER 20 * y =19, x = 5 | X IS NOT UNDER 20 * Due to the different answers NOT SUFFICIENT Considering the 2 together * Y \< 20 * x and Y sum \< 20 * x = 25, y = -6 | X IS NOT UNDER 20 * x = 19, y = 1 | X IS UNDER 20 * Due to the different answers NOT SUFFICIENT

Answer 27

1. What's 8% of 5,000? * 400 2. Work backwards from the answers to identify which # has 400 as 6.5% * Start with 5% of each answer to eliminate values that are too small * Then you can calculate 1% and .5% respecively to identify the final answer E must be right!

Answer 28

1. Whats being asked for: How many sweaters were sold? * In order to identify number of sweaters sold I need to know total revenue and SP 2. Whats been given? * From Question: Profit margin on Sweater * Need to calculate cost to identify selling price * Statement 1: Total revenue $270 * Ok this is 1 piece of the puzzle now I need SP * NOT SUFFICIENT * Statement 2: Profit margin on sweater 50% * OK this is 1 piece of the puzzle, no I can back into selling price (1.5cost = 30; cost = $20) * Cost + profit: 20 + 30 = 50 * NOT SUFFICIENT * Together: Revenue $270, cost $50, now I can calculate the number of sweaters sold * SUFFICIENT

Answer 29

The question includes variables, and lets you know that the value is between 0 and 1 (*i.e. a fraction)* * Because you have to calculate for a square root, pick a fraction that's easy to take the root of (*i.e. 1/4)*

Answer 30

1. What's being asked? * *$ value to finish 2 spheres* 2. What's been given? * Cost per square meter $92 * Formula for surface area of a sphere 4πr² * Circumerference of spheres * 5.5M * 7.85 3. Plan * You know the circumference formula = 2πr * Use these to solve for r * 5.5 = 2πr * r = 5.5/2π * Now that you have r you can plug this into the surface formula to calculate the cost * Surface Area = 4πr² * 4π(5.5/2π)² * Remember you can simplify down to 5.5²/π * Multiply this value by 92 4. Repeat the same for the other sphere

Answer 31

1. What's the question asking for? * *value fo x and value for y that allows for a simple interest rate of 5* 2. What's been given? * Simple interest formula r = 4x + 8y/x + y * Original value of loans: * 10,000x at 4% * 10,000y at 8% * Loan Z will consolidae the two 3. Plan * What do I need to solve? * Ignore the 10,000 values as this is to confuse * We simply need to plug 5 into the simple interest formulat and solve for x / y 4. Solve: * 5 = (4x + 8y)/(x + y) * This solves to x = 3y which is a ration for every 1 x there are 3 ys * Which of the answer choices gives you that option?

Answer 32

1. You have to make sure you understand what the graph is showing * Horizontal axi shows Issue preference * Vertical axis shows probability to vote 2. With this in mind the drop downs become easier to populate 3. The graph is identifying the probability that each person voted with their prior preference, not a change from AGAINST to FOR but rather the % that stayed with AGAINST or FOR. 1. e.g. Delta: 80% of those that had a preference of FOR voted FOR

Answer 33

Trust your gut! You identified that there were overlapping data sets with conflicting averages. With that in mind it's not possible to calculate an exact number. * Statement 1: Not sufficient, partial population * Statement 2: Not sufficient, partial population * Both statements together: Not sufficient, overlapping data sets with conflicting averages

Answer 34

* Pay attention to what the question is asking for! * It says reciprocals so we know were dealing with a lot of really small fractions 1/43..........1/48 * Theres no way we'll find a LCD for these fractions, so we'll have to estimate

Answer 35

Remember the following: 1. Negative exponents turn the base into a fraction * e.g. 2^-2= 1/2² = 1/4 2. Negative odd exponents maintain the sign of the base * -2^-1 = 1/-2¹ = 1/-2 * -3^-3 = 1/-3³ = 1/(-3 \* -3 \* -3) = 1/-27

Answer 36

Set up a table to identify what's been given, in the question, and whats been given in each statement to see if we can calculated what's been asked for. "Statements (1) and (2) Together are NOT sufficient

Answer 37

Remember that your formulas. Convert the problem to easy math

Answer 38

Remember to solve for the unknown multipler and read the answer choices!

Answer 39

The standard deviation will not change if each variable is changed by the same amount

Answer 40

If a triangle is on a coordinate plane, and the lines aren't horizontal / vertical, calculate the area of the surrouding rectangle / triangles to find it's area.

Answer 41

You know time is constant as both drivers are in the same car * Back into the ration of time Tom spent driving (3/5) * To get the ratio of Peter to Tom Divide Peters rate by toms * 2/5 divided by 3/5 gives you 2/3 or 2:3 the ration

Answer 42

What's constant? *The base fee* * *Back the base fee out of the total and solve for the remainder*

Answer 43

Although you can identify the numbers who's products total 14, remember that these number could be in any order 127, 217, 712, etc. * Because you can't identify one consistent answer, neither statement is sufficient

Answer 44

This is a variable question in which you're given the variables in two separate equations: * Use each equation to solve for the value of 1 variable, and then plug that into the the other formula

Answer 45

TEST CASES! * Testing cases will easily identify the right answer

Answer 46

Don't eliminate choices too early. - Remember idiom Not only, but also - If the "Not only" isn't included, "but it also" would work

Answer 47

1. Find which Fractions have the same denominator and eliminate easy wrong answers 2. Identify how to compare the remaining? * Easier to simplify some of the larger fractions to make them comparable * If you have simplified fractions with at least one common denominator, you can normalize by multiplying by the the common variable over 1 Correct answer is D This is Quantitative :: Problem Solving:: 11561 from the GMAT problem set.

Answer 48

1. Remember the limitations * You are selecting 3 people from a group of 10 * The 10 candidates are made up of 5 couples and you cannot select two people that are married 2. Option 1: Can be any of the 10 people 3. Option 2: Cannot be the option 1 selection, or Option 2 selection, so 8 available option (10-2) 4. Option 3: Cannot be option 1 or 2 selections, or their respective spouses, so 6 available options (10-4) * You have 6 potential ordering for those 3 people (10 \* 8 \* 6) / 6 = 80 You can also think about it differently using the combination calculation approach: * We have 5 couples, from which we need to select 3 people * We can the select one person from each couple selected * Stage one, how many combinations of folks from the three couple selection? * 5C3 = 10 * This approach: https://www.youtube.com/watch?v=05a0A7vjG8I&t=248s) * The first 3 factors in 5! divided by 3! = (5 \* 4 \* 3) / (3 \* 2 \* 1). * This is a simplified version of n! / r!(n-r)! * We then have to select 1 from each couple * We have the option of selecting each person so thats 2 options from each couple 2 \* 2 \* 2 = 8 * 10 \* 8 = 80

Answer 49

* Remember to read carefully and test cases * Although you're given rate of one machine and are told that 1 machine operates at twice the rate of the other, we're not told which machine we've been given the rate for. * Calculation output could be different dependent upon the question

Answer 50

* Identify what's been provided * N is even * When N is / 9 there's a remainder of 8 * What's being asked? * Which of the values (1, 4, 9, 10, 17) if added to N would maek it divisible by 18 (which is a multiple of 9) Need to think of this like algebraic translation: * N = 9(multiplied by sum #) + 8 (because there's a remainder of 8 when N is divided by 9) * n = 9q + 8 * Now we can plug the answer choice in to see how it effects our formula

Answer 51

1. What's being asked? * How many bottles of C were ordered? 2. What's been given? * Total bottles 63 In order to solve we need to identify the ratio of the bottles ordered * Statement 1: R = .8 of G * This does not provide us with a ratio to the total or to C * NS * Statement 2: C = .75 of (R+G) * We now how C relates to the other two drinks * All we need to do now is identify how the two drinks relate to 63 * We can back into this answer! * Sufficient

Answer 52

1. Remember that each team is playing each team once (so games can't be double counted as unique, between each team) * e.g. when team A plays team B, that is a unique game on both team A and team B's schedules, so A vs. B, is the same as B vs. A 2. Map out a the first few games on a few of the teams schedules * You'll see that theres a decreasing number of unique games 3. You can either estimate an answer or use the sum of consecutive integers formula (Avg.) \* # of terms 1. To use this formula you must remember the start and end of the unique game values 4. Easiest way is to use the Combinations Formula: n!/(r!(n-r)!)

Answer 53

* Similar to a race problem, if the order in which things take place matters, then it changes our formula * In a race, if runner A finishes first, runner B, second, and runner C third, this is 1 unique list * If runner B finishes first and A finished second and C finishes third, this is a seperate unique list * Although the same participants, their orders are different and the order matters * The Combinations formula changes from: n!/(r!(n-r)!) to * n!/(n-r)!

Answer 54

1. Although this is a combinatorics problem, you may not be able to use the combinatorics formula 2. Use the Slot method How to solve: * Digit 1 can be 8 possible values (anything other than 0,1) * Digit 2 can be 1 digit, with two possible values (that will have two different effects) * If Digit 2 is 0, then Digit 3 will have (9 possible values 1-9) * If Digit 2 is 1, then Digist 3 will have 10 possible values 0-9) * Calculate the possibilities and add them together: * Possibility 1: 8 \* 1 \* 9 = 72 * Possibility 2: 8 \* 1 \* 10 = 80 * Sum = 152

Answer 55

* You've been given the range * Range is the dial which has 8 intervals * You've been given values for some of the intervals * The ask: Where will the pointer stop after 1,174 intervals? Don't think about dividing the 1174 by the interval values, as this will give you potentially multiple values. * First identify how far each lettered interval is * 1 = Blank, 2 = A, 3 = B, 4 = C, 5 = D, 6 = E, 7 = Blank, 8 = S * Now remember that the dial has 8 intervals in total * Can 8 divide equally into 1,174? * No it cannot. You'll arrive at ~146 and some change * Now we know what the closest multiple of 8 to 1,174 * Multiple 8 by 146 = 1,168 * 1,174 - 1,168 = 6. * Because the pointer is at S after 1,168 intervals, it will have to travel 6 more intervals to land at 1,174. * Which letter has an interval of 6? * E

Answer 56

Because of the variables in question this requires calculating both the combined and alternative probabilities: Remember what's been given, what's been asked and how to get there 1. Given: Apples and Oranges in each basket 2. Ask: Probability of 1 apple and 1 oranges being selected 3. How to get there? * We need to calculate both probabilitites separately and add them together Combined Probability 1: You select an apple from box 1 and an orange from box 2 * A = 4/6 of box 1, Oranges = 5/8 of Box 2 * Multiply the two to get a probability of 20/48 Combined Probability 2: You select 1 orange from box 1 and one apple from box 2 * A = 3/8, O = 2/6 * Multiply the two to get a probability of 6/48 Alternative probabilities: Add the two probabilities together to get your total alternative probability 20/48 + 6/48 = 26/48 = 13/24

Answer 57

When solving for probabilities you want to initially identify what the probability is asking for? 1. Probability of Alternatives: e.g. Selecting 1 apple and 1 orange, or selection from a deck of cards bein divisible by 2 or divisible by 7 2. Combined Alternatives: e.g. Neither pen selected from a box will be defective. * When solving for alternatives you are calculating the probabilities separately, and then adding those probabilities together * When solving for combined alternatives you are calculating the probabilities separatelh then multiplying them by eachother

Answer 58

Be mindful of what the question is asking for and what's been given * What's being asked? *Least possible value of the actual area* * What's been given? *Side length, rounded to the nearest centimeter is 6 centimiters* Because the question states that 6 is rounded to the nearest centimeter than the possible side values are 5.5 ≤ x \< 6.5 * Now calculate the area of a square region with a length of 5.5 * 5.5² = 30.25

Answer 59

1. What's been given? * The window is made up of a rectangle and a semi-circle * **not a complete circle.** Keep this in mind when calculating area 2. What's being asked: What's the area of the window * Area of the semi circle * Are of a circle = πr² * D given = 4 * r = d(1/2) * Area of circle = π2² = πr4 * Area of the semi-circle = 1/2(π4) = π2 * Area of a rectangle * Base \* Height * Base = 4 * Height = 10 - (radius of semi circle 2) = 8 * 4 \* 8 = 32 * Total area = 32 + π2 Answer E

Answer 60

1. What's being asked? * *Asking for the which of the answers equals the height of the carton* 2. What's been given? * Length, width, height ration 3:2:2 3. How would I solve? * Let's use smart numbers * Draw the carton with the metrics L = 3, W = 2, H = 2 * Calculate the volume of the carton as 3 \* 2 \* 2 = 12 * Now plug the volume X (12) into the formulas in the answer choices to see which one equals 12 Answer B works

Answer 61

1. What's being asked: Is the result of a formula divisible by 15? 2. Whats been given? * Formula x¹⁶- y⁸ + 345y² * Statements Solving: When looking at the equation realize that 345 is divisible by 15, as such, we no longer need to consider it as a part of the problem. * Now our modified ask is is x¹⁶- y⁸ divisibile by 15

Answer 62

1. If you have two consecutive even integers, one of them is always divisible by 4, and the product of those two would be divisible by 8 (2 \* 4) 2. How many times would a consective group of integers be divisible by 8? * How would we determine this?

Answer 63

1. What is the question asking for? * Probability that 3 balls selected, 1 will be green, and the 2 others will not be yellow 2. What's been given? * 10 balls: 1 green, 1 yellow? 3. How to solve? * There are three alternatives here because there are three separate ball selections, but we have to calculate the scenarios for each (combined probabilities) then sum them to identify the alternative probability

Answer 64

* What's been asked? * Probability that in choosing 4 individuals socks, that 2 are the same color? * What's been given? * Your population has three separate colors (White, Black, Grey) * Number of pairs of each color of sock * How can I solve? * Realize that you're picking 4 individual socks, from a population including three different colors * Regardless of the # of paired of each color of socks, there is a 100% change you will pick 2 of the same color, because their are less variants than you are picking

Answer 65

You have to assess the information given prior to being able to solve: * Statement 1 tells you that y is \< = 8 * Statement 2 tells you that y is \>= 4 You have to understand how each of these numbers effects the probability before you can answer.

Answer 66

Identifying that this question requires the prime identification of the product number, to find the answer: * The question identifies that this is a prime multiplication question by saying "*if the product of the point values of the selected chips is 88,000, how many purple chips were selected)*

Answer 67

* Identify that the existing ratio is given 30:36 or 5:6 * Total of 11: 5+6 =11 * Then you're adding 6 females to the ratio * As such, the answer can only be a multiple of 11 + 6 Test the answer choices to see which one fits.

Answer 68

W = R \* T * You're given the information required to calculate each persons rate * A = 50 per hour * B = 55 per hour * Collectively 105 / hour (50 +55) * Plug this into the formulat to identify how long it will take the two working together * 1,400 = 105 \* T * T = 1,400 / 105 Beware not to convert the rate to minutes too early.

Answer 69

Remember that an average hides the actual # of days taken by employee, and that it could be drastically effected by outliers. With that in mind, applying %'s to an average, would have varying outcomes, without knowing the specific employees vacation days.

Answer 70

1. Always map out a coordinate plane question 2. Slope formula y = mx + b * If the x intercept is given, then we can solve the equation as follows * x =6 * Y will always be zero at the x-intercept * Line formula provided y = 2x + b * 0 = 2(6) + b * b = -12 By drawing the plane, you'll see that the y intercept must be negative

Answer 71

1. For any product to be even, only one of the variables has to be even 2. Product will also be odd if all variabls are odd To solve we must determine if x,y,p are odd or even

Answer 72

1. Look at the answer choices, I could have worked backwards to identify the correct answer 2. Or solve algebraically * If solving algebraically and you have two factors that make up a whole, remember how to set up the equation * Let x = 20 ounce bottles, let 48-x represent the 40 ounce bottles * (x(20) + (48-x)(40))/48 = 35

Answer 73

1. Identify how to solve 2. TEST CASES!!!!

Answer 74

1. Identify how to solve 2. TEST CASES!!!

Answer 75

1. Understand how the formula works * P = -2(S-4)² + 32 * In looking at this because the parenthese are multiplied by -2, that product will always be negative, unless the parentheses sum was 0 * Which answer will give us zero?

Answer 76

1. A Triangle within a semi-circle is always a right triangle 2. 30: 60 :90 triangles has a length ratio of 1: √3 : 2

Answer 77

1. Don't rush! 2. Pay attention to the sign!!!

Answer 78

1. Don't rush 2. Pay attention to the sign! 3. When the question is asking about which formula doesn't have a root in common, it means which formula doesn't simplify down to one of the potential values of the formula in question

Answer 79

1. Parallelograms are made up of: * Squares: All sides are equal and all angels are 90° * Rectangeles: All angels are 90° and diagonals are equal * Rhomubuses: All sides are equal

Answer 80

1. Permutation calculation when order matter: * Order matters, more variations possible (no extra r) 2. Combination when order doesn't matter * Order doesn't matter, fewer possibilities (extra r)

Answer 81

1. Remember that the complete quadratic equation must be equal to 0 in order to identify the possible values of x 2. When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root.

Answer 82

1. As the problem asks for the smallest number, and all of the fractions are over 1, the number with the biggest denominator will be the smallest number 2. To solve more rapidly, recognize that all of the denominators include 5 raised to some power * You can normlize the 5^s to make it easier to identify the biggest denomintor * Remember that if you're multiplyng the 5^ in the denominator, to increase the exponent, then you have to divide the other factor in the denominator by the same number * Vice Versa if you're dividing the 5^ to reduce the exponent, you have to multiple the other denominator factor by the same number

Answer 83

1. Remember what makes positives / negative numbers

Answer 84

Look at the answer choices. They are in consective 10 point increments. Work backwards!

Answer 85

What is the question asking for? * What is y in terms of x? (*i.e. What does y =)* * Simplify the quadratic * The question states that y doesn't = 4, so eliminate the y-4 possibilites * Then simplify

Answer 86

Work through the quadratics to identify values for each variable

Answer 87

1. Know the geometrical formulas * Circumference of a circle = 2πr * Perimeter of square = 4s * Isosceles triange has a 45: 45: 90 relationship and a x: x: x√2 length relationship

Answer 88

Remember to always apply the 10% rule to back into a single digit percent

Answer 89

When addressing divisibility problems, remember that in order for something to be divisible by another number, it must contain all of the same prime factors

Answer 90

What is the question asking for? * Pay attention to the details. The question identifies that they are consecutive **EVEN** numbers!

Answer 91

Remember that if you have multiple inequalities, you can add them together.

Answer 92

* Identify how to solve? * Estimate for each of these fractions * Remember that a number gets smaller, if the same value is reduced from both the numerator and denominator *

Answer 93

As the population is doubling every two hours, and the volume listed isn't too large, you can build a table to back inot the value You don't have to solve everything algebraically

Answer 94

* Anything raised to the power of zero is equal to 1 * Regardless if the numberis negative or positive * Read the question carefully. It's asking if a number is greater than 1, not greater than zero

Answer 95

Remember you're trying to see if each statement will allow you to solve for the question. * The question asks what is X

Answer 96

We need to identify if either p or q is equal to 2

Answer 97

* In order for an output to be and even number, the numerator must be even

Answer 98

Two ways to solve: 1) Back into an answer with the ratios provided, 2) Algebraically. **KNOW BOTH** * The question identifies that the triangle is right * If it's a right triangle lean on the pythagorean theorum, to identify the side lengths * Back into the side lengths by leveraging the ratios provided * Remember the common right triangles: 3:4:5, 5:12:13, 30:60:90, 45:45:90 * If the perimeter equals 4x, and the sides are x,y,z we can high back into a ratio * e.g. x =3, 4x = 12, what combination, would allow for 3 + y + z = 12? * 3 + 4 + 5 = 12 * With that in mind, x to y is 3: 4 **Algrebraically** We can solve this algebraically, by looking at what we have * We know the Pythagorean theorum: a² + b² = c² * Given: x + y + z = 4x * z = 4x - (x +y) * z = 3x - y * Plug this back into pythagorean theorum: * x² + y² = (3x-y)² * x² + y² = (3x-y)(3x-y) * x² + y² = 9x² - 3xy - 3xy + y² * x² + y² = 9x² - 6xy + y² * 6xy = 8x² * 6y = 8x * x/y = 6/8 = 3/4

Answer 99

Look at the answer choices, this is a prime example to work backwards: * You're given the calories per 3 meals (combined) 2,400 * You're given the snack / dessert intake (combined) 200 * These total to a regular base of 2,600 (2,400 + 200) * Tom splurges on some days eating 3 times snacks / dessert 600 (3 \* 200 * Total on these days would be 2,400 + 600 = 3,000 * Now you have your regular day totals (2,600) and splurge day total (3,000) Question is asking how many days did he splurge if his 10 day average was 2,720? * Looking at the answer choices, consecutive singe digit integers * Let's try the second option, then fourth option to see what works * ((2,600 \* 6) + (3,000 \* 4))/ 10 = 2,760 too big, must be answer A * Let's test answer A to confirm * ((2,600 \* 7) + (3,000 \* 3))/10 = 2,720 CORRECT

Answer 100

Remember process: Understand, Plan, Solve * Understand: Will Patrick have time to complete task before guests arrive? * Plan: We know he has to: * Vaccum * Fold Laundry * Put away dishes, after Dish Washer completes cycle * Cycle has 55 minutes remaining, and guests arrive in 1 hour * In order to solve we need to know how long the tasks will take in total, or if one task would put him over an hour * Solve: * Statement 1: We have a time value of Vaccuming and Launrdy * Without an understanding of how long Dishes will take, this is NS * Statement 2: We know the cycle will take 55 minutes, then it will take 7 minutes to put dishes away. This is 62 minutes, which exceed an hour, so we know Patrick does not have enough time. Sufficient

Answer 101

* Understand: How many games were played * Plan: We need need to know what y was and what % that is.

Answer 102

Heavy algebraic translation: * You know from the statement that Jennifer has 60 more dollars than brian * J = B + 60 * You also know if she gave him 1/5 of her money Brian would have 25% less than Jennifer * J - 1/5j = 4/5J * B = B + 1/5J * We can then deduce that b + 1/5j = (1-25%)(4/5j) * This simplifies to b + 1/5j = 75%(4/5j) * b = 3/5j - 1/5j; b = 2/5j * Plug this back into the original J = B + 60 * J = 2/5j + 60 * 3/5J = 60 * J = 100

Answer 103

1. Remember to draw the plane 2. Slope = Rise / run (*i.e. vertical over horizontal)* * *However, points on a plane are presented (x,y)* Alternatively, you can plug a points coordinates into the equation for a line to see if the coordinates match (*i.e. option A coordinates (3,1)* * We're given the equation y = 3x - 8 * If we plug in the (3,1) coordinates we see: * y = 3(3)-8 = 1 * y = 1 in the coordinates given so this works!