GRE Misc. Math

They're going in opposite directions so you add the two distances to equal 260 miles apart.

*If Jordan travels 40 mph east for 2 hours and Connor travels 60 mph west for 3 hours, they're going in opposite directions. If they start from the same point at the same time, how far apart are they?

60; 60; 24; 7; 52; 365; 366

3. Time * __ seconds = 1 minute * __ minutes = 1 hour *__ hours = 1 day *__ days = 1 week *__ weeks = 1 year *___ days = 1 year *___ days = 1 leap year

x = 89.5 on both exams

*Average of seven exams is 85. Scores of the first five exams: 86, 79, 82, 85, 84. Find the average score of each of the remaining exams.

even; odd

*Composite numbers have more than two factors and can be divided by more than just 1 and themselves. Examples: 4, 6, 8, 9, 12, 14, and 15. Note: Composite numbers (called that because they are composed of more than two factors) can be ____ or _____.

45/90 x 100 = 50%

*If you can't ignore the percentage, remember that a percent is part/whole x 100 *What percent is 45 of 90?

neither; "zero and 1 are neither prime nor composite" c. the two quantities are equal

*We said that 0 and 1 aren't prime. They're also not composite. So what are they? ______. You express this fact as, "______________". Perhaps you're also wondering whether 0 is positive or negative. Nope, 0 is neither positive nor negative. Knowing this fact can win you 10 points on the GREs (the app. value of one correct math question). Ex: Column A The number of prime numbers from 0 to 10 inclusive Column B The number of prime numbers from 11 to 20 inclusive a. if the quantity in Col. A is greater b. if the quantity in Col. B is greater c. if the two quantities are equal d. if the relationship cannot be determined from the information given.

16.67%; 27.27%; 100%

*In 2006, Coach Jarchow won 30 prizes at the county fair by tossing a basketball into a bushel basket. In 2007, he won 35 prizes. What was his percent increase? *Two years ago, Haylie scored 22 goals while playing soccer. This year, she scored 16 goals. What was her approximate percent decrease? *Carissa has three quarters. Her father gives her three more. Carissa's wealth has increased by what percent?

18

*The mode is the most frequent number. Mode is the most used term. We suggest you put the number in order again. The one that shows up the most often is the mode. *Ex: find the mode of 11, 18, 29, 17, 18, -4, 0, 19, 0, 11, 18

33

*The range is the distance from the greatest to the smallest. In other words, take the biggest term and subtract the smallest term. Your answer is the range. *Find the range of the numbers: 11, 18, 29, 17, 18, -4, 0, 19, 0, 11, 18

(0,0); 45

Graphing *Be able to find a point on a graph given its (x,y) coordinates. Remember that the point of origin is ____. If you connect all the points where x and y are the same, such as (4,4) or (-3, -3), you get a line that forms a ___ degree angle.

100; 25; 5,000; 1,250

Graphs: 4 basic types 1. Circle or pie graph: The circle represents ___ %. The key to this graph is noting of what total the percentages are a part of. Below the graph, you may be told that in 2001, 5,000 students graduated with Ph.D.s. If a 26% segment on the circle graph is labeled "Ph.D.s in history." you know that that the number of history Ph.D.s. is __% of _____, or _____.

12/5 or 2 2/5

Linear Algebraic Equations *Isolate the variables. That is, get the variables on one side of the equal sign and the non variables on the other side (remembering to change from a positive to a negative or vice versa when crossing over the equal sign). Add like terms. Then divide both sides by what's next to each variable. Ex: 4x - 3(x +2) = 6(x-3)

Counting numbers: 1, 2, 3.... Note that 0 is not a counting number. Whole numbers: 0, 1, 2, 3... Note that 0 is a whole number Integers:... -3, -2, -1, 0, 1, 2, 3....When a questin asks for integral values, it wants the answers in integers only. For example, you can't give an answer like 4.3 because that's not an integer. You need to round down to 4. Rational numbers: Rational numbers can be expressed a/b, where a and b are integers. Ex: 1 (because 1 = 1/1 and 1 is an integer), 1/2 (because 1 and 2 are integers), 9/2 (because 9 and 2 are integers), and -4/2 (because -4 and 2 are integers).

Ready, Set, Go: Number Sets Counting numbers:____________________ Whole numbers: _____________________ Integers: _________________ Rational numbers: _________________

counting; whole; integers; rationals; irrationals

Real numbers: Briefly put, real numbers include all the preceding number sets - _____ numbers, _____ numbers, ______, _______, and _____. *For all practical purposes, real numbers are everything you think of as numbers. When a question tells you to "express your answer in real numbers," don't sweat it. That's almost no constraint at all, because nearly everything you see is a real number.

...

Refer to page 164 and 165 to look at graphs and answer example questions.

First simplify any roots: square root 20 = square root 4x 5 = 2square root 5. Then multiply 2square root 5 x square root 2 = 2 square root 10

Square Roots *Know how to multiply and divide like radicals and how to simplify radicals. Ex: simplify square root20 x square root2

1/2; 1.5

Statistics *The median is the middle number when all the terms are arranged in order. *If the list has an even number of terms, put them in order and find the middle two. Then find the average of those two terms. *ex: Find the median of -3, 18, -4, 1/2, 11 *Ex: Find the median of 5, 0, -3, -5, 1, 2, 8, 6

-2; x + x +2 = 26

Symbolism: Remember that the GRE tests two basic types of symbolism: 1. Plugging the numbers into the expression: Ex: f(x) = x^3 - 6x + 2 if f(x) = 2 2. Talking through the symbolism explanation in English: If you're asked to translate the expression "The sum of two consecutive even integers is 26" What would you do? Refer to page 168 if confused.

16; 2,000; 2; 2; 4

Units of Measurement 1. Quantities * __ ounces = 1 pound *____ pounds = 1 ton *__ cups = 1 pint *__ pints = 1 quart *__ quarts = 1 gallon

Distance = Rate x Time; Jennifer drives 50 minutes longer than Ashley.

When you have a distance, rate, and time problem, always use the DIRT formula: ___________________. *Jennifer drives 40 miles an hour for two and a half hours. Her friend Ashley goes the same distance but drives at one and a half times Jennifer's speed. How many minutes longer does Jennifer drive than Ashley? - Refer to page 143 on how to work these problems.

Work = time put in/capacity (time to do the whole job); 1/6; 3.43 days

Work Problems *The formula most commonly used in a work problem is: ___________________ *Ex: Sarah can paint a house in six days and has been working for one day, what fraction of the work has she done? *Ex: Sarah can paint a house by herself in six days and Evelyn can paint a house by herself in eight days. Working together, how long will it take them to paint one house?

5/6

Dividing Fractions *To divide by a fraction, invert it (turn it upside down) and multiply. Ex: 1/3 / 2/5 =

middle; 68;

1. The average of evenly spaced terms is the ______ term. *Find the average of the following numbers: 32, 41, 50, 59, 68, 77, 86, 95, 104.

50/100; 33/100; 75/100

2. Another way to ignore a percentage is to convert it to a fraction. The word percent means per cent, or per hundred. Every percentage is that number over 100. * 50% = *33% = *75% =

12; 3; 36; 5,280; 1,760; 144

2. Length *___ inches = 1 foot *__ feet (__ inches) = 1 yard *_____ feet (___ yards) = 1 mile *____ inches in a square foot

27.5

2. The average of evenly spaced terms is (first + last)/2. *Find the average of the following numbers: 3, 10, 17, 24, 31, 38, 45, 52

...

2. Two axes line graph: A typical line graph has a bottom axis and a side axis. You plot a point or read a point from the two axes. This is probably the simplest type of graph you'll come across.

She needs an 82 to obtain the 88 average.

2. You can solve missing term average problems the common-sense way. *A student takes seven exams. She gets an 88 average on all of them. Her first six scores are 89,98,90,82,88, and 87. What does she get on the seventh exam?

...

3. Three axes line graph: This type of graph, with its left side axis, bottom axis, and right side axis, is rare. The left side axis may represent, for example, the number of crates of a product, whereas the right side axis may represent the percentag that those crates are of the whole shipment. You read the points on a three axes graph the same as you do on a two axes graph - by paying special attention that you answer what the question is asking you. If the question asks you for the number of crates, read the left side. If the question asks you for the percentage of crates, read the right side.

100

4. Bar graph: A bar graph has vertical or horizontal bars that may represent actual numbers or percentages. If the bar goes all the way from one side of the graph to the other it represents ___ %

*Sure, you can multiply 15 and 6 to get 90 but that's not the LCD. Instead, count by 15's because 15 is the largest of the 2. 15? no, 5 doesn't go into 15. 30? yes, both 15 and 6 go into 30. That's the LCD. *20

4. To find the lowest common denominator, count by the highest denominator. *Find the LCD of 15 and 6. *Find the LCD of 2, 4, and 5.

13/30

5. In many problems, you don't even have to find the lowest common denominator. You can find any common denominator by multiplying the denominators, and cross multiplying. Ex: 4/15 + 1/6 =

...

Decimals: Basically just remember to: 1. Keep a wary eye on the decimal point. 2. Go to extremes. Determine the far-left or far-right digit and use that info to eliminate incorrect answer choices.

3; 3; -3; -5

Absolute Value *The absolute value is the magnitude of a number. In other words the absolute value is the positive form of a number and is indicated by two vertical parallel lines. * l3l = * l-3l = * -l-3l = * -l-l-5ll =

percent increase or decrease = number increase or decrease/ original whole

Determining percent increase/decrease: *To find a percent increase or decrease use this formula: ________________________

divisor; 444/6 = 74 - don't forget to check your answer with multiplication

Dividing Decimals: *To divide decimals, turn them into integers by moving the decimal point to the right the appropriate number of places for both terms - the one you're dividing and the one you're dividing by (called the ______). Ex: 4.44 / .06 =

C = 2pie(r); A = pie(r)^2; Length of an arc in a sector: Find the ratio of the number of degrees in the sector to 360 degrees. Then multiply this fraction times the circumference of the whole circle.; Area of the sector: Find the ratio of the number of degrees in the sector to 360 degrees. Then multiply this fraction times the area of the whole circle.; Central angles: Equal to the arc.; Inscribed angles: equal to half the arc

Circles: *Circumference: _____ *Area: _____ *Length of an arc in a sector: ______ *Area of the sector: ______ *Central angles: ______ *Inscribed angles: ______

a. the quantity in Column A is greater ($27.27)

Column A Quantity Column B Black t-shirts 5 $20 Denim 8 $25 Blue jeans 20 $30 Average cost of clothing $25 a. if the quantity in Column A is greater b. If the quantity in column B is greater c. if the two quantities are equal d. if the relationship cannot be determined from the information given.

3:4:5; 5:12:13; 7:24:25; s:s:square root2; s:s(square root3): 2s

Common Pythagorean ratios: Keep in mind that in a right triangle, the sides may be in the following ratios: * _______ *_______ *________ *_______ *_______

.35; .83; .50; .333; .666

Converting percentages to decimals or fractions 1. Ignore the percentage's very existence. You can express a percentage as a decimal, which is a lot less intimidating, by putting a decimal point two places to the left of the percentage and dropping the % sign. *35% = *83% = *50% = *33.3% = *66.6% =

144 x 3 = 432 which is greater than 36. Answer is A

Ex: Column A: Number of square inches in 3 square feet Column B: 36 a. if the quantity in Column A is greater b. if the quantity in Column B is greater c. If the two quantities are equal d. if the relationship cannot be determined from the info given.

12 x 12 x 12 = 1,728 inches

Ex: How many cubic inches are there in a cubic foot?

74x^5

Exponents *Understand how to add, subtract, multiply, and divide like bases. Also, remember that: -A number or variable to the zero power equals ___. -A number or variable to a negative power is the _____ (upside-down version) of that number or variable. Ex: simplify (2x)^3(-3x)^2 + 2x^5

x^2 - 4x - 12

Foil Method of Algebra *Use the FOIL method: First, Outer, Inner, Last to multiply algebraic equations. Ex: (x-6)(x+2)

denominator; numerator; lowest common denominator

Fractions: Adding or Subtracting Fractions 1. You can add or subtract fractions only when they have the same _______. 2. When fractions have the same ", add or subtract the ______ only. 3. When fractions don't have the same ", you must find the _____ ______ _______.

PRT = I; $50

Interest Problems *Remember the formula: _________ P = Principle, the amount you start with R = Rat, the interest rate you're earning on the money, expressed as a decimal T = Time, the amount of time, ALWAYS in years, that you leave the money in the interest-bearing account. I = Interest, the amount of interest you earn on the investment. An interest problem usually asks you how much interest someone earned on his or her investment. *Ex: Janet invested $1,000 at 5 percent annual interest for one year. How much interest did she earn?

terminate; repeat; fraction; nonterminal; nonrepeating; counting numbers; whole; integers; rationals;

Irrational numbers: The highly technical definition here is anything not rational. That is, an irrational number can't be written as a/b, where a and b are integers. Numbers whose decimals don't _______ and don't ____ can't be written as a _____ and therefore are irrational. *Example: pie cannot be written exactly as 3.14, because its ______ and _______. *Irrationals don't' include the previous number sets. That is, irrational numbers don't include ______ numbers, _____ numbers, ______, or _____ numbers.

4; February 29; $43.83

Leap year comes around every ___ years. The extra day is ______ ___, makes 366 days in a year. You need to know this fact for math problems that may look something like this: *Mr. Pellaton's neon sign flashes four hours a day, every day all year, for four years. If it costs him three cents a day for electricity, how much will he owe for electricity at the end of the fourth year?

acute; obtuse; right; straight; S = 180(n-2); sides

Math Concepts You Absolutely Must Know Angles: Understand the various types of angles: ____, ____, ____, and ____. Also, make sure you know how to identify exterior angles and how to solve for the sum of the interior angles of any polygon. *The sum of the interior angles is S = _____, where n is the number of _____ in the polygon.

x = 10 lbs of sequins

Mixture Problems *A mixture problem is a word problem that looks much more confusing than it really is. Plan to encounter two types of mixture problems: those in which the items remain separate , and those in which the two elements blend. Ex: Marshall wants to mix 40 pounds of beads selling for 30 cents a pound with a quantity of sequins selling for 80 cents a pound. He wants to pay 40 cents per pound for the final mix. How many pounds of sequins should he use? (hint: make a chart for what you know and figure out what your x is).

3/10

Multiplying Fractions *This is easy. Just do it. Multiply horizontally, starting with the numerators and then moving to the denominators. *Always check whether you can cancel anything out before you begin working to avoid having to deal with big, awkward numbers and to avoid having to reduce at the end. Ex: 3/4 x 2/5 =

1. Work with the parentheses. 2. Work with the power. 3. Multiply or divide. 4. Add or subtract.; 41; 11 11/16

Order of Operations: 1. 2. 3. 4. An easy mnemonic for remember this is Please Excuse My Dear Aunt Sally. Ex: 10(3-5)^2 + (30/5)^0 Ex: 3 + (9-6)^2 - 5(8/2)^-2

7/3; 22/5; 19/2

Playing with Mixed Numbers *A mixed number is a whole number with a fraction tagging along behind it, like 2 1/3, 4 2/5, 9 1/2. Multiply the whole number by the denominator and add that to the numerator. Then put the sum over the denominator. *Ex: 2 1/3 = Ex: 4 2/5 Ex: 9 1/2

positive x 2; one; themselves; 0; 1; 2; odd

Prime and Composite Numbers *Prime numbers are positive/negative integers that have exactly two positive/negative integer factors; they can't be divided by numbers other than ____ and ______. Examples include 2, 3, 5, 7, and 11. Tricks to prime numbers: *_____ is not a prime number. *_____ is not a prime number *_____ is the only positive prime number. *Not all ____ numbers are prime.

1:3; 1:3 (3:9); 12 - a multiple of 4

Ratios *Remember that the possible total is a multiple of the sum of the numbers in the ratio. A ratio is written as of/to or of:to. Ex: For example, say a recipe calls for 1 cup of milk and 3 cups of flour. The ratio of milk to flour is ____. That means 1 cup and 3 cups = 4 total cups in your recipe. If you needed to make three times this amount, what would the ratio be? what would the sum of the indigence be?

x = 95 on test 7

Solving Missing Term Average Problems *A student takes seven exams. Her scores on the first six are 91, 89, 85, 92, 90, and 88. If her average on all seven exams is 90, what did she get on the seventh exam? 1. Solve this problem the basic algebraic way: Average = Sum/Number of terms *90 = Sum/7 *Because we don't know the seventh term, call it x. Add the first six terms and x and cross multiply.

Average score on the exam: 75.29

Working with Weighted Averages *In a weighted average, some scores count more than others. Number of students Score 12 80 13 75 10 70 *Multiply the number of students by the score they each received then sum the scores and divide by the total number of students.

33.3%; 32

You can also solve by using the equation is/of = %/100. Here's an example: 42 is what percent of 126? *What is 40% of 80?