GRE Math Review/Terms/Tips

Term
1 / 51
Significance of: (1,1); (2,2); (3,3); (4,4); (5,5); (6,6)
Click the card to flip 👆
Terms in this set (51)
Significance of: (1,1); (2,2); (3,3); (4,4); (5,5); (6,6)
Terrible Dice Roll Probability Qs - if the selected sum can result from a snake eyes, don't count it twice! ~~~~ e.g Sum 6 = (1,5); (2,4); (5,1); (4,2) THEN + (3,3), NO DUPLICATE
Avoid needless division in card problems.
In a 52-card deck, there are 4 suits, each of which contain: 13 cards total, 2-10 ranks, 3 royals, and 1 ace.
Real #s
All rational & irrational #s - no pesky imaginary #s
Integers
(+) & (-) whole #s - i.e. no fractions
Whole #s
0 +, no fractions
Natural/Counting #s
What you can count on your hands - i.e. without 0, negatives, or fractions
Composite #s
not prime; [is this necessary, math powers that be?]
Closure
Achieved by burning your math textbook, ahem OR when all answers fall into the original set - e.g. even #s are closed because adding any of them together produces another even #; problem is,the emotionally-troubled "odd"s kill each other when together and produce evens
Commutative Property (of + & X)
The order does not make any difference - e.g. 5+2=2+5; does not hold for subtraction or division; a "commute" to work can refer to the morning trip to or the evening trip back
Associative Property (of + & X)
The grouping makes no difference - e.g. (5+3)+2=(2+3)+5; also does not hold for division and subtraction; all the numbers that associate together get along just fine, so they can mingle all they want with no trouble
Identity ElementLike a mirror; when introduced, does nothing to the answer; 0 for addition (7+0=7) and 1 for multiplication (4X1=4)Additive Inversethe opposite value on a number line; 3 &-3, 5&-5Multiplication Inverse= reciprocal; when two are multiplied together, they equal 1 - e.g. 1/2 & 2, 1/9 & 9Expanded Notationused to point out the place value of each digit - e.g. 456 = 400+ 50 + 6 = (4X100) + (5X10) + (6X1)(4X10^2) + (5X10^1) + (6X10^0)A # is divisible by 3 if...the sum of its digits is divisible by 3A # is divisible by 4 if...the number formed by the last two digits is divisible by 4A # is divisible by 6 if...it is divisible by 2 AND 3A # is divisible by 8 if...the number formed by the last three digits is divisible by 8A # is divisible by 9 if...the sum of its digits is divisible by 9Eights Shortcuts3/8 = .125, 12.5% 5/8 = .375, 37.5% 7/8 = .625, 62.5%Sixths Shortcuts1/6 = .1666..., 16.66.... 5/6 = .8333..., 83.33....The square root of 2 is approximately...1.414The square root of 3 is approximately...1.732When multiplying and dividing mixed fractions, is it okay to operate on the standalone whole numbers first?No, they must be converted to irregular fractions first. Only work on the standalones like that in addition and subtraction problems.If multiplying/dividing two values with exponents, when is it appropriate to add/subtract?ONLY when they share a base; 8^2 X 3^2 does not = 24^4What does a negative exponent mean?It indicates a multiplicative inverse; e.g. 5^-2 = 1/25 and 3^-3 =1/27What does a fraction exponent mean?It indicates a root; e.g. 36^1/2=6, 64^1/3=4What's so forbidden about using "o", "e", and "i" as variables?"o" can be confused w/ 0 "e" is used in logs and "i" for imaginary numbers Further, "z", if used, should have a cross through it to differentiate it from 2What is an "element" of a set?A single value belonging to a set - e.g. 3 in {4, 7, 3} The relationship is symbolized rounded E/trident looking symbol between the # in question (3) and the set {.........}How do elements and subsets differ?A subset (symbolized by sideways u/ stretched c) has multiple values contained in a set while an element only refers to a single value. Set > Subset > ElementWhat are three ways of describing sets?1. Rule - e.g. {x | x > 3} referring to a concrete number 2. Roster - listing the elements - e.g. {4, 5, 6} 3. Venn diagram/Euler circles"Equal" vs. "Equivalent" Sets"=" the exact same elements contained in each "~" the same number of elements"Union" vs. "Intersection" of SetsUnion: all the elements of 2+ sets combined; symbolized by u-shaped symbol Intersection: the element or subset that 2+ sets share - e.g. {1,2,3} & {3,4,5} would intersect at 3; symbolized by upside-down u/union symbolNumber Lines & Inequalities - dots/circlesDots mark numbers that are included in an answer set - i.e. for greater/less than or equal to Hollow dots/circles mark, conversely, mark numbers that are not included - i.e. for pure greater/less than problems.Binary Operationsarbitrary symbols - e.g. *, @, $ - that stand in place of a certain (set of) operation(s) Ex: For all integers x and y, the binary operation # is defined by x # y = (x-y)/xy What is the value of 8 # 7? (8-7)/(8X7) = 1/56To compare fractions, cross multiply (w/ arrows facing up)e.g. 5/6 < 6/7 because (6X6=36)>(7X5=35)sqrtX*sqrtY = _, sqrt(x/y) = _sqrtXY, sqrtX/sqrtYCentral Angles vs Inscribed Angles (Circle)Central: from center point, has same angle as arc Inscribed:from opp edge of circle, has 1/2 angle of arcExterior AngleIn a triangle, an exterior angle is equal to the sum of its remote interior angles.......That is because it is equal to 180-adjacent angle.When counting indivs in overlapping groups (e.g. kids in 2 classes), .....Total = Group 1 + Group 2 - Overlap ------- Think VennInclusiveTake into account the first number 10-5 = 5, but {5,6,7,8,9,10} has 6 numbers On a related note, if asked to find the # of peeps btwn two indivs in a line/set, they are asking for you to DISREGARD the 1st and last #s, so it would be: diff - 1(the last indiv)A number X that yields a remainder w/ a number Y will yield what remainder with 10Y? 1/10Y?the same remainder, just as a clean division simply moves the 0 of the quotient when the divisor is multiplied or divided by 10 - e.g. 300/3 = 100, 300/30 = 10The remainder is r when p is divided by kp = kq + r Integer q = "quotient"Even & OddsEven + Even & Even * Even = Even Odd * Odd = Odd, BUT Odd + Odd = Even Even * Odd = Even In sum, Odd * Odd = OddConsecutive even or odd integers written asx, x+2, x+4Numbers ending in 0,1,5, or 6...All exponents of them end in the same digit - e.g. 10X10=100, 11X11=121, 15X15=225, 16X16=25664 and 14 raised to the same power have the same last digit. Why?They too have the same last digit. Exceptions are base numbers (2 through 9)Quantitative Comparisons1. Look for terms that are identical in both columns. These can be subtracted or divided out (if signs are same) 2. If there are no variables in the prob, the answer cannot be D 3. If plugging in, check all cases unless otherwise specified ----- 0,1,2, -2, 1/2 4. For probs w/ 2 vars, you must check the case where they are equivalent unless otherwise specified (e.g. x=y). 5. Plug in the first three numbers of a set using the givens (but never more than 3 numbers). 6. Check for double cases in the givens ALWAYSGCF x LCM = V x Ve.g. 18 & 45 18 x 45 = 9 x LCM --> 810 = 9 x LCM ---> LCM = 903rd and 4th exponent lawsIII. (2^2)^3=2^6 IV. 2^2 x 7^2 = (2 x 7)^2Distributive law applies to division too!Just as a(b+c) = ab + ac, (a-b)/c = a/c - b/c