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| Question | Answer |
| Quantitative Q# / Time | 0 / 75 5 / 65 10 / 55 15 / 45 20 / 35 25 / 25 30 / 15 35 / 5 |
| Verbal Q# / Time | 0 / 75 5 / 66 10 / 57 15 / 48 20 / 39 25 / 30 30 / 21 35 / 12 40 / 3 |
| Data Sufficiency Question order | A) Statement (1) alone is sufficient B) Statement (2) alone is sufficient C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient D) EACH statement ALONE is sufficient E) Statements (1) and (2) TOGETHER are NOT sufficient |
| Data Sufficiency Choice Elimination | Statement 1 sufficient -> eliminate B, C, & E insufficient -> eliminate A & D Statement 2 sufficient -> eliminate A, C, & E insufficient -> eliminate B & D If BOTH statements are insufficient, combine statements sufficient -> answer is C insufficient -> answer is E |
| Good numbers to plugin | -10, -1, -1/2, 0, 1/2, 1, 10 |
| Things to consider in Geometry Q's | -Do not estimate lengths and angles -To find one length requires at least one other length -Sketch diagram and add information -Mentally grab and move points and lines |
| When the two statements in a data sufficiency question provide identical info... | The correct answer will be either D or E |
| Dividing and multiplying by 5 | Dividing: double number and move decimal place once to the left Multiplying: half the number and move decimal once to right |
| The Half and Double trick when multiplying big numbers | A X B = 2A X 1/2B 4 X 18 = 8 X 9 = 72 |
| Add or subtract 2 or 3 digit numbers trick | Round off one of the numbers and add or subtract the difference. 144 + 48 = 144 + 50 - 2 = 192 1385 - 492 = 1385 - 500 + 8 = 893 |
| Multiply numbers between 11 & 19 | Add the ones digits of bottom number to top number, multiply by 10, and then add the product of the ones digits 14 X 13 = (17 X 10) + 12 = 182 12 X 16 = (18 X 10) + 12 = 192 |
| Square any number between 11 & 99 trick | 1) Find the nearest multiple of ten 2) Find out how much you have to add or subtract to get that number "k" and then do the opposite function 3) Multiple the two numbers 4) Add the square of k 23^2 = (20 X 26) + 3^2 = 529 97^2 = (100 X 94) + 3^2 = 9409 |
| Estimated values of Root 2 and Root 3 | Root 2 = 1.4 Root 3 = 1.7 |
| Definition of Real numbers and Integers | Real numbers are any number on the number line including "0", negative, positive, fractions Integers are only whole numbers positive or negative including "0". |
| Fractions with bigger denominators Fractions with bigger numerators | Fractions with bigger denominators are smaller Fractions with bigger numerators are bigger |
| 1 --- a - b equals | b - a |
| 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 | 0.5 or 50% ~0.333 or ~33.3% 0.25 or 25% 0.2 or 20% ~0.166 or ~16.6% ~0.14 or ~14% 0.125 or 12.5% ~0.11 or ~11.1% |
| What is 40% of 90? 15% of what number is 60? 120 is what % of 80? | Part/Whole = Percent/100 Part/90 = 40/100 60/Whole = 15/100 120/80 = Percent/100 |
| Finding percent of change | (Change X 100) / Original |
| 2^1 2^2 2^3 2^4 2^5 2^6 2^7 | 2 4 8 16 32 64 128 |
| 3^1 3^2 3^3 3^4 | 3 9 27 81 |
| 4^1 4^2 4^3 | 4 16 64 |
| 5^1 5^2 5^3 5^4 | 5 25 125 625 |
| Squaring integers ending in "5" | 1) Let "n" be the number before the 5 2) Write the product of "n" and "n+1", followed by 25 45^2 = 2025 |
| Units digits in large exponents | Look for a pattern in the units digits. When "n" is divisible by cycle number, the units digit is what in the pattern? Then build from the closest number the exponent is divisible by the cycle number. |
| Sq. root of 2 Sq. root of 3 Sq. root of 5 | 1.4 1.7 2.2 |
| If 0 < X < 1 If X > 1 | Then Sq. root of X > X Then Sq. root of X < X |
| Products of Roots and Roots of Products | (n Sq. root of X) * (n Sq. root of Y) = (n Sq. root of X*Y) |
| Quotients of Roots and Roots of Quotients | (n Sq. root of X) / (n Sq. root of Y) = (n Sq. root of X/Y) |
| Addition and Subtraction of Roots | 2 Sq. root 7 + 9 Sq. root 7 = 11 Sq. root 7 11 3root 2 - 5 3root 2 = 6 3root 2 7 5root 3 + 2 5root 3 - 5root3 = 8 5root 3 |
| Multiplying Roots | 2 root 3 * 7 root 5 = 14 root 15 11 3root 4 * 5 3root 7 = 55 3root 28 |
| X^a/b | (b root X)^a |
| If b^x = b^y | Then x = y if b doesn't equal 0, 1, or -1 |
| Fraction that is a terminating decimal | Denominator in its most reduced form must be a power of 2 and/or a power of 5 |
| Two cases you get an odd | Odd */divided Odd Odd +/- Even |
| Classic Quadratics (a^2 - b^2) (a + b)^2 (a - b)^2 | (a + b)(a - b) (a +b)(a + b) = a^2 + 2ab + b^2 (a - b)(a - b) = a^2 - 2ab + b^2 |
| Divisible by 3 | sum of all digits is divisible by 3 |
| Divisible by 4 | If last two digits are together divisible by 4 |
| Divisible by 7 | If difference between its unit digit multiplied by 2 and the rest of the number is divisible by 7 |
| Divisible by 8 | If its last 3 digits compose a 3 digit number that is divisible by 8 |
| Divisible by 9 | If sum of its digits are divisible by 9 |
| Divisible by 11 | If the difference between the sum of its odd placed digits and the sum of its even placed digits is divisible by 11 |
| Divisible by 6 | Must pass both divisibility tests of 2 and 3 |
| Divisible by 44 | Must pass both divisibility tests of 4 and 11 |
| Average of a consecutive sequence or evenly spaced sequence equals | Average of the first and last numbers in the sequence |
| Sum of values of a sequence equals | Avg value * Number of values [(First number + Last number) / 2] * (Last number - First number + 1) |
| In a sequence of consecutive or evenly spaced integers the mean equals | the median |
| nCk n choose k | n! / [k! (n-k)!] |
| nPk | n! / (n-k)! |
| To find the probability that one OR another of two mutually exclusive events will occur: | add the probabilities of the two events |
| To find the probability that one AND another of two independent events will occur: | multiply the probabilities of the two events |
| Rate Speed Average | Quantity A / Quantity B Distance / Time Sum of terms / number of terms |
| Combined Rates and work Rate = | Number of Tasks / Time to complete tasks |
| Combined worked formula for two workers | T = (a * b) / (a + b) |
| Combined work formula for more than 2 workers | 1/T = 1/a + 1/b + 1/c +..... |
| Evidence Keywords | because for since as a result of due to |
| Conclusion Keywords | therefore hence thus so clearly consequently |
| Correct: Regarded as Considered Credited with Believe it to be Estimated to be Decide whether Forbidden to enter Significant as to | Wrong: Regarded to be Considered to be Credited to Believe it is Estimated at Decide if Forbidden from entering Significant to |
| Which always must be: | preceded by a comma and refer to the noun just before the comma except when used "in which". |
| He demanded that the door be opened If I were rich, I would quit my job | No "to" before the "opened" were and would not was and would |
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