2024 GregMat GRE Quant 1 | To Memorize

========== 1.1 Divisiblity Rules ========== 1) Divisibility Rules 1... > a) Rule of 2 > b) Rule of 3 > c) Rule of 4 > d) Rule of 5 > e) Rule of 6 2) Divisibility Rules 2... > a) Rule of 8 > b) Rule of 9 > c) Rule of 10 > d) Rule of 11 > e) Rule of 12 3) How can you check if 14,350,770914 is divisible by 7? 4) Rule of 13 https://byjus.com/maths/divisibility-rules/#:~:text=The%20rule%20for%20divisibility%20by%209%20is%20similar%20to%20divisibility,is%20not%20divisible%20by%209.

- 1) Divisible if... (% X => Divisible by X) > a) Last Digit => Is even > b) (Sum+of+digits) % 3 = 0 // 516 => 12%3 => 0, so divisible > c) Last 2 Digits % 4 = 0 // 2308 => 08%4=0, so divisible > d) Last Digit {0,5} > e) Divisible by both {2,3} => => Even Number AND (Sum+of+digits)%3=0 2) > a) Last 3 Digits % 8 = 0 > b) (Sum+of+digits) % 9 = 0 > c) Last digit = 0 > d) (Sum of digits in odd places) - (Sum of digits in even places) = 0 or a multiple of 11 => 121 => (1+1) - (2+0) => 2 - 2 = 0 % 11 = 0 > e) Divisible by both 4 & 3 3) ==> 14bil + 350mil + 770tho + 91 + 4 4) Multiply last digit by 4, add to remaining digits, rinse repeat until 2-digit number (check if divisible by 13) For example: 2795 → 279 + (5 x 4) → 279 + (20) → 299 → 29 + (9 x 4) → 29 + 36 → 65 OLD RULE OF 7 Multiply last digit by 5, add to remaining digits, rinse/repeat until divisible by 7 => 8743 example below: - 3x5=15, 874+15 = 889 - 9×5=45, 88+45=133. - 3×5=15, 13+15=28.

========== 1.2.1 Random Memorization ========== 1) Percent formulas for... > a) Increase? > b) Decrease? > c) Time series? > d) 26% of 50 is equal to... 2) What are the following equal to? > a) b is 150% of c... > b) b is 150% larger than c... > c) b is 150% greater than c... 3) Decimals Rules... > a) What guarantees a terminating decimal? > b) What guarantees a repeating decimal? > c) What guarantees a 2-place repeating decimal? > d) What guarantees a 3-place repeating decimal? > e) What is (-1/2)^(-2)? What about (-1/2)^(-3)?

1) > a) (L-S)/S > b) (L-S)/L > c) (2nd-1st)/1st > d) 50% of 26 2) > a) b = 1.5c > b) b = 1.5c + c = 2.5c > c) b = 1.5c + c = 2.5c 3) > a) Denominator = {2,5} ONLY!!! > b) Denominator => Any Prime Factor other than {2,5} > c) Denominator => 99 > d) Denominator => 999 > e) -4. -8.

==== 2.7 | Interest ===== 1) > a) Simple Interest formula? > b) Compound Interest formula? 2) > a) When is the interest added for Simple Interest? > b) When is the interest added for Compound Interest? > c) Is there a difference in Simple & Compound interest equations when compounded annually?

1) > a) V = P(1+rt) > b) V = P(1+r/n)^nt 2) > a) End of Year > b) n times (per year) > c) Yes (see below) ==> P(1+rt) ==> P(1+r)^t

========== 1.2 Random Memorization ========== 1) Random Memorization 1... > a) sqrt(2)? > b) sqrt(3)? > c) Is 0 a positive integer? > d) What's a real number? > e) What's a non real number? > d) How can you break down digits for a number? (ie. 3976 => {A,B,C,D}) 2) Integer Formulas... > a) Number of Integers (ie. "n" items) in Interval (ie. "l"-"f") ? > b) Number of Integers in interval 5-10? > c) Sum of Integers in Interval? 3) "Multiples" Formulas > a) What are "l"/"f" here? > b) Number of Multiples in Interval? > c) Sum of Multiples in Interval => Median? What happens if it's a decimal? > d) Sum of Multiples in Interval => # of Items? > e) Full Equation? 3) Formula for finding number of positive divisors for a Number? > a) For 16,000, which has prime factorization => 2^7 * 5^3, what is the answer? ==> HINT - If N=(p^a)*(q^b)*(r^c)..., & p,q,r are prime numbers

1) > a) 1.41 > b) 1.73 > c) No > d) Can be represented as a fraction > e) Can NOT be represented as fraction > d) (A*10^3 + B*10^2 + C*10^1 + D*10^0) 2) MEDIAN * Number of ITEMS!!! > a) n=(l-f+1) > b) 10-5+1 = 6 {5,6,7,8,9,10} > c) n(l+f)/2 3) > a) "l"/"f" => first/last MULTIPLE, n=divisor > b) 1 + [(l-f)/n] > c) (l+f)/2 => If decimal, keep/use it. > d) 1 + (l-f)/n > e) NumberOfMultiples(b) * Median => [(l+f)/2] * [1 + (l-f)/n] 3) Total number of positive divisors of N == (a+1)(b+1)(c+1) > a) (a+1)(b+1)... => (7+1)(3+1) = 8*4 = 32

========== 1.2.1 | Prime Numbers ========== 1) Factors of... > a) 51,57 > b) 63,69 > c) 87 > d) 91,93 1.5) Is 1 a Prime Number???? 2) Prime Numbers from... > a) 1-10 [4]? > b) 11-20 [4]? > c) 21-30 [2]? > d) 31-40 [2]? > e) 41-50 [3]? 3) > a) 51-60 [2]? > b) 61-70 [2]? > c) 71-80 [3]? > d) 81-90 [2]? > e) 91-100 [1]? 4) > a) 101-110 [4]? > b) 111-120 [1]? > c) 121-130 [1]? > d) 131-140 [3]? > e) 141-150 [1]?

1) > a) 17*3, 19*3 > b) 21*3, 23*3 > c) 29*3 > d) 13*7, 31*3 1.5) NO 2) > a) 2,3,5,7 > b) 11,13,17,19 > c) 23,29 > d) 31,37 > e) 41,43,47 3) > a) 53,59 > b) 61,67 > c) 71,73,79 > d) 83,89 > e) 97 4) > a) 101,103,107,109 > b) 113 > c) 127 > d) 131,137,139 > e) 149

========== 1.3 | Absolute Values & Real Numbers ========== 1) > a) What is | 2x^5 | > 64 equal to? > b) Rewrite 4^(1/4) using sqrt(2) > c) (0.25)^(0.25) vs sqrt(0.5)?

1) > a) 2x^5 > 64 AND 2x^5 < -64 => x > 2 AND x < -2 > b) 4^(1/4) => (2^2)^(1/4) ==> 2^(1/2) => sqrt(2) > c) Same

========== 4.X | ========== 1) For a normal distribution, what percentages correspond to the following std. deviations > a) 1 std. deviation? > b) 2 std. deviations? > c) 3 std. deviations? https://www.mathsisfun.com/data/standard-normal-distribution.html 2) Characteristics of a normal distribution [2]?

1) > a) 68% (~2/3) > b) 95% > c) 99.7% (almost all) 2) > a) Mean,Median,Mode -> all nearly equal > b) Data mostly grouped around mean

========== CH 1 | TEST TIPS ========== 1) > a) When mixing fractions,decimals,percents, just do... > b) For some particular number, when does the number of positive even factors == positive odd factors? > c) What determines number of trailing zeroes in a factorial? What digit to be looking for? > d) How can you determine if a number is prime (say 101) ? 2) Sum of 2 primes... > a) Every EVEN number == Sum of > b) Every ODD number == Sum of 3) What is... > a) (3^4)^4)^4 ? > b) 3^4^4^4 ?

1) > a) Decimals (Plug into calculator) > b) When there is a 2^1 factor > c) Number of 10s. Look for 5. > d) Test divisibility of primes against it (2,3,5,7,11...) ==> Stop when a prime^2 (ie. 11^2 = 121) eclipses # 2) > a) Two Prime Numbers > b) 2 + Prime Number 3) > a) 3^64 > b) 3^4^256

========== 1.0 Random Properties ========== 1) What is a... > a) Natural Number? > b) Whole Number? > c) Integer? NonInteger? > d) Rational? > e) Irrational? > f) Real number? 2) How can you check if a large number is divisible by a small number without divisibility rules? (ie. 14,350,770914 / 4) 3) 0 properties... > a) 0 is a factor of...? > b) 0 is a multiple of...? > c) What is 0!? https://byjus.com/maths/real-numbers/

1) > a) N = {1, 2, 3, 4,......} > b) N = {0,1, 2, 3, 4,......} > c) N = {-Inf...,-2,-1,0,1,2,...,Inf} > d) Can be expressed as fraction. > e) Doesn't have to be represented as fraction (eg. sqrt(2), pi, etc.) > f) Union of Irrational/Rational Numbers 2) Break into subnumbers and check if those are divisible: ==> 14bil + 350mil + 770tho + 91 + 4 3) > a) Itself > b) Every Integer > c) 1

========== TEMPLATE =========== 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) > a) > b) > c) > d) > e)

========== TEMPLATE ========== 1) 2) 3) 4) 5) > a) > b) > c) > d) > e)