├── aptitude.docx └── README.md /aptitude.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/shubhh-eagle/GFG-aptitude-series-cheatsheet/HEAD/aptitude.docx -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # GFG-aptitude-series-cheatsheet 2 | Its a list of tips, tricks and formulas from the entire GFG aptitude series which can work as major takeaways / cheatsheet from the series 3 | 4 | ## Arithmetic aptitude 1 5 | 6 | • Multiply with 125 convert to 1000/8 7 | 8 | • (a+b)^2 formula 9 | 10 | • 3 divisibilty, 39 => 13*3 so 3 divisibilty 11 | 12 | • P and q work = a and b so 1/a + 1/b together for 1 day 13 | 14 | • (4446)x + (2222)x = (10001)x , here 6 + 2 = 8 but here is 1 so , 8-x = 1 , x = 7 , 7 is base, so every calc just replace 1 with 7 15 | 16 | • Loss profit sale , direct %add or multi or subtract 17 | 18 | • Series- maybe 2 series together 19 | 20 | • Inequality x1 + x2 + x3 <= r, => x1 + x2 +x3 +x4 = r , C(n – 1 + r , n-1) 21 | 22 | • Two numbers with high power add- (35)6 + (63)6 ,here 5 power always 5, another unit number cyclicity check 23 | 24 | • Smallest num div by many small num gives some remainder, small num factors multi 25 | 26 | • Digit n number and sum to p => n-1+pCp 27 | 28 | ## Arithmetic aptitude 2 29 | 30 | • Divisible by many num – LCM 31 | 32 | ## Arithmetic aptitude 3 33 | 34 | • Ratio ques – 4:5 take 4x and 5x and put in eqn 35 | 36 | ## Arithmetic aptitude 4 37 | 38 | • Power of n ,? = m (large num) ,? = log m / log n 39 | 40 | • Ratio and HCF , a:b , ax , bx , x = HCF 41 | 42 | • 4 consecutive odd num – numbers assume = 2x+1 , 2x+3 … 43 | 44 | • Sum of 2 num and sum of sq of two num , (a+b)^2 45 | 46 | ## Arithmetic aptitude 5 47 | 48 | • Tens num = x + 10y 49 | 50 | • if we get prod and subtract of two num , we need the nums, => (a+b)2 = (a-b)2 + 4ab, solve a+b and a-b 51 | 52 | • AI concepts , modus tollen , knowledge base.. 53 | 54 | ## Arithmetic aptitude 6 55 | 56 | • Min num to add in P to be divisible by Q, => div P by Q ans = x.65564, just inc x by 1, now Q*(x+1) , calc excess by P, => Q*(x-1) – P 57 | 2nd method , div P by Q, remainder R, ans = P-R 58 | 59 | ## General Aptitude 60 | 61 | • If irrational num at deno , multi with irrational on numerator and den, , multi with root(1)-root(2) at num and den, (a-b)(a+b) = a2 – b2 62 | 63 | • In ques of maxi or min , take derivative 64 | 65 | • Prob ques, A and B producers , x% and y% positive ft respectively , ques ask = positive ft by A => (prob made by A * positive(x)) / (prob made by A * positive(x)) + (prob made by B * positive(y)) 66 | 67 | • Log relation? Log A = 1/2log B , take one term equal to constant C, log A = C, A = Bc, where B is base of log 68 | 69 | • Root(12 + root(12 + …infinity , y = Root(12 + root(12 + …infinity, => y = root(12 + y) , quad soln 70 | 71 | • Clock ques , find speed in common units, hour = 360 deg / 12 * 60 min = 0.5deg/min, minute = 360/12min = 6deg/min, current angles = angle swept already + 0.5t (t in min) 72 | 73 | • Prime factorization of 2014 = 21x191x531 Therefore, total number of factors of 2014 = (1+1)x(1+1)x(1+1) = 2x2x2 = 8 74 | 75 | • The subtraction of octal numbers follows the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. In the decimal system, you borrow a group of 10(10). In the binary system, you borrow a group of 2(10). In the octal system you borrow a group of 8(10) 76 | 77 | • Num of divisor in 2100, 2100 = 22 * 31 * 52 * 71 so for 2 we have 3 choices , power 0,1 or 2 , same for others , => 3 * 2 * 3 * 2 = 36 78 | 79 | • Num of rectangles in rectangle made up of rectangles, mC2 nC2, m is total horizontal lines, n is total vertical lines, 2 from both are req for rectangle 80 | 81 | • Coprime – ex – coprime of 14, a number that shouldn’t be multiple of factors of 14, i.e. 2 and 7 82 | 83 | ## Probabilty (still in progress) 84 | 85 | • poisson distribution, u is mean of prob, e- expo (2.71), x- num of success, P(x;u)- prob of these x success where mean is u 86 | 87 | • Commulative distribution func = P(X<=x), x given point , basically prob of success less than or eq to x 88 | 89 | • Mutually Exclusive Events => P(A intersection B) = P(A) x P(B) 90 | 91 | • f(x) be the continuous probability density func¬tion of a random variable X. The probability that a < X ≤ b, is 92 | 93 | 94 | ## Misc 95 | 96 | • sum of numbers on opp faces of general dice = 7 97 | 98 | • river problem - For downstream ----> Rate of (boat /steamer) in still water + rate of stream 99 | For upstream ----> Rate of (boat /steamer) in still water - rate of stream 100 | 101 | 102 | --------------------------------------------------------------------------------