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# GMAT Speed Tips

### GMAT Traps

2^2 4
2^3 8
2^4 16
2^5 32
2^6 64
2^7 128
2^8 256
2^9 512
2^10 1024
1! 1
0! 1
2! 2
3! 6
4! 24
5! 120
6! 720
7! 5040
8! 40320
9! 362880
10! 3628800
0 Squared Undefined
1 Squared 1
2 Squared 4
3 Squared 9
4 Squared 16
5 Squared 25
6 Squared 36
7 Squared 49
8 Squared 64
9 Squared 81
10 Squared 100
11 Squared 121
12 Squared 144
13 Squared 169
14 Squared 196
15 Squared 225
16 Squared 256
17 Squared 289
18 Squared 324
19 Squared 361
20 Squared 400
21 Squared 441
22 Squared 484
23 Squared 529
24 Squared 576
25 Squared 625
12 X 1 12
12 X 2 24
12 X 3 36
12 X 4 48
12 X 5 60
12 X 6 72
12 X 7 84
12 X 8 96
12 X 9 108
12 X 11 132
13 X 2 26
13 X 3 39
13 X 4 52
13 X 5 65
13 X 6 78
13 X 7 91
13 X 8 104
13 X 9 117
13 X 11 143
13 X 12 156
14 X 2 28
14 X 3 42
14 X 4 56
14 X 5 70
14 X 6 84
14 X 7 98
14 X 8 112
14 X 9 126
14 X 11 154
14 X 12 168
15 X 4 60
15 X 5 75
15 X 6 90
15 X 7 105
15 X 8 120
15 X 9 135
15 X 11 165
15 X 12 180
16 X 2 32
16 X 3 48
16 X 4 64
16 X 5 80
16 X 6 96
16 X 7 112
16 X 8 128
16 X 9 144
16 X 10 160
16 X 11 176
16 X 12 192
Y = MX + B X, Y = Coordinates on the Line M = Slope B = Y Intercept
X^A + X^B X^A+B
RootA X RootB Root(A X B)
RootA / RootB Root(A / B)
RootA^2 Absolute Value A
X% of Y Equals Y% of X
Work Formula T = AB/A+B
A Root C + B Root C (A + B) Root C
Name all the Pythagorean Triplets 3:4:5 5:12:13 7:24:25 8:15:17 9:40:41
Surface Area of a Rectangular Solid 2(LW+LW+WH)
Surface Area of a Cylinder 2 Pie R^2 + 2 Pie R H
Volume of a Cylinder Pie R^2 H
Volume of a Rectangular Solid LWH
1/9 .111 repeating or 11.1%
1/8 .125 or 12.5%
1/7 .14 or 14%
1/6 .166 repeating or 16.6%
1/5 .20 or 20%
1/4 .25 or 25%
1/3 .333 repeating or 33.3%
1/2 .50 or 50%
3/8 .375 or 37.5%
2/9 .222 repeating or 22.2%
2/7 .28 or 28%
3/7 .42 or 42%
4/7 .57 or 57%
5/7 .71 or 71%
6/7 .85 or 85%
5/6 .83 or 83%
5/8 .625 or 62.5%
Why do decimals repeat? Because they are divided by 9
How to convert a repeating decimal to fraction? Put it over 9. for example .545454 = 54/99 .0787878 = 78/990
7/8 .875 or 87.5%
1/11 .0999 repeating or 9%
1/12 .083 or 8.3%
{A} + {B} = {A+B} ONLY when A*B >=0 otherwise {A} + {B} > {A+B}
(a+b+c) * (1/a +1/b+1/c) >= 9
For any positive integer N, (1+1/N)^N is >= to what? <= to what? =>2 and <=3
a^2 + b^2 + c^2 >= ab + bc + ca ... if a=b=c then the case of equality holds true
a^4+b^4+c^4+d^4 = 4abcd (equality arises when a=b=c=d=1)
(n!)^2 > n^n
If N is even, n(n+1)(n+2) is divisible by what? 24
x^n - a^n = x-a will be a multiple of x^n - a^n
(m + n)! is divisible by m! * n!
When a 3 digit # is reversed and the difference is taken of these two #'s, the middle # is always what and sum of other two #'s is always what? middle number is always 9, sum of other two numbers is 9
the sum of the first "n" positive integers = n(n+1)/2
the sum of the squares of first "n" positive integers = n(n+1)(2n+1)/6
the sum of the first "n" even numbers = n(n+1)
the sum of the first "n" odd numbers = n^2
If "N" is represented as a^x * b^y * c^z where (a,b,c... are prime) the total # of factors is (x+1)(y+1)(z+1)
total number of prime numbers between 1-50 15
total number of prime numbers between 51-100 10
total number of prime numbers between 101-200 21
2^10 = 4^What = 32^what 2^10 = 4^5= 32^2
3^8 = 9^what = 81^what 3^8 = 9^4 = 81^2
7*11*13 = 1001
11*13*17 = 2431
13*17*19 = 4199
19*21*23= 9177
19*23*29= 12673
When the digits of a # are added up and the result is either blank or blank or blank or blank, then what? the number could be a perfect square if the digits add up to 1 or 4, or 7 or 9
To find out the sum of three digit numbers formed with a set of given digits... (sum of digits) * (# of digits - 1)! * (1 * # of digits, i.e. 3# =111)
x^n + y^n + z^n will not have a solution if n is >= to 3
What is the only 3 digit number expressed as the sum of factorials of the individual digits? 145 (1! +4!+ 5!)
when a number is of the form a^n -b^n then the # is always divisible by a-b
Pascals triangle for compounding interest Number of years 1 - 1 2 - 1 2 1 3 - 1 3 3 1 4 - 1 4 6 4 1
Explain pascals triangle for CI given P=1000, R=10%, and N=3 years 1 * 1000 + 3 *100 + 3*10 + 1*1= 1331 coefficients of each number
Suppose product is increased by X%, then decreased by Y%, the final change in % is what formula? X-Y-XY/100 = profit or loss. To find the price sold, the profit or loss % will be multiplied to get 100% to find cost. Add cost plus profit/loss to find selling price
When the cost price of 2 articles is the same, and % marked up is the same, which one should be assumed as 100? the marked price
When P represents principal, R represents rate of interest, then, the difference between 2 years simple interest and compounding is P * (R/100)^2
When P represents principal, R represents rate of interest, then, the difference between 3 years simple interest and compounding is ((P * R^2)*(300+R))/100^3
If A can finish the work in X time and B can finish the same work in Y time, then both can finish the time in - (X*Y)/(X+Y) time
If A can finish the work in X time and A+B together can finish the same work in S time, then B can finish the time in - (XS)/(X-S) time
If A can finish the work in X time and B in Y time and C in Z time then all of them working together can finish the work in - (XYZ)/(XY+YZ+XZ)
If A can finish the work in X time and B in Y time and A+B+C together in S time then C can finish that work alone in - (XYS)/(XY-SX-SY)
If A can finish the work in X time and B in Y time and A+B+C together in S time then B+C can finish that work in- (SX)/(X-S)
If A can finish the work in X time and B in Y time and A+B+C together in S time then A+C can finish that work in- (SY)/(Y-S)
When there are "n" items and "m" out of such items should follow a pattern then the probability is given by 1/m! i.e. 10 girls dance, one after the other. what is prob. A dance before B before C? n=10, m=3 (A,B,C) 1/3! =1/6
For any regular polygon, the sum of exterior angles is = to what? what is measurement of any external angle? 360 degrees and each angle is 360/n when "n" is # of sides
For any regular polygon, the sum of interior angles is = to what? what is measurement of any external angle? (n-2)*180 degrees where "n" is number of sides and measurement of one angle is (n-2)/n*180
If any parallelogram can be inscribed in a circle then it must be a rectangle
If a trapezium can can be inscribed in a circle, it must be an isosceles trapezium (oblique sides equal)
Area of Rhombus = product of two diagonals
Given the coordinates, (a:b), (c:d), (e:f), (g:h) of a parallelogram, the coordinates of the meeting point of the diagonals can be found by {(a+e)/2, (b+f)/2} = {(c+g)/2, (d+h)/2}
Let W be any point inside a rectangle ABCD, then WD^2 + WB^2 = WC^2 + WA^2
Distance between a point (x,y) and a line represented by the equation ax+by+c=0 is {ax1+by1+c/Sq(a^2+b^2)
When a rectangle is inscribed in an isosceles right triangle, then the length of the rectangle is: and ratio of area to triangle area is: length is twice it's width and ratio of area of a rectangle is triangle is 1:2
Length of longest diagonal in a cube is always XRoot3 where X is the side
When base area = base perimeter then length of diagonal is always 4
What is the 3D distance formula: ROOT(L^2 + W^2 + H ^2)
X^1/2 = SQ ROOT X
X^1/3 = Cube Root X
X^A/B = 4 different ways which are: (X^1/B)^A = (X^A)^1/B = (B Root of X)^A = B Root of X^A
(X-1)^2/X-1 = (X+1)(X-1)/(X-1) The X-1's cancel out, leaving you X+1
3^3 27
3^4 81
3^5 243
3^6 729
3^7 2187
3^8 6561
4^3 64
4^4 256
4^5 1024