Exceptions Quant

8/12/2019 Exceptions Quant

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Quant Exceptions By ASAX

Sept, 2012

Arithmetic/Numbers:

1. Numbers means: -1,- 1/2),0, 1/2),1[Unless specified]2. All Prime numbers are not odd. 2 is the ONLY even prime number3. Watch out for 0/1/-1 exceptions in all numerical related problems4. Number-Reverse always divisible by 9. Number+Reverse always

divisible by 11.

5. AP:a. Sequence a1, a2,an, so that a(n)=a(n-1)+d (constant)b. nth term an = a1 + d ( n 1 )c. Sn=n*(a1+an)/2 or Sn=n*(2a1+d(n-1))/2

6. GP:a. The general sum of a N term GP with common ratio R

=A1*(RN1)/(r-1), A1first term.

b. If an infinite GP (|r|


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19. (N! + 1) is not divisible by any positive integer less than or equal toN.

20.Maximum number of factors a number when a is divided by

results in 0 remainder31. S.P=(100P)/CP Discount=(S.P-M.P)/M.P32.Successive Discounts=M.P(100-D1)(100-D2)/10033.SI=PNR/10034.CI=P(1+(R/100t)tntnumber of times per year. Half yearly =>2 times

year. Etc

35.R=[(Final/Initial)(1/n)-1]Special Interest Perfect Squares:36.Perfect square has oddnumber of DISTINCT factors37.Sum of DISTINCT factors is odd38.Odd number of Odd-factors and Even number of Even factors

(1,3,9) & (2,8,18,36) for 36

39.Even powers for PRIME factors

Exponents:


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Sept, 2012

40.n0=00=1-1=1141. X2=(X)2 - Even power masks the SIGN.42.When raised to powers Positive number increase in value, except

those between 0 and 1.43.x = bY is the same as y = logbx44.(a+b)2= a2+b2+2ab45.(a3+b3)=(a+b)(a2-ab+b2)46.(a3-b3)=(a+b)(a2+ab+b2)47.(a+b)3=a3+b3+3ab(a+b)48.Any positive integer root from a number more than 1 will be

more than 1. For example: .

Algebraic expressions:

49.X X-1)=X-1 => NEVER cancel out the like termsin algebraicexpressions.Expandto get maximum roots.

50.Equation with two unknown we can always find outthe valueof one or two of the unknowns if extra condition implicit orexplicit) such as real/whole number is given.

51. Root= -b(b2-4ac)/2aInequalities:

52.To multiply/Dividevariables you need to know the SIGN of theVariables.

53.Two inequalities can be added if pointed it at the same directions54.Two inequalities can be multiplied if pointed it at the same

directions and are positive.55.You cannotDIVIDE two inequalities.56.One side is other side is + you cannot square.57.a1/x158.X2> 0 if X059.x > y & x2> Y => x > y60.|X| for X >0, X


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62.Substitute the values in to the expression, for an absolute valueequation; both the solutions need not be valid.

63.An absolute Value is ALWAYS >0,whenever you see absolute valueon one side of the equation keep that in Mind!

a. 3|x24| = y2, LHS always +ve(absolute value) => RHS cant be ve => y264.- M = | - M | => -M never Negative => -M total # =

even else odd.

68.Mean = 0, either all are 0 or sum is zero. [-1, 1] or [-1,0,1]69.Standard Deviation: 3 ways to express:

a. Sqrt(mean squared distances of the numbers from themeanof the numbers)

b. Sqrt(X2(x)2) Square of mean-mean of squares of numbersc. Sqrt(variance of the set)

70.PERCENTAGE bound by 1SD,2SD,3SD = 62.8%,95.4%,99.7%71. Maximize Range X,X,Mean,Mean,Y -----Then mean keep it least => equal to mean and then

largest

Sets: 3 Set diagram

72.In a set 42 people in group, 29 employed, 24 students employedstudents? Cant say as we dont know how many people are NOTemployees or NOT students.

73.X (total/Given number)=I+II+III [I is only, II is two over lapping, III All]74.I=IA+IB+IC75.S=I+2II+3III76.S-X=II+2III77.X is max when S=X78.X is second Max when II(min)+2III79.X is third Max when only III exists all are over lapping.80.III Min

100 (total)A 90 100-90=10B 80 20C 70 30


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Sept, 2012

III Min= 100-60 = 40 60

Geometry

81. Parallel lines in a circlegiven one angle all the arcs lengthsmade by chords can be found.

82.ImposterParallel lines it may seem, but might not be.83.Maximum # 90degree angle in triangle is 1.84.For lengths of triangles A-B Rectangle or Square95.All squares are rectangles96.Maximize a product by equaling the numbers. Square has the

maximum areafor any given perimeter A+B=Constant, AB]maxwhenA=B

97.Similarly, Square has minimumperimeterfor given area.AB=Constant, A+B]minwhen A=B

98.For diagonals, use 2 for Square and 3 for Cuboid99.For an isosceles triangle, the area will be maximum when it is a

right angled triangle.An isosceles triangle can be considered

as one half of a rhombus with side lengths 'b'. Now a rhombus of

greatest area is a square, half of which is a right angled

isosceles triangle

100. Radius Circle inscribed in a right angle triangle. = (a+b-c)/2


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Probability

101.In simultaneous picks, pretend it not simultaneous, Break itdown. Work it as without replacement problems.

102. Probability of A cannot be used to determine Probability of B.(independent events)

RTD

103. Average Speed = Total Distance/Total time NOT (speed1+speed2)/2104. Unit conversion minutes hours => kmph=5/18 mps105. Speed Proportional 1/Time

a. 40% Inc Speed == 28%Decrease Time orb. (2/5) Inc Speed ==(2/5+2) Decrease Time

106.

Circular

total distance = distance of circular path forboth the cases kiss and depart

107. Overtaking (Same direction) A & B same distance108. Meeting (Opposite directions)A & B Same time109. A=======B One Starting at A at certain time, another Starting

at B at another time, First meet= [Common Time x Speed component

(either First Starting/reaching) ] + Time of Late Starter

110.A=======B First Meet = D, Second Meet = 2D+1D111. Circular First Meet = D, Second Meet = 1D+1D112.Circular Meeting Time:

Time Same Direction Opp DirectionFirst Meet Distance/(a-b) Distance/(a+b)First Meet @Starting Pt LCM (D/a, D/b) LCM (D/a, D/b)

113.Average Speed: Total.D/Total.Timea. Same Distance , Avg.Speed= Harmonic Mean of Speeds =

2ab/(a+b)

b. Same Time, Avg, Speed = Arithmetic Mean of Speeds = (a+b)/2RTW114.rate1 +rate2= total Rate [we usually do, 1/time1 +1/time2=1/total time,

which is also right]

Co-ordinate Geometry

115.Area of Triangle: Determinants: XY1 (1,0,1)(2,3,1)(5,7,1)


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116.Parallel Lines m1=m2, perpendicular lines m1*m2=-1117.A certain square is to be drawn on a coordinate plane. One of

the vertices must be on the origin, and the square is to have an

area of 100. If all coordinates of the vertices must be integers,

how many different ways can this square be drawn? 12not 8.118.Perpendicular bisector passes through the mid-point119.+/- Slope120. Parabola = ax2+bx+c. +/- value of a = Up/Downward. |a| High/low

= Narrow/wide

121.b2-4ac > 0 => 2 roots/intercepts =0 => equal roots nosolution/no intercepts

122. Reflection along Y axis. X=-x123. Reflection along X axis. Y=-y124. Reflection along x=y line. Y=x125. Reflection along y=|x| => v126. Graphhttp://gmatclub.com/forum/quick-way-to-graph-

inequalities-76255.html

127. Using Graph to solvehttp://gmatclub.com/forum/graphic-approach-to-problems-with-inequalities-68037.html

128. Positive slope: if +ve X intercept => -ve Y intercept.Mixtures:

129. Initial Volume P. Q Volume taken out and replaced n times.Final Volumein Solution= ((P-Q)/P)n

Permutation & Combination:

130. Combination - Permutation where x elements are identical:nPk/x!

131.Circular Permutation = (n-1)!132. Consider 0s and 1s.

a. How many ways to give 12 chocolates among 3 children(A,B,C). ABC can be 0

i. A+B+C=12 => One scenario - 0|00|000000000 1,2,9.There are 12 0s and 2 |s =>Number of

ways=(12+2)C2=14C2 ways

b. 3 dice thrown. Probability sum=12. Here, A,B,C can takevalues from (1-6)
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Sept, 2012

c. Routes North & south roads: Rows(r) Columns (c).Number of routes from point A to B via R*C = (r+c)Cr

Other Misconceptions:

133. If it is said, A is preceded by B, B is preceded by C. Then, wecannot, take it as. ABC,ABC, but only as ABC. It is not a pattern.

Numbers:

16 2/3% = 1/6 33 1/3% = 1/3 66 2/3% = 2/3 83 1/3% = 5/6 40% = 2/5 60% = 3/5 80% = 4/5 12 1/2% = 1/8 37 1/2% = 3/8 62 1/2% = 5/8 87 1/2% = 7/8 Prime Numbers 2 3 5 7, 11 13 17 19, 23 29, 31 37, 41 43 47, 53 59, 61 67, 71 73 79,

83 89, 97 101

Perfect Numbers: 6,28,496,8128 2=1.414 & 3=1.732 pi=3.14 Unique Number37K=111,222,333,.. Last Digit Patterns:

o 2 = 2,4,8,6o 3 = 3,9,7,1o 4 = 4,6o 5 = 5o 6 = 6o 7 = 7,9,3,1o 8 = 8,4,2,6o 9 = 1,9

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