Quantitative Aptitude Cheat Sheet

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2 Proper fractionwill have(p<q) and improper fraction will have (p>q)Factors:A positive integer f is said to be a factor ofagiven positive integer 'n' if f divides n withoutleaving aremainder. 1, 2, 3, 4, 6 and 12 are thefactors of Numbers:A prime number is a positivenumberwhich has no factors besides itself and Numbers:A composite number is anumberwhich has other factors besides itself :For a natural number 'n', its factorial isdefined as: n! = 1 x 2 x 3 x 4 x .. x n (Note: 0! = 1)Absolute value:Absolute value of x (written as |x|) isthe distance of 'x' from 0 on the number line. |x| isalways positive. |x| = x for x > 0 OR-x for x < 0 Laws of Indices =+ = ()=/= =/= = 1 HCF and LCMFor two numbers, HCF x LCM = product of the of Fractions =LCM of Fractions =Relatively Prime or Co-Prime Numbers: Two positiveintegers are said to be relatively prime to each other iftheir highest common factor is RulesA number is divisible by.

3 2, 4 & 8 when the numberformed by the last, last two,last three digits aredivisible by 2,4 & 8 & 9 when the sumof the digits of the number isdivisible by 3 & when the difference between the sum of the digitsinthe odd places and of those in even places is 0 or amultiple of , 12 & 15 when it is divisible by 2 and 3, 3 and 4 & 3and 5 , if the number of tens added to five times the numberof units is divisible by , if the number of tens added to four times thenumber of units is divisible by , if the number of tens added to twice the number ofunits is divisible by Formulae = (a b)( ab +). Hence, isdivisible by ((a b)and ( ab +). = (a b)( + b + + .. + )(for all n). Hence, is divisible by a bfor all n. = (a+b) ( + b + + .. )(n even). Hence, is divisible by a+b Aptitude Cheat += (a + b) ( b ++.))

4 +(n odd). Hence,+is divisible by a+bforoddn.++ 3abc=(a + b + c) (+ ab ac bc)Hence,++= 3abc if a + b +c = 0 AverageSimple Average=Weighted Average = Arithmetic Mean = (a1 + a2 + a3 ..an)/nGeometric Mean = Mean = PercentageFractions and their percentage equivalents:FractionPercentageFractionPe rcentage1/250%1 = Principal + InterestSimple Interest = PNR/100 CompoundInterest =P1 Population formula P =P1 Depreciation formula = initial value 1 Growth and Growth RatesAbsolute Growth = Final Value Initial ValueGrowth rate for one year period = 100 SAGR or AAGR =. 100 CAGR = (). 1 Profit and Loss%Profit/Loss =100In case false weights are used while selling,% Profit =( 1)100 Discount % = 100 Mixtures and AlligationsAlligation The ratio of the weights of the twoitems mixed will be inversely proportional to thedeviation of attributes of these two items from theaverage attribute of the resultant mixture=Ratio and ProportionCompounded Ratio of two ratios a/b and c/d isac/bd,Duplicate ratio of a : b is:Triplicate ratio of a : b is:Sub-duplicate ratioof a : b is : Sub-triplicate ratio of a : b is : Reciprocal ratio of a : b is b : aComponendo and DividendoIf=& ab then= Quantitative Aptitude Cheat += (a + b) ( b ++.)

5 +(n odd). Hence,+is divisible by a+bforoddn.++ 3abc=(a + b + c) (+ ab ac bc)Hence,++= 3abc if a + b +c = 0 AverageSimple Average=Weighted Average = Arithmetic Mean = (a1 + a2 + a3 ..an)/nGeometric Mean = Mean = PercentageFractions and their percentage equivalents:FractionPercentageFractionPe rcentage1/250%1 = Principal + InterestSimple Interest = PNR/100 CompoundInterest =P1 Population formula P =P1 Depreciation formula = initial value 1 Growth and Growth RatesAbsolute Growth = Final Value Initial ValueGrowth rate for one year period = 100 SAGR or AAGR =. 100 CAGR = (). 1 Profit and Loss%Profit/Loss =100In case false weights are used while selling,% Profit =( 1)100 Discount % = 100 Mixtures and AlligationsAlligation The ratio of the weights of the twoitems mixed will be inversely proportional to thedeviation of attributes of these two items from theaverage attribute of the resultant mixture=Ratio and ProportionCompounded Ratio of two ratios a/b and c/d isac/bd,Duplicate ratio of a : b is:Triplicate ratio of a : b is:Sub-duplicate ratioof a : b is : Sub-triplicate ratio of a : b is : Reciprocal ratio of a : b is b : aComponendo and DividendoIf=& ab then= Quantitative Aptitude Cheat += (a + b) ( b ++.)

6 +(n odd). Hence,+is divisible by a+bforoddn.++ 3abc=(a + b + c) (+ ab ac bc)Hence,++= 3abc if a + b +c = 0 AverageSimple Average=Weighted Average = Arithmetic Mean = (a1 + a2 + a3 ..an)/nGeometric Mean = Mean = PercentageFractions and their percentage equivalents:FractionPercentageFractionPe rcentage1/250%1 = Principal + InterestSimple Interest = PNR/100 CompoundInterest =P1 Population formula P =P1 Depreciation formula = initial value 1 Growth and Growth RatesAbsolute Growth = Final Value Initial ValueGrowth rate for one year period = 100 SAGR or AAGR =. 100 CAGR = (). 1 Profit and Loss%Profit/Loss =100In case false weights are used while selling,% Profit =( 1)100 Discount % = 100 Mixtures and AlligationsAlligation The ratio of the weights of the twoitems mixed will be inversely proportional to thedeviation of attributes of these two items from theaverage attribute of the resultant mixture=Ratio and ProportionCompounded Ratio of two ratios a/b and c/d isac/bd,Duplicate ratio of a : b is:Triplicate ratio of a : b is:Sub-duplicate ratioof a : b is : Sub-triplicate ratio of a : b is : Reciprocal ratio of a : b is b.

7 AComponendo and DividendoIf=& ab then= Quantitative Aptitude Cheat (non-zero) quantities of the same kinda, b, c, dare said t o be in proportion if a/b = non-zero quantities of the same kind a, b, c, d aresaid be in continued proportion if a/b = b/c = , b, c , d are said to be in proportion if=a, b , c, d are said to be in continued proportion if==Time Speed and DistanceSpeed = Distance / Time1 kmph = 5/18 m/sec; 1 m/sec = 18/5 kmph==..If the distance covered is constant then the averagespeed is Harmonic Mean of the values (,,..)=..=(for two speeds)If the time taken is constant then the average speed isArithmetic Mean of the values (,,..)=,,..=(for two speeds)Races & ClocksLinearRacesWinner s distance = Length of raceLoser s distance = Winner s distance (beatdistance + start distance)Winner s time = Loser s time (beat time + start time)Deadlock / dead heat occurs when beat time = 0 orbeat distance = 0 Circular RacesTwo people are running on a circular track oflength L with speeds a and b in the same directionTime for 1stmeeting =Time for 1stmeeting at the starting point = LCM (,)Clocks:To solve questions onclocks, consider acircular track of length 360.

8 The minute hand movesat a speed of 6 per min and the hour hand moves at aspeed of per and WorkIf a person can do a certain task in t hours, thenin 1 hour he would do1/t portion of the does a particular job in a hours and B does thesame job in b hours, together they will takehoursA does a particular job in a hours more than Aand B combined whereas B does the same job in b hours more than A and B combined, thentogether they will take hours to finish the and Angles Sum of the angles in a straight line is 180 Vertically opposite angles are always equal. If any point is equidistant from the endpointsof a segment, then it must lie on theperpendicular Aptitude Cheat (non-zero) quantities of the same kinda, b, c, dare said t o be in proportion if a/b = non-zero quantities of the same kind a, b, c, d aresaid be in continued proportion if a/b = b/c = , b, c , d are said to be in proportion if=a, b , c, d are said to be in continued proportion if==Time Speed and DistanceSpeed = Distance / Time1 kmph = 5/18 m/sec; 1 m/sec = 18/5 kmph==.

9 If the distance covered is constant then the averagespeed is Harmonic Mean of the values (,,..)=..=(for two speeds)If the time taken is constant then the average speed isArithmetic Mean of the values (,,..)=,,..=(for two speeds)Races & ClocksLinearRacesWinner s distance = Length of raceLoser s distance = Winner s distance (beatdistance + start distance)Winner s time = Loser s time (beat time + start time)Deadlock / dead heat occurs when beat time = 0 orbeat distance = 0 Circular RacesTwo people are running on a circular track oflength L with speeds a and b in the same directionTime for 1stmeeting =Time for 1stmeeting at the starting point = LCM (,)Clocks:To solve questions onclocks, consider acircular track of length 360 . The minute hand movesat a speed of 6 per min and the hour hand moves at aspeed of per and WorkIf a person can do a certain task in t hours, thenin 1 hour he would do1/t portion of the does a particular job in a hours and B does thesame job in b hours, together they will takehoursA does a particular job in a hours more than Aand B combined whereas B does the same job in b hours more than A and B combined, thentogether they will take hours to finish the and Angles Sum of the angles in a straight line is 180 Vertically opposite angles are always equal.

10 If any point is equidistant from the endpointsof a segment, then it must lie on theperpendicular Aptitude Cheat (non-zero) quantities of the same kinda, b, c, dare said t o be in proportion if a/b = non-zero quantities of the same kind a, b, c, d aresaid be in continued proportion if a/b = b/c = , b, c , d are said to be in proportion if=a, b , c, d are said to be in continued proportion if==Time Speed and DistanceSpeed = Distance / Time1 kmph = 5/18 m/sec; 1 m/sec = 18/5 kmph==..If the distance covered is constant then the averagespeed is Harmonic Mean of the values (,,..)=..=(for two speeds)If the time taken is constant then the average speed isArithmetic Mean of the values (,,..)=,,..=(for two speeds)Races & ClocksLinearRacesWinner s distance = Length of raceLoser s distance = Winner s distance (beatdistance + start distance)Winner s time = Loser s time (beat time + start time)Deadlock / dead heat occurs when beat time = 0 orbeat distance = 0 Circular RacesTwo people are running on a circular track oflength L with speeds a and b in the same directionTime for 1stmeeting =Time for 1stmeeting at the starting point = LCM (,)Clocks:To solve questions onclocks, consider acircular track of length 360.