Top 100 Quant Tips and Tricks by IIM Topper
This is a special notes for all
CAT and MBA aspirants.. by IIM Topper.
QUANT THEORY
1) nPr =
n!/(n-r)!
2) nPn
= n!
3) nCr =
n!/(n-r)!r!
4) nCn =
1
5) nP0
= 1
6) nC0
= 1
7) AP An
= a + (n-1)d
Sn = n/2[2a + (n-1)d]
GP An = ar(n-1)
Sn = a(rn
– 1 )/ (r-1)
S∞ = a/(1-r)
9) 1 mile = 1760 yards
10) 1 yard = 3 feet
11) 1 mile2 =
640 acres
12) I gallon = 4 quarts
13) 1 quart = 2 pints
14) 1 pint = 2 cups
15) 1 cup = 8 ounces
16) 1 pound = 16 ounces
17) 1 ounce = 16 drams
18) 1 kg = 2.2 pounds
19) 30-60-90 triangle è 1:√3:2
sides
20) 45-45-90
triangle è 1:1:√2 sides
21) a3>b3
è a>b
22) If A than B => not B
than not A
23) Zero divided by any
nonzero integer is zero.
24) Division by 0 is
undefined.
25)
26) The standard deviation
is a statistic that tells you how tightly all the various examples are
clustered around the mean in a set of data. When the examples are pretty
tightly bunched together and the bell-shaped curve is steep, the standard
deviation is small. When the examples are spread apart and the bell curve is
relatively flat, that tells you have a relatively large standard deviation.
27) n(A U B U C)
= n(A) + n (B)+ n(C) – n(A n B) – n(A n C) –
n(B n C) + n(A n B n C)
28) n(Aonly) = n(A)
– n(A n C) – n(A n B) + n(A U B U C)
29) Dividend = Divisor *
Quotient + Remainder
30) LCM * HCF = Product of
2 numbers.
31) 1 + 2 + 3
………………..n = n * n+1 / 2
32) Sum of squares of 1st
n natural numbers = n (n+1)(2n+1) / 6
33) Sum of cubes of 1st
n natural numbers = [n (n+1)/2]2
34)
Squares and Cubes
|
Number
( x )
|
Square
( x 2 )
|
Cube
( x 3 )
|
|
1
|
1
|
1
|
|
2
|
4
|
8
|
|
3
|
9
|
27
|
|
4
|
16
|
64
|
|
5
|
25
|
125
|
|
6
|
36
|
216
|
|
7
|
49
|
-
|
|
8
|
64
|
-
|
|
9
|
81
|
-
|
|
10
|
100
|
-
|
|
11
|
121
|
-
|
|
12
|
144
|
-
|
|
13
|
169
|
-
|
|
14
|
196
|
-
|
|
15
|
225
|
-
|
|
16
|
256
|
-
|
|
17
|
289
|
|
|
18
|
324
|
|
|
19
|
361
|
|
|
21
|
441
|
|
|
22
|
484
|
|
|
23
|
529
|
|
|
24
|
576
|
|
|
25
|
625
|
|
35)
Fractions and Percentage:
|
Fraction
|
Decimal
|
Percentage
|
|
1 / 2
|
0.5
|
50
|
|
1 / 3
|
0.33
|
33
1/3
|
|
2 / 3
|
0.66
|
66
2/3
|
|
1 / 4
|
0.25
|
25
|
|
3 / 4
|
0.75
|
75
|
|
1 / 5
|
0.2
|
20
|
|
2 / 5
|
0.4
|
40
|
|
3 / 5
|
0.6
|
60
|
|
4 / 5
|
0.8
|
80
|
|
1 / 6
|
0.166
|
16 2/3
|
|
5 / 6
|
0.833
|
83 2
/ 3
|
|
1 / 8
|
0.125
|
12 1
/ 2
|
|
3 / 8
|
0.375
|
37 1
/ 2
|
|
5 / 8
|
0.625
|
62 1
/ 2
|
|
7 / 8
|
0.875
|
87 1
/ 2
|
|
1 / 9
|
0.111
|
11
|
|
2 / 9
|
0.222
|
22
|
|
1 /
10
|
0.1
|
10
|
|
1 /
20
|
0.05
|
5
|
|
1 /
100
|
0.01
|
1
|
36) Average speed = Total distance / Total Time
When equal distances are covered
in different speed then we take the harmonic mean
Av Speed = 2ab / a + b
Different distances in same time
we take AM
Av Speed is = a + b /
2
37) Simple Interest: SI = PRT /
100, A = P + SI
38) 1 Nickel = 5
cents
1 dime = 10 cents
1 quarter = 25 cents
1 half = 50 cents
1 dollar = 100 cents
39) Equilateral triangle, Area =
(√3 * a2)/4
40) Area of trapezium = ½
(Height * Sum of parallel sides)
41) Arc Length = (θ/ 360) 2 ∏ r
42) Area of sector = (θ/ 360) ∏
r2
43) Equal chords are equidistant
from the center.
44) (x+y) 8 = 8C8x8 + 8C7x7y +
8C6x6y2 + 8C5x5y3 + … + 8C2x2y6 + 8C1xy7 + 8C0y8
45) Sometimes we get so involved
with the nitty-gritties of mathematics that we start functioning like
automatons and stop thinking. Don’t fall prey to this trap. For example, what
is the probability that a number amongst the first 1000 positive integers is
divisible by 8? Don’t start counting the multiples of 8! The figure of 1000 is
a red herring. Use a little common sense. The numbers will be 8,16,24,32…So, 1
in every 8 numbers is a multiple of 8, even if you consider the first million
integers. So Probability is 1/8
46) The number of integers from
A to B inclusive is = B -A +1
47) Average of consecutive
numbers:
Eg from 13 to 77 = (13+77)/2
48) Slope = (change in
y)/(change in x)
49) 00 = undefined
50)
51) Sum of
interior angles of a polygon with n sides = (n-2)*180
52) Degree measure
of one angle in a regular polygon with n sides
= {(n-2)*180 }/n
53) When
multiplying or dividing both sides of an inequality by a negative number, the inequality sign reverses.
–x < y => -(-x) > y
=> x > -y
54) Fraction > (fraction)2
for all positive fractions
55) Fraction > √(fraction )
for all positive fractions
56) If n is a positive integer,
(n6)/2 = √(n12 / 4)
57) If z1, z2, z3 … zn are
consecutive positive integers and their average is an odd integer => n is
odd => sum of series is odd
58) In a triangle with sides of
measure a, b and c SHAPE \* MERGEFORMAT , a-b a + b = odd
59) Before confirming try and back solve and make sure that u have
answered what has been asked.
60) When the question
mentions prime number, remember to think of 2 too.
61) In a triangle, if the
sum of two angles = third angle, then it is a right angled triangle.
62) Do not transport
information from another statement unless considering both collectively.
63) A-b = odd => a + b =
odd
64)
65)
66) If a DS question simply asks
whether a, b, c and d are consecutive integers; use your brain. It has just
asked u to answer if they are consecutive, not if they are consecutive in
order.
67) Measure
of an angle of a cyclic polygon = 180 – 360/n , where n is the number of sides
of the polygon.
68) Sometimes, mistakes might
also be committed by simply misreading the statement. Eg
Both Tim and Harry received an
acre of land more than Neel => t = n + 1, h = n + 1
Tim and Harry received an acre
more than Neel => t + h = n+1
69)
Let Triangle ABC be equilateral
with each side of measure ‘a’ and AC ^ BD
ð AB = BD = AD = a
ð Ða = Ðb = Ðc = 600
ð AC
= √(a2 + a/2 2)
= √3*a/2
ð Area = √3 * a2/4
ð Perimeter = 3a
ð Radius of circle
O = a/√3 = AC * 2/3
Radius of circle
O’ = √3a/6 = AC * 1/3
70) Two 
circles will touch each or
intersect each other if the distance between their centers d is such that
R – r £ d £ R + r, where R and r
are the radii of the two circles
71) Remainder of less than two
means not just one; it also means remainder of zero.
72) Do not make unwarranted
assumptions. 12 midnight to 12 noon does not mention what days, and hence you
cannot find out the time period.
73) Standard deviation of a set
is always negative and equals zero only if all elements of the set are equal.
74) If the difference between
the largest and the smallest divisor of a number is X, the number is X + 1
75) Always remember the special
watch out cases in DS questions. If the question mentions mean of a set, the
mean can be ZERO also.
76) If area of a rectangle is
known, diagonal is known, perimeter can be found
a2 + b2 = diagonal2
a2 + b2 + 2ab = diagonal2+ 2ab
(a + b)2 = diagonal2+ 2*area
77) √(y2) = |y| => y if y is
positive, -y if y is negative
78) angle
= mod [(60H - 11M) /2 ]
H = value of hour hand
M = value of minute hand
M = value of minute hand
eg, if time is 2:30, then H =2
and M =30
79) Every
number raised to power 5 has the number itself as unit digit
80) If a + b + c = Z, than the
largest of a, b, and c cannot be greater than the mean of the other two.
81) The rule that one side of a
triangle cannot be > sum of other two, only applies to sides, not angles
82) FINALLY, MAKE SURE OF WHAT
THE QUESTION SAYS – INTEGER MEANS INTEGRAL LENGTH. And, DIVIDING A WIRE INTO
PIECES, DOES NOT NECESSARILY IMPLY THAT THEY WILL BE INTEGRAL LENGTHS.
Similarly, that a boat covers a distance upstream in 3 hours, states only the
time, even if it has been mentioned that it covers a a distance 12 km
downstream in 2 hours.
83) x2 = 9*y2 does not
necessarily imply that x2 > y2. (Hint : consider x=y=0)
84) When we say multiples
between 16 and 260, and inclusive/exclusive is not mentioned, take 16 and 260
to be exclusive.
85) The statement implies :
The hourly wage for each
employee ranges from $5 an hour to $20 an hour.
minimum average = (20 + 5 + 5 +
5 + 5)/5
maximum average = (5 + 20 + 20 +
20 + 20)/5
Just mug up these notes and you
will be able to crack any MBA exam like CAT,XAT,XLRI,FMS and GMAT.
1.A number is divisible by 2, if its unit’s place digit is 0, 2, 4, or 8
2. A number is divisible by 3, if the sum of its digits is divisible by 3
3. A number is divisible by 4, if the number formed by its last two digits is divisible by 4
4. A number is divisible by 8, if the number formed by its last three digits is divisible by 8
5. A number is divisible by 9, if the sum of its digits is divisible by 9
6. A number is divisible by 11, if, starting from the RHS,
(Sum of its digits at the odd place) – (Sum of its digits at even place) is equal to 0 or 11x
7. (a + b)2 = a2 + 2ab + b2
8. (a - b)2 = a2 - 2ab + b2
9. (a + b)2 - (a - b)2 = 4ab
10. (a + b)2 + (a - b)2 = 2(a2 + b2)
11. (a2 – b2) = (a + b)(a - b)
12. (a3 + b3) = (a + b)(a2 - ab + b2)
13. (a3 – b3) = (a - b)(a2 + ab + b2)
14. Results on Division:
Dividend = Quotient × Divisor + Remainder
15. An Arithmetic Progression (A. P.) with first term ‘a’ and Common Difference ‘d’ is given
by: [a], [(a + d)], [(a + 2d)], … … …, [a + (n - 1)d]
nth term,
Tn = a + (n - 1)d
Sum of first ‘n’ terms,
Sn = n/2 (First Term + Last Term)
16. A Geometric Progression (G. P.) with first term ‘a’ and Common Ratio ‘r’ is given by:
a, ar, ar2, ar3, … … …, arn-1
nth term, Tn = arn-1
Sum of first ‘n’ terms Sn = [a(1 - rn)] / [1 - r]
17. (1 + 2 + 3 + … … … + n) = [n(n + 1)] / 2
18. (12 + 22 + 32 + … … … + n2) = [n(n + 1)(2n + 1)] / 6
19. (13 + 23 + 33 + … … … + n3) = [n2(n + 1)2] / 4
H.C.F & L.C.M of Numbers solved problems
Quantitative Apptitude Percentage Solved problemPercentage
32. To express x% as a fraction, we have x% = x / 100
33. To express a / b as a percent, we have a / b = (a / b × 100) %
34. If ‘A’ is R% more than ‘B’, then ‘B’ is less than ‘A’ by
OR
If the price of a commodity increases by R%, then the reduction in consumption, not
to increase the expenditure is
{100R / [100 + R] } %
35. If ‘A’ is R% less than ‘B’, then ‘B’ is more than ‘A’ by
OR
If the price of a commodity decreases by R%, then the increase in consumption, not to
increase the expenditure is
{100R / [100 - R] } %
36. If the population of a town is ‘P’ in a year, then its population after ‘N’ years is
P (1 + R/100)N
37. If the population of a town is ‘P’ in a year, then its population ‘N’ years ago is
P / [(1 + R/100)N]
Profit & Loss
38. If the value of a machine is ‘P’ in a year, then its value after ‘N’ years at a depreciation of
‘R’ p.c.p.a is
P (1 - R/100)N
39. If the value of a machine is ‘P’ in a year, then its value ‘N’ years ago at a depreciation of
‘R’ p.c.p.a is
P / [(1 - R/100)N]
40. Selling Price = [(100 + Gain%) × Cost Price] / 100
= [(100 - Loss%) × Cost Price] / 100
Ratio & Proportion
41. The equality of two ratios is called a proportion. If a : b = c : d, we write a : b :: c : d and
we say that a, b, c, d are in proportion.
In a proportion, the first and fourth terms are known as extremes, while the second and
third are known as means.
42. Product of extremes = Product of means
43. Mean proportion between a and b is
44. The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf)
45. a2 : b2 is a duplicate ratio of a : b
46. : is a sub-duplicate ration of a : b
47. a3 : b3 is a triplicate ratio of a : b
48. a1/3 : b1/3 is a sub-triplicate ratio of a : b
49. If a / b = c / d, then, (a + b) / b = (c + d) / d, which is called the componendo.
50. If a / b = c / d, then, (a - b) / b = (c - d) / d, which is called the dividendo.
51. If a / b = c / d, then, (a + b) / (a - b) = (c + d) / (c - d), which is called the componendo &
dividendo.
52. Variation: We say that x is directly proportional to y if x = ky for some constant k and we
write, x α y.
53. Also, we say that x is inversely proportional to y if x = k / y for some constant k and we
write x α 1 / y.
Partnership
54. If a number of partners have invested in a business and it has a profit, then
Share Of Partner = (Total_Profit × Part_Share / Total_Share)
Chain Rule
55. The cost of articles is directly proportional to the number of articles.
56. The work done is directly proportional to the number of men working at it.
57. The time (number of days) required to complete a job is inversely proportional to the
number of hours per day allocated to the job.
58. Time taken to cover a distance is inversely proportional to the speed of the car.
Time & Work
59. If A can do a piece of work in n days, then A’s 1 day’s work = 1/n.
60. If A’s 1 day’s work = 1/n, then A can finish the work in n days.
61. If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1,
Ratio of times taken by A & B to finish a work = 1 : 3
Pipes & Cisterns
62. If a pipe can fill a tank in ‘x’ hours and another pipe can empty the full tank in ‘y’ hours
(where y > x), then on opening both the pipes, the net part of the tank filled in 1 hour is
(1/x – 1/y)
Time And Distance
63. Suppose a man covers a distance at ‘x’ kmph and an equal distance at ‘y’ kmph, then
average speed during his whole journey is
[2xy / (x + y)] kmph
Trains
64. Lengths of trains are ‘x’ km and ‘y’ km, moving at ‘u’ kmph and ‘v’ kmph (where, u > v) in
the same direction, then the time taken y the over-taker train to cross the slower train is
[(x + y) / (u - v)] hrs
65. Time taken to cross each other is
[(x + y) / (u + v)] hrs
66. If two trains start at the same time from two points A and B towards each other and after
crossing they take a and b hours in reaching B and A respectively.
Then, A’s speed : B’s speed = ( : ).
67. x kmph = (x × 5/18) m/sec.
68. y metres/sec = (y × 18/5) km/hr.
Boats & Streams
69. If the speed of a boat in still water is u km/hr and the speed of the stream is v hm/hr,
then:
Speed downstream = (u + v) km/hr.
Speed upstream = (u - v) km/hr.
70. If the speed downstream is a km/hr and the speed upstream is b km/hr, then:
Speed in still water = ½ (a + b) km/hr.
Rate of stream = ½ (a - b) km/hr
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