Lets Start with Syllabus, list of topics in Quantitative Aptitude
Section- I Arithmetical Ability
Best Aptitude study materials here -> Aptitude questions and answers
This article about Quantitative aptitude and numerical ability to solve a question in a seconds with the help of basic mathematic formula and tricks contains 70 formulas
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
Percentage
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
114 Handy Formulae for Quantitative Aptitude Problems
Author: Sagar Sonker
Page 4 of 12
Copyright © 2006 www.sonker.com
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.
114 Handy Formulae for Quantitative Aptitude Problems
Author: Sagar Sonker
Page 5 of 12
Copyright © 2006 www.sonker.com
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.
Section- I Arithmetical Ability
Best Aptitude study materials here -> Aptitude questions and answers
- 1. Numbers
2. H.C.F. & L.C.M. of Numbers
3. Decimal Fractions
4. Simplification
5. Square Roots & Cube Roots
6. Average
7. Problems on Numbers
8. Problems on Ages
9. Surds & Indices
10. Percentage
11. Profit & Loss
12. Ratio & Proportion
13. Partnership
14. Chain Rule
15. Time & work
16. Pipes & Cistern
17. Time & Distance
18. Problems on Trains
19. Boats & Streams
20. Alligation or Mixture
21. Simple Interest
22. Compound Interest
23. Logarithms
24. Area
25. Volume & Surface Areas
26. Races & Games of Skill
27. Calendar
28. Clocks
29. Stocks & Shares
30. Permutations & Combinations
31. Probability
32. True Discount
33. Banker's Discount
34. Heights & Distances
35. Odd Man Out & Series
- 36. Tabulation
37. Bar Graphs
38. Pie Charts
39. Line Graphs
This article about Quantitative aptitude and numerical ability to solve a question in a seconds with the help of basic mathematic formula and tricks contains 70 formulas
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
Quantitative Apptitude Percentage Solved problemH.C.F & L.C.M of Numbers solved problems
Percentage
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
114 Handy Formulae for Quantitative Aptitude Problems
Author: Sagar Sonker
Page 4 of 12
Copyright © 2006 www.sonker.com
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.
114 Handy Formulae for Quantitative Aptitude Problems
Author: Sagar Sonker
Page 5 of 12
Copyright © 2006 www.sonker.com
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.
4 comments :
informative :)
For easily solving any question on work and time, one must have clear understanding of concepts. While searching google, I found this page:
http://learnapti.com/Numerical-Aptitude/Time-and-work.aspx .
I found this quite useful, so i am sharing this with all of you.
70 formulae?? its better to learn the concepts only and replace those 70 formulae
You missed 6 in your very first formula...
1.A number is divisible by 2, if its unit’s place digit is 0, 2, 4, or 8
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