Shortcuts to solve Aptitude questions

Hi can you please provide me the shortcuts and tricks to solve the Aptitude questions?

[Arun Vats]

Quantitative aptitude section is the most important one. Many of you guys can solve all the aptitude questions given in the paper easily.
If your speed is not fast in solving the aptitude then for you here I am providing you the Shortcuts to solve Aptitude questions.

Shortcuts to solve Quantitative Aptitude Formula

I. Arithmetic Progression.
Definition: If each term of a series differs from its preceding term by a constant, then such
a progression is called arithmetic progression.
e.g: 2,5,8,11

In the above sequence the difference between any two terms in 3.

Formula:
Consider an AP : a, (a + d), (a + 2d), (a + 3d),(a + 4d),....
1) n th term of the above sequence = Tn = a + (n - 1)d
2) Sum to n no of terms Sn = n / 2 (2a + (n - 1)d)
3) Another formula for Sn = n / 2 (first term + last term)

II. Geometric Progression.
Definition: Any progression or sequence with successive terms having a common ration is
called geometric progression.
e.g: 2,4,8,16...

In the above sequence the common ratio is 2 for any two successive terms

Formula:
Consider a GP - a, ar, ar2.... where a is the first term and r is the common ratio
4) n th term, Tn = arn-1
5) Sum to n terms, Sn = a(1 - rn)/(1-r)
6) In case r lies between -1 and +1 then Sum of all terms of the series = a/ (1 - r)

III. HCF and LCM
7) Product of two numbers = Their HCF X Their LCM

IV. Percentages

18) How to express a/b as percentage?
Ans: (a/b) x 100

19) How to express a percentage of b?
Ans: (a/100) x b

20) If the price of an item increases by A%, then the reduction in consumption so as
not to increase the expenditure is
Ans: A / (100 + A) x 100 %

21) If the price of an item decreases by A%, then the increase in consumption so as not
to decrease the expenditure is:
Ans: A / (100 - A) x 100 %

V. Profit And Loss
22) Profit = Selling Price - Cost Price
23) Loss = Cost Price - Selling Price
24) Profit Percentage = (Profit / Cost Price) x100
25) Loss Percentage = (Loss / Cost Price) x100

VI. Time And Work
26) N1 x R1 = N2 x R2 = W
Here: N = number of working men; R = rate of work done per man; D = days; W =
total work done.

VII. Boats And Streams
Let b = boat speed, s = stream speed, d = distance and t = time

27) Smooth water equation

b = d / t
28) Upstream equation
b + s = d/t
29) Downstream speed.
b - s = d/t

Hi I am preparing for the competitive exam and I am weak in Aptitude section so please provide me the tricks and shortcuts to solve aptitude questions?

[Raman Vij]

Quantitative Aptitude is a very essential paper in mainly exams. Quantitative Aptitude shortcut tricks are very important thing to know for your exams.

Competitive exams are all about time. If you know time management then everything will be easier for you.

Here I am providing you the some short cut and formulas to solve aptitude questions.

Formulas of Number Series

1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
(12 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6
(13 + 23 + 33 + ..... + n3) = (n(n + 1)/ 2)2
Sum of first n odd numbers = n2
Sum of first n even numbers = n (n + 1)

Mathematical Formulas

(a + b)(a - b) = (a2 - b2)
(a + b)2 = (a2 + b2 + 2ab)
(a - b)2 = (a2 + b2 - 2ab)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
(a3 + b3) = (a + b)(a2 - ab + b2)
(a3 - b3) = (a - b)(a2 + ab + b2)
(a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
When a + b + c = 0, then a3 + b3 + c3 = 3abc
(a + b)n = an + (nC1)an-1b + (nC2)an-2b2 + … + (nCn-1)abn-1 + bn

Shortcuts for number divisibility check

A number is divisible by 2, if its unit's digit is any of 0, 2, 4, 6, 8.
A number is divisible by 3, if the sum of its digits is divisible by 3.
A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
A number is divisible by 5, if its unit's digit is either 0 or 5.
A number is divisible by 6, if it is divisible by both 2 and 3.
A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.
A number is divisible by 9, if the sum of its digits is divisible by 9.
A number is divisible by 10, if it ends with 0.
A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.
A number is divisible by 12, if it is divisible by both 4 and 3.
A number is divisible by 14, if it is divisible by 2 as well as 7.
Two numbers are said to be co-primes if their H.C.F. is 1. To find if a number, say y is divisible by x, find m and n such that m * n = x and m and n are co-prime numbers. If y is divisible by both m and n then it is divisible by x.