Quantitative and Logical Aptitude
Analytical Skills 1 – PEA305
Answer Key of Unit 1:
NUMBER SYSTEM :
Natural Numbers
The counting numbers are commonly called
natural numbers.
For example Natural Number, N = {1, 2, 3 ...}
● All natural numbers are positive.
● The smallest natural number is 1.
● Zero (0) is not a natural number.
Whole Numbers
All the natural numbers including Zero are
called Whole Numbers. It is also known as
non-negative integers.
For example Whole Numbers, W = {0, 1, 2, 3
...}.
Integers
Whole numbers as well as negative numbers
form the set of integers. It can be classified
into two types,
(i) Positive integers {1, 2, 3...}
(ii) Negative integers {– 1, – 2, – 3...}
(iii) Zero i
FACTORS or DIVISORS:
In order to find the factors of a number
Nidentify the prime factors and their
respective powers thereof and rewrite the
number where a, band c are the prime factors
and x, y and z are their respective powers as
N=a x * b y * c z
Number of factors = (x+1)(y+1)(z+1)
Remainder theorem
The basic remainder theorem formula is:
Dividend = Divisor* Quotient + Remainder
If remainder = 0, then the number is divisible
by the divisor and divisor is a factor of the
number.
For example when 8 divides 40, the
remainder is 0 and it can be said that 8 is a
factor of 40.
Cyclicity of Remainders:
Cyclicity is the property of remainders, due to
which the remainders start repeating after a
certain point.
Euler’s theorem
Euler’s theorem states that for any co prime
numbers
P and Q,
P Ï†(n)
R( Q ) = 1. Where Ï† (n) is Euler’s totient.
It is applicable only for co-prime numbers.
Euler’s totient
Ï† (n) = n x (1 - 1/P 1 ) x (1 - 1/P 2 ) x (1 -
1/P 3 ) x....
Fermat’s theorem
a p−1
Remainder of p = 1, which is Fermat’s little
theorem,where p is a prime number and a
and p are co primes.