## Friday, August 23, 2019

##### Answer Key Quantitative and Logical Aptitude Analytical Skills 1 – PEA305

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 φ(n)
R( Q ) = 1. Where φ (n) is Euler’s totient.
It is applicable only for co-prime numbers.
Euler’s totient
φ (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.

AVERAGE:

An average or more accurately an
arithmetic mean is, in crude terms, the sum of
n different data divided by n.
Averages of a group are defined as the ratio of
sum of all the items in the group to the
number of items in the group.
Average = (Sum of all items in the group)/
Number of items in the group
Some Important Concepts:
Average =total of data/No. of data
If the value of each item is increase by the
same value a, then the average of the group or
items will also increase by a.
If the value of each item is decreased by the
same value a, then the average of the group of
items will also decrease by a.
If the value of each item is multiplied by the
same value a, then the average of the group or
items will also get multiplied by a.
If the value of each item is multiplied by the
same value a, then the average of the group or
items will also get divided by a.
If we know only the average of the two
groups individually, we cannot find out the
average of the combined group of items.
 Average of n natural no's = (n+1)/2
 Average of even No’s = (n+1)
 Average of odd No's = n