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

**Quantitative and Logical Aptitude**

Analytical Skills 1 – PEA305

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

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