Quantitative Aptitude Preparation Numbers

44 Pages·2015·1.54 MB·English

Quantitative Aptitude
Preparation
Numbers
Prepared by:
MS. RUPAL PATEL
Assistant Professor
CMPICA, CHARUSAT
Numbers
• Numbers – In Hindu Arabic system, we have
total 10 digits.
• Namely, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Number is a group of digits called numeral.
• Places of each digit in a numeral
5 6 1 3 0 7 0 9 0

Ten
Crores Ten Lakhs Ten Thousand Hundreds Tens Units
Crores
Lakhs Thousands
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Face value and Place Value
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Types of Numbers
Numbers Quick Description Symbol
Natural {1, 2, 3, ………….} N
Whole {0,1, 2, 3, …………} W
Integers {…..-3, -2, -1, 0, 1, 2, 3, ………} Z
Rational Q
Irrationals Not Rational
Real All Rational and Irrational R
Imaginary I
Complex C
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Even and Odd Numbers
• The integers which are divisible by 2 are
called even numbers.
• E.g. 0, 2, 4, 6, 8, ……, etc.

• The integers which are not divisible by 2
are called odd numbers.
• E.g. 1, 3, 5, 7, 9, …….., etc.
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Prime Numbers
• A counting number which has only two
factors: 1 and itself is called prime
number.
• E.g. Prime numbers between 1 and 100
• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
89, 97
• IMP: The only even prime number is 2.

Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Composite Numbers and Co-primes
• The natural numbers which are not prime are
called composite numbers.
• E.g. 4, 6, 8, 9, 10, 12, 14, 15, 16, etc.
• Two natural numbers a and b are said to be
co-prime if their HCF is 1.
• Means both a and b has no common factor.
• E.g. (2,3), (4,5), (7,9), (8,11), etc.
• IMP: 1 is neither prime nor a composite
number
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Important
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Modulus or Absolute value of a
Real Number
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa
Test of Divisibility of Numbers
Div. Rule Example (s)
2 If the last digit is an even 84, 138, 2, 1920
number or zero(0)
3 If the sum of the digits 3705
divisible by 3 3+7+0+5 = 15 is divisible by 3
4 If the last two digits 21660, 5100
divisible by 4 or it ends with 21660- since 60 is divisible by 4
‘00’ 5100- last 2 digits 00
5 If the last digit is 0 or 5 865, 1705, 25, 4270, 3300
6 If the number is divisible by 629130
both 2 and 3 last digit 0 so divisible by 2
6+2+9+1+3+0=21 is divisible by 3
8 If the last three digits 81976, 6145000
divisible by 8 or it ends with 81976- since 976 is divisible by 8
‘000’ 6145000- last 3 digits 000
Ms. Rupal Patel, Assistant Professor, CMPICA, CHARUSAT, Changa