Download The only even prime number..?

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Number System & Simplification
Composite Numbers
Prime Numbers
Odd Numbers
Numbers which are not divisible by 2
Ex: 1, 3, 5, 7, ........
Numbers divisible by one and the number
itself or numbers having only two factors.
Numbers which are divisible by 2
2
Natural Numbers (N)
11
All counting numbers
Ex: N = {1, 2, 3, ...... }
n(n + 1)
Sum of first 'n' natural numbers is ⎯⎯⎯
2
Sum of squares of first 'n' natural
C) 1642
3
13
23
5
7
17
D) 2464
19
29
37
47
43
53
0 and all natural numbers
Ex: W = { 0, 1, 2, 3, ... }
Integers (Z)
Natural numbers, zero and negative of natural numbers
Ex: I = { ......, −3, −2, −1, 0, +1, +2, +3, ...}
Rational Numbers (Q)
p
,
These are of the form of ⎯
q where q ≠ 0
1 , 2 ,
Ex: Q = ⎯ ⎯ 0, −3 etc
5 3
Irrational Numbers
Can't be written in p/q form, where q ≠ 0
⎯
√ 2, √ 5, 4 + √ 7, π etc
E) None of these
5
3 × −
4 × 3284 = 821
Sol: −
× −
(Ans: B)
6
8
5
2. Two-fifth of a number is 1312. What will be
67
73
83
79
89
Some points about prime numbers
★ All prime numbers end with 1, 3, 7 or 9
except 2 and 5
★ 2 is the only even prime number
★ '1' is neither a prime nor composite number.
It is a unitary.
★ There are 25 prime numbers upto 100 and 15
prime numbers upto 50.
Twin prime numbers
A) 3280
B) 4264
D) 2132
E) None of these
Numbers not having any common factors
Ex: 3, 5 and 8 are co primes to each other.
3. If 232 is subtracted from the
G.S.
cube of a number, the answer so
obtained is 802. What is the number?
A number is divisible by 2 if the last digit is 0 or
Even.
2758 is divisible by 2 since the last digit is 8.
A number is divisible by 3 if the sum of the digits is divisible by 3.
168 is divisible by 3 since the sum of the digits is 15 (1 + 6 + 8 = 15) is divisible by 3.
A number is divisible by 4 if the number formed
by the last two digits is divisible by 4.
7216 is divisible by 4 since 16 is divisible by
4.
A number is divisible by 5 if the last digit is either
0 or 5.
3815 is divisible by 5 since the last digit is 5.
A number is divisible by 6 if it is divisible by 2
and 3.
6198 is divisible by 6 since it is divisible by 2
AND it is divisible by 3.
A number is divisible by 8 if the number formed
by the last three digits is divisible by 8.
7152 is divisible by 8 since 152 is divisible by 8.
A number is divisible by 9 if the sum of the digits is divisible by 9.
54279 is divisible by 9 since the sum of the digits 27 (5 + 4 + 2 + 7 + 9 = 27) is divisible by 9.
A number is divisible by 10 if the last digit is 0.
8370 is divisible by 10 since the last digit is 0.
A number is divisible by 11 if the difference
between the sum of digits of the odd places and
even places is 0 or multiple of 11.
3978295783 is divisible by 11 since difference of sum of odd place digits (3 + 7 + 2 +
5 + 8 = 25) and even place digits (9 + 8 + 9
+ 7 + 3 = 36) is 11 (36 − 25 = 11)
Ex: Which of the following number is divisible by 9?
A) 37589457
B) 74655835 C) 89472519
D) 91632734
E) 83652927
Sol: Sum of the digits of the number 89472519 (8 + 9 + 4 + 7 + 2 + 5 + 1 + 9 = 45) is only
divisible by 9 hence answer is (C)
the number is written in algebraic form.
2 = −
2x
Two-fifth of a number = x × −
5
5
Double of a number = 2x,
D − Division
M − Multiplication
Thrice of a number = 3x
A − Addition
S − Subtraction
Ex: 64097 ÷ (44 × 0.25) + 3218 = ?
A) 9133
D) 67
B) 9256
E) None of these
For example Let the number be 'x'
Then
x
3 =3
Three-fourth of a number = x × −
−
4
4
O − Of
C) 9045
To solve the equations based on numbers,
B) 121
30
3x
30% of a number = ⎯ × x = −
100
10
2 of one-fourth of
40% of −
3
1
2
40
2x
a number = x × − × − × −− = −
4
3
100
30
D) 6 E) 5
Exercise - 2
Giridhar
1. 12.7 × 22.68 ÷ 2.7 = ?
A) 208.88
C) 13
C) 106.68
E) None of these
B) 135.48
D) 126.38
E) None of these
2. 7.9 × ? = 650.17
Sol: Let the number be x
x3 − 232 = 802 ⇒ x3 = 802 + 529 = 1331
∴ x = 11
4. The cost of four calculators and two stencils
is Rs.6,200. What is the cost of ten calculators and five stencils?
(RBI Assts 2012)
A) Rs.15500
B) 2 C) 9
Sol: To be divisible by 72, the number must be divisible by 8 and 9.
So, 6 should come in place of
asterisk.
(Ans: D)
Numerical Ability
D) 23
Example
B − Bracket
(Ans: D)
Ex: 3 − 5, 5 − 7, 11 − 13 etc
Divisibility Tests
V − Vinculum or Bar
2
A) 7
Test of Divisibility
In simplifying an expression the mathematical
operations are performed in the following order.
y
2. If the number 52473∗ is completely divisible
by 72, then which of the following numbers
should replace the asterisk (∗)?
The only even prime number..?
The difference between two prime numbers
is '2'
Co prime numbers
C) 1:2 D) 5:7 E) None
Sol: Let the first and second numbers be x, y
40
x × ⎯ + y = 1.2 y
100
2 × x = 1.2 y −y ⇒ 2x = 0.2 y × 5 = y
⇒−
5
x
1
∴ − =−
⇒ x : y = 1:2
(Ans: C)
C) 2312
2 × x = 1312
Sol: −
5
⇒ x = 3280
∴ 65% of 3280
65
= ⎯ × 3280 = 2132
100
A) 1331
Simplifications
Some more models
1. When 40% of first number is added to the
second number, the second number
becomes 1.2 times of itself. What is the ratio
between the first and second numbers?
A) 2:3 B) 4:3
65% of that number?
59
97
)
n(n + 1) 2
⎯⎯⎯⎯
2
Whole Numbers (W)
⎯ ⎯
31
41
61
71
n(n + 1)(2n + 1)
numbers is ⎯⎯⎯⎯⎯⎯⎯
6
Sum of cubes of first 'n' natural
(
B) 821
Prime Numbers
Ex: 2, 4, 6, 8, .......
Ex:
5 of −
3 of −
4 of
1. −
6
8
5
3284 = ?
A) 1268
Ex: 2, 3, 5, 7, 11, 13, ..... etc
Even Numbers
numbers is
Exercise -1
Numbers having more than two factors
Classification of Numbers:
1
B) Rs.14875
C) Rs.16200
D) Cannot be determined
E) None of these
Sol: Let the calculator be C and stencil be S
∴ 4C + 2S = 6200
⇒ 2C + 1S = 3100
Then 10C + 5S = 5 × 3100 = Rs.15500
(Ans: A)
★ Three consecutive odd numbers are x,
(x + 2) and (x + 4), or (x − 2), x and (x + 2),
where x is an odd number.
★ Three consecutive even numbers are x,
(x + 2) and (x + 4) or (x − 2), x and (x + 2)
where x is an even number.
A) 82.3
B) 78.6
E) None of these
C) 62.7
D) 74.3
3. 4216 ÷ 34 ÷ 8 = ?
A) 992 B) 17918 C) 496 D) 15.5 E) None
4. 65% of 654 − ? % of 860 = 210.1
(RBI Assts 2012)
A) 25
B) 15
E) None of these
C) 20
D) 30
A) 768
B) 1168
C) 73
D) 5329
E) None of these
5. 56064 ÷ ? = 48 × 16
6. 68% of 595 − 43% of 372 = ?
A) 224.34
B) 212.84
C) 278.44
D) 244.64
E) None of these
7. One-seventh of a number is 384. What will
be 42% of that number?
A) 1123.56
B) 1128.96
C) 1328.46
D) 1182.44
E) None of these
Laws of Indices
1. am × an = am+n
Ex: 74 × 73 = 7 4+3 = 77
am
2. ⎯n = am−n
a
29
Ex: = ⎯3 = 29 − 3 = 26
2
n
3. (am) = amn
m
4. (ab)
5.
= am × bm
1
a−m = ⎯
am
1
⎯a = a ⎯
m
6. m√
7. a0 = 1
2
Ex: (93) = 9 3×2
Ex: (3 × 5)2 = 32 × 52
1
1
Ex: 8−2 = ⎯
=⎯
82
64
⎯
Ex: 7√ 19 = 19
Ex: 30 = 1
Ex: 498 ÷ 75 = (7)?
(72)8
7 16
Sol: ⎯ = 7? ⇒ ⎯ = 7?
73
73
16 − 3
⇒ 7
= 7?
⇒ 7113 = 7?
∴ ? = 13
1
⎯
7
8. If (92)2 is added to the square of a number,
the answer so obtained is 10768. What is
the number?
A) 46
D) 2116
B) 2304 C) 48
E) None of these
9. The mean of three consecutive even numbers is 16. Which is the highest number?
A) 14
B) 18
C) 16
D) Can't be determined
E) None of these
⎯⎯⎯⎯
⎯⎯
10. √√ 2704 + 12 = ?2
A) 64
B) 8
D) 128
E) None of these
C) 4096
ANSWERS
1) C
2) A
3) D
4) A
5) C
6) D
7) B
8) C
9) B
10) E.
(Writer - Director, RACE Institute, Hyderabad)