**Points to remember:**
1.

43/7

7
=>divisor

43
=>dividend

6
=>Quotient

1
=>Remainder

2.

Factors

42
= 7*2*3

Here
7,2 and 3 are factors of 42.

42
is a multiple of 6.

42
is a multiple of 7.

If
a, b are integers(b is not 0)and a/b is an integer.

=>
b is a factor of a.

=>a
is divisible by b.

=>a
is a multiple of b.

E.g.
Positive factors of 12 = 1,2,3,4,6,12.

E.g.
Multiples of 12 = 12,24,36,0, -12,-36.......

3.

To
find total number of factors.

180=
2^2 *3^2 *5

=>(2+1)*(2+1)*(1+1)=18

=>18*2=
36 ;to include negative factors

4.

Always
consider intensive counting unless mentioned otherwise.

5.

Never
forget to check negative numbers.

6.

Numbers
with exactly three divisors:

Squares
of prime numbers.

E.g.
=> 49,121

They
have exactly three factors : 1,7,49 & 1,11,121.

7.

Numbers
with exactly 4 divisors:

product
of two prime numbers.

E.g.=>21

They
have exactly four factors : 1,3,7,21.

8.

Zero
is neither positive nor negative.

9.

All
integers except zero are factors of zero and zero is multiple of
every integer.

10.

Divisibility
rules for:

- Last digit must be divisible by 2.
- Sum of digits must be divisible by 3.
- Number formed by last two digits must be divisible by 4.
- Last digit must be 0 or 5.
- Number must be divisible by both 2 and 3.

11.

In
the number 456.789

4
is the Hundred's digit

5
is the Ten's digit

6
is the Unit's digit

7
is the Tenth's digit

8
is the Hundredth's digit

3444.782
rounded to nearest tenth's will be 3444.8

3444.749
rounded to nearest tenth's will be 3444.7

12.

Comparison
of fractions:

By
Cross multiplication:

compare
6/11 OR 5/9

compare
6*9 OR 11*5

compare
54 OR 55

R.H.S
is greater so, 5/9 > 6/11.

**General rules for fraction comparison.**
If
numerator increases, and denominator remains same, then ratio
increases.

=>
6/21 > 3/21

If
denominator increases, and the numerator remains same, then ratio
decreases.

=>
6/21 > 6/22

If
a constant is multiplied to both numerator and denominator, then
ratio remains same.

=>
2/5 = 6/30 = 12/60

**Sample Questions:**
1.

A=
165*125*866

B=
342*154*788

Quantity
A Quantity B

unit
digit of number A unit digit of number B

Ans.B

2.

M
is a positive odd integer.

Quantity
A Quantity B

Number
of positive (N-1)/2 less
than N.

Ans.
C

3.

M
is a positive integer

Quantity
A Quantity B

Remainder
when (N^2-N) 0
is divided by
2.

Ans.
C

4.

If
a, b, c are three positive integers greater than 1 such that abc =
231, what is the value of x+y+z?

A.9

B.15

C.21

D.
24

E.Cannot
determine

Ans.
C

5.

How
many divisors of 72 have 4 in units digit?

A.0

B.1

C.2

D.5

E.4

Ans.
E

***Until
asked for positive factors only, consider both positive and negative
factors.

6.

Greatest
prime factor of 5^25+5^26+5^27

A.9

B.5

C.31

D.23

E.Cannot
determine

Ans.
C

7.

X
is an integer which leaves a remainder 5 when divided by 12.What is
the remainder when square of integer is divided by 8.

A.9

B.5

C.2

D.3

E.1

Ans.
E

8.

How
many numbers between 400 and 700, inclusive, are multiple of both 2
and 3.

A.52

B.51

C.49

D.50

E.48

Ans.
D

9.

In
the fraction 2/7, the digit in the 75

^{th}place to the right of decimal is ?
Ans.
5

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