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 75th place to the
right of decimal is ?
Ans.
5
My best wishes to all aspirants.Do comment if you want to know something specific about the exam.
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