Number System: Concepts and Sample Questions.

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:

2. Last digit must be divisible by 2.
3. Sum of digits must be divisible by 3.
4. Number formed by last two digits must be divisible by 4.
5. Last digit must be 0 or 5.
6. 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