The sample questions for the Concepts Tested in Number Properties, Number System & Number Theory for GRE Examination are as follows:

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

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.