Numbers Basics 1/1

1.  If x is even, y is odd, then which of the following are false?
a.  $x(x + y)$ is even
b.  ${x^n} \times {y^n}$ is even
c.  $3x + 5y$ is odd
d.  $\left( {{x^2} + x - 1} \right)\left( {{y^2} + y - 1} \right)$ is even

2.  Let $x,y$ are even numbers and $z$ is an odd number. Then which of the following is false?
a.  ${\left( {x - z} \right)^2}$ is odd number
b.  $\left( {x - y} \right)z$ is even number
c.  $\left( {z - x} \right){y^2}$ is even number
d.  ${\left( {x - y} \right)^2} + z$ is even number

3.  Which of the following is a prime number?
a.  221
b.  323
c.  629
d.  727

4.  Let $x$ be prime and $y$ be composite. Then
a.  $xy$ is always even
b.  $y - x$ is never even
c.  $\dfrac{{x + y}}{x}$ is never even
d.  None of the above

5.  Prime factorization of 12600 is
a.  ${2^3} \times {3^2} \times {5^2} \times 7$
b.  ${2^2} \times {3^2} \times {5^2} \times 7$
c.  ${2^2} \times {3^2} \times {5^3} \times 7$
d.  ${2^1} \times {3^1} \times {5^2} \times 7$

6.  What least number must be subtracted from 12702 to get number exactly 99 ?
a.  49
b.  30
c.  29
d.  31