Real Numbers

Given that p is a non-negative integer, which of these gives positive integers that are multiple of 5?

• 10p and 10p+2

• 10p and 10p+3

• 10p and 10p+4

• 10p and 10p+5

Rahul has 40 cm long red and 84 cm long blue ribbon. He cuts each ribbon into pieces such that all

pieces are of equal length. What is the length of each piece?

• 4 cm as it is the LCM of 40 and 84

• 4 cm as it is the HCF of 40 and 84

• 8 cm as it is the LCM of 40 and 84

• 8 cm as it is the HCF of 40 and 84

Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All

three flash together at 8:00 am. At what time will the three bulbs flash altogether again?

• 9:00 am

• 9:12 am

• 10:00 am

• 10:12 am

Which of the following is an irrational number?

• $\frac{\sqrt{2}}{\sqrt{8}}$

• $\frac{\sqrt{3}}{3\sqrt{5}}$

• $\frac{\sqrt{5}}{\sqrt{20}}$

• $\frac{\sqrt{63}}{\sqrt{7}}$

Which of the following is NOT an irrational number?

•  $2\ \times\ \frac{1}{\sqrt{2}}$  
  

•  $\sqrt{2}\times\frac{1}{2}$  

•  $\sqrt{2}\times\frac{1}{\sqrt{3}}$  

•  $\sqrt{2}\times\frac{1}{\sqrt{2}}$  

Is 9 - √2 an irrational number?

• No, because if 9 - √2 = a/b , where a and b are integers and b ≠ 0, then √2 = (9b - a ) / b ,but √2 is an irrational number. So, 9 - √2 ≠ a/b.

• No, because if 9 - √2 = a/b , where a and b are integers and b ≠ 0, then √2 = (9b + a ) / b ,but √2 is an irrational number. So, 9 - √2 ≠ a/b.

• Yes, because if 9 - √2 = a/b , where a and b are integers and b ≠ 0, then √2 = (9b - a ) / b ,but √2 is an irrational number. So, 9 - √2 ≠ a/b.

• Yes, because if 9 - √2 = a/b , where a and b are integers and b ≠ 0, then √2 = (9b + a ) / b ,but √2 is an irrational number. So, 9 - √2 ≠ a/b.

Which of the following is equivalent to a decimal that terminates?

• 
  

  $\frac{1}{5^2\ \times\ 2^2}$
  

• $\frac{1}{2^2\ \times\ 3}$

• $\frac{1}{5^2\ \times\ 7}$

• $\frac{1}{5^2\ \times\ 11^2}$

The fractions 3/a and 7/b are equivalent to decimals that terminate. Which best describes the product of a and b?

• It is a prime number.

• It cannot be an odd number.

• It is of the form 21k, where could be multiples of 2 or 5.

• It is of the form 21k, where could be multiples of 7 or 9.