Solve Examples 2

9. The difference between √150  and √54 is
A) 2√6  B) 16√6   C) 9√6   D)  6√2    E) 8√6  

Ans: √150 = √150x10 = √5x5x3x2  = 5√6
       √54 = √6x9  = 3√6  
      :. √150  - √54  = 5√6 - 3√6   = 2√6 
Ans: (A) 



10. If n and P are odd numbers then which of the following must be even number?
A) NP   B) 2N+P   C) N+P   D) NP+2   E) None of these 
Ans: Let, N= 3, P=5
     :. NP= 3x5 = 15 Which is odd
        2N+ P =2x3+5=11 Which is odd
        N+P= 3+5 = 8 Which is even
        NP + 2= 3x5+2=  17 Which is odd
Ans: (C)

11. How many prime numbers are there between 45 and 72 ?
 A) 5   B) 6   C) 8   D) 7   E) Not of these 
Ans: Prime numbers are 47, 53, 59, 61, 67, 71 
Ans: (B)

12. The sum of a number and its inverse (or reciprocal ) is equal to twice the number. What is the number? 
 A) 1   B)  -1   C) 1 or-1   D) -2   E)  2
Ans: Let, the number be x. So,
       x +(1/x)= 2x
      ((x)x+1)/x = 2x= (x)x+1 = 2x(x)
Or,  x(x) = 1= x= ± 1
Ans: (C)

13. How many prime numbers are there between 56 & 100? 
A) 9   B) 8   C) 10   D) 11    E) 12

 Ans: Prime numbers are 59, 61, 67, 71, 73, 79, 83, 89, 97
       Total =  9
Ans: (A)

14. The average of four consecutive odd positive integers is  always ?
 A) an odd number
B) divisible by 4
C) an even number
D) both (B) & (C)
E) Either (B) or (C)
Ans: Let, The four odd numbers be
        2n + 1, 2n+3, 2n+5, 2n+7, Where n is a positive integer.
     :. Their average = (8n+16)/4 = 2n+4 = 2 (n+2)
2(n+2) is certainly an even number. But we cannot say conclusively that it is divisible by 4.
Ans: (C)

15. How many of the integers between 110 & 120 are prime numbers?
A) 0   B) 1   C) 2   D) 3   E) 4
Ans: first let us list all the integers between 110 & 120 which are:
111,112,113,114,115,116,117,118,119

Posted in: Number System