Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
81.  The difference of the squares of two consecutive even integers is divisible by which of the following integers ? 

Answer: Option B Explanation: Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^{2} = (2n + 2 + 2n)(2n + 2  2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. 
82.  Which one of the following is a prime number ? 

Answer: Option E Explanation: 551 > 22 All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23. 119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19. So, none of the given numbers is prime. 
83.  The sum all even natural numbers between 1 and 31 is: 

Answer: Option C Explanation: Required sum = (2 + 4 + 6 + ... + 30) This is an A.P. in which a = 2, d = (4  2) = 2 and l = 30. Let the number of terms be n. Then, t_{n} = 30 a + (n  1)d = 30 2 + (n  1) x 2 = 30 n  1 = 14 n = 15

84.  The difference between the place value and the face value of 6 in the numeral 856973 is 

Answer: Option C Explanation:
(Place value of 6)  (Face value of 6) = (6000  6) = 5994

85.  If a and b are odd numbers, then which of the following is even ? 

Answer: Option A Explanation:
The sum of two odd number is even. So, a + b is even.

86.  Which one of the following numbers is completely divisible by 99? 

Answer: Option D Explanation: 99 = 11 x 9, where 11 and 9 are coprime. By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99. 
87.  The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ? 

Answer: Option B Explanation: This is an A.P. in which a = 6, d = 6 and S_{n} = 1800
3n (n + 1) = 1800 n(n + 1) = 600 n^{2} + n  600 = 0 n^{2} + 25n  24n  600 = 0 n(n + 25)  24(n + 25) = 0 (n + 25)(n  24) = 0 n = 24 Number of terms = 24. 
88.  (51+ 52 + 53 + ... + 100) = ? 

Answer: Option D Explanation: This is an A.P. in which a = 51, l = 100 and n = 50.

89.  1904 x 1904 = ? 

Answer: Option C Explanation:

90.  What is the unit digit in(7^{95}  3^{58})? 

Answer: Option B Explanation: Unit digit in 7^{95} = Unit digit in [(7^{4})^{23} x 7^{3}]
Unit digit in 3^{58} = Unit digit in [(3^{4})^{14} x 3^{2}]
Unit digit in (7^{95}  3^{58}) = Unit digit in (343  9) = Unit digit in (334) = 4. So, Option B is the answer. 