Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
101.  The sum of even numbers between 1 and 31 is: 

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

102.  If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be: 

Answer: Option C Explanation: Then number 6x2 must be divisible by 8. x = 3, as 632 is divisible 8. 
103.  2056 x 987 = ? 

Answer: Option B Explanation:

104.  On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: 

Answer: Option A Explanation: By hit and trial, we find that 47619 x 7 = 333333. 
105. 


Answer: Option B Explanation: Let the number be x. Then
Required number = 100 
106.  If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ? 

Answer: Option A Explanation: 80 = 2 x 5 x 8 Since 653xy is divisible by 2 and 5 both, so y = 0. Now, 653x is divisible by 8, so 13x should be divisible by 8. This happens when x = 6. x + y = (6 + 0) = 6. 
107.  The difference of the squares of two consecutive odd integers is divisible by which of the following integers ? 

Answer: Option D Explanation: Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then, (2n + 3)^{2}  (2n + 1)^{2} = (2n + 3 + 2n + 1) (2n + 3  2n  1) = (4n + 4) x 2 = 8(n + 1), which is divisible by 8. 
108.  What is the unit digit in (4137)^{754}? 

Answer: Option D Explanation: Unit digit in (4137)^{754} = Unit digit in {[(4137)^{4}]^{188} x (4137)^{2}} =Unit digit in { 292915317923361 x 17114769 } = (1 x 9) = 9 
109.  587 x 999 = ? 

Answer: Option A Explanation:

110.  A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is: 

Answer: Option A Explanation: 4  x z = 6 x 1 + 4 = 10  5  y 2 y = 5 x z + 3 = 5 x 10 + 3 = 53  6  z  3 x = 4 x y + 2 = 4 x 53 + 2 = 214   1  4 Hence, required number = 214. 