Number System - Study Mode
[#186] The remainder when 7 84 is divided by 342 is :
Correct Answer
(B) 1
Explanation
Solution: 7 84 = (7 3 ) 28 = (343) 28 Now, (x n - a n ) is divisible by (x - a) for all values of n ∴ [(343) 28 - 1] is divisible by (343 - 1) ⇒ [(343) 28 - 1] is divisible by 342 ⇒ (7 84 - 1) is divisible by 342 ⇒ On dividing 7 84 by 342, we get 1 as remainder.
[#187] The difference between the square of two consecutive odd integers is always divisible by :
Correct Answer
(D) 8
Explanation
Solution: Let the two consecutive odd integers be (2m + 1) and (2m + 3) Then, (2m + 3) 2 - (2m + 1) 2 = [(2m + 3) + (2m + 1)] [(2m + 3) - (2m + 1)] = (4m + 4) × 2 = 8m + 8 = 8(m + 1), which is always divisible by 8
[#188] The smallest number that must be added to 803642 in order to obtain a multiple of 11 is :
Correct Answer
(C) 7
Explanation
Solution: On dividing 803642 by 11, we get 4 as remainder. Required number to be added = (11 - 4) = 7
[#189] A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by :
Correct Answer
(D) Smallest 3-digit prime number
Explanation
Solution: Clearly, 2525 is not divisible by any of the numbers 7, 11 and 13 The smallest 3-digit prime number is 101 Hence (D) is true.
[#190] 12345679 × 72 is equal to -
Correct Answer
(C) 888888888
Explanation
Solution: 12345679 × 72 Shortcut method : Since 72 is factor of 9, So the answer should be divisible by 9. Now check with option by adding the digits of option and check which one is divisible by 9. Here option (c) 888888888 is divisible by 9, so this is the multiple of 12345679 × 72 Alternate 12345679 x 72 = 12345679 x (70 +2) = 12345679 x 70 + 12345679 x 2 = 864197530 + 24691358 = 888888888