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Learn AIR FORCE MCQs with answers [Page 11 of Department 40]
105) A six digit number is formed by repeating a three digit number; for example, 256, 256 or 678, 678 etc. Any number of this form is always exactly divisible by :
(A) 11 only
(B) 7 only
(C) 1001
(D) 13 only
Correct Answer - Option
(C)
Explanation :
The number (x y z x y z) can be written, after giving corresponding weightage of the places at which the digits occur, as 100000 x + 10000y + 1000z + 100x + 10y + z
= 100100x + 10010y + 1001z
= 1001 (100x + 10y + z)
Since 1001 is a factor, the number is divisible by 1001.
7 × 11 × 13 = 1001
As the number is divisible by 1001, it will also be divisible by all three namely, 7, 11 and 13 and not by only one of these because all three are factors of 1001.
110) A number consists of two digits. If the number formed by interchanging the digits is added to the original number, the resulting number (i.e. the sum) must be divisible by
(A) 9
(B) 11
(C) 3
(D) 5
Correct Answer - Option
(B)
Explanation :
Let the number be 10x + y
After interchanging the digits, the number obtained = 10y + x
According to the question,
Resulting number
= 10x + y + 10y + x
= 11x + 11y
= 11 (x + y) which is exactly divisible by 11.
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