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Q.

Find the number by which (49)15−1 is exactly divisible by:


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a

50

b

51

c

29

d

8 

answer is D.

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Detailed Solution

We know that xn−an is exactly divisible by x−a.
We can write (49)15−1 as (49)15−115
Then, we can say (49)15−115 is exactly divisible by 49−1=48
But we do not have any option as 48.
Also, since 48 divides the given number completely, the factors of 48 will also divide the given number completely.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 24, 48.
From the given options, we can say 8 divides the given completely.
Hence, Option (4) is the correct answer.
  
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