Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 55)
55.
Which of the following numbers will completely divide (4915 - 1) ?
Answer: Option
Explanation:
(xn - 1) will be divisibly by (x + 1) only when n is even.
(4915 - 1) = {(72)15 - 1} = (730 - 1), which is divisible by (7 +1), i.e., 8.
Discussion:
16 comments Page 2 of 2.
Pooja said:
7 years ago
From divisibilty tricks,
1.-> (a^n-b^n) is always divisible by (a-b).
2.-> (a^n-b^n) is divisible by (a+b) when 'n' is even.
In the question,
(49^15-1), it could also be written as (49^15-1^15) as,(1^n=1) but '49' is the square of '7'. By simplifying, we have,
(7^2)^15-(1^)^15 as, 7^2=49 and 1^n=1.
= 7^30-1^30 (here n=30 is an even number).
So, by using formula 2. We have,
= 7+1,
= 8 (answer).
1.-> (a^n-b^n) is always divisible by (a-b).
2.-> (a^n-b^n) is divisible by (a+b) when 'n' is even.
In the question,
(49^15-1), it could also be written as (49^15-1^15) as,(1^n=1) but '49' is the square of '7'. By simplifying, we have,
(7^2)^15-(1^)^15 as, 7^2=49 and 1^n=1.
= 7^30-1^30 (here n=30 is an even number).
So, by using formula 2. We have,
= 7+1,
= 8 (answer).
(6)
Zaki said:
6 years ago
Why not 50?
Gayathri Thota said:
5 years ago
(x^n-1) is divisible by x-1 when n is odd
Given
(49^15-1) is divisible by 49-1 i.e 48
48 is completely divisible by 8.(Here 15 is odd right)
Can we do it in this way?
Given
(49^15-1) is divisible by 49-1 i.e 48
48 is completely divisible by 8.(Here 15 is odd right)
Can we do it in this way?
Silverstar Tariang said:
5 years ago
a^n-b^n=a-b i.e 49-1=48 which is divisible by 8.
So the answer is 8.
So the answer is 8.
Alok Niranjan said:
4 years ago
Why it's not 48? Please explain in detail.
(4)
Aadhithyan said:
3 years ago
Simpliy, find the unit digit of 49^15, which is 49^15 = 9.
Then,(9-1) = 8.
Thank you very much!
Then,(9-1) = 8.
Thank you very much!
(11)
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