fskilnik wrote:sanju09 wrote:For what least value of x, both 4^(n + 1) + x and 4^(2 n) - x are divisible by 5, n is an even positive integer?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Hi sanju09,
Nice idea for a problem, and I guess gmatmachoman "got the picture" and realized that the "key" was controlling the unit´s digit of the integer powers of 4...
Just a small detail: I guess you should have put that x is (for instance) a non-negative integer in the question stem, otherwise it is not hard to see that x=-4 is also possible, and also x=-4-5=-9 , x=-14, etc...
Thank you very much fskilnik for liking the idea, yeah gmatmachoman did justice with that and he came up with a nice suggestion too. Although, we can ignore his this statement that "
4^(2 n) always end with 6 in its unit's digits provided n is an even positive integer", but we cannot ignore his suggestion to modify answers, really; let's not forget that he was feeling sleepy too.
I must confess in the end that the question should have been worded as under:
For what
least non-negative integer value of x, both 4^(n + 1) + x and 4^(2 n) - x are divisible by 5, n is an even positive integer?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Thanks
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
