Bunuel
If N =10^36 - 8240, which of the following CANNOT be a factor of N?
A. 3
B. 4
C. 5
D. 8
E. 11
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation! Alternate way:Test a smaller number say \((10)^5\)
\((10)^5 -8240 = 91760\), we can rule out \(4, 5\) and \(8\)
As we increase the power of \((10)^5\) the # of \(9\)'s to the left of \(91760\) increases, this operation doesn't effect the factor status of \(4, 5\) and \(8.\)
(Factor status of \(4, 5\) and \(8\) are dependent on last two digits, last digit etc.)
Raising the power to \(6\),we see that \( 991760\) is divisible by \(11\) and not by \(3.\)
We can infer that even # of \(9'\)s will make \(11\) a factor.
Even \(9'\)s implies \(10\) raised to even. Thus \((10)^{36} - 8240 \) has \(11\) as a factor.
Ans A
Hope it helped.