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29 May 2025, 00:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:00) correct
32%
(01:59)
wrong
based on 174
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History
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Time
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Not Attempted Yet
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!
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!
29 May 2025, 00:51
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N =10^36 - 8240
Both the terms are multiple of 4,5 and 8. So the operation will result in a number divisible by 4,5 and 8. B,C,D are out
10^36 will result in a remainder of 1 when divided by 3
8240 will result in a remainder of 2 when divided by 3
The above operation will result in a number that cannot be divisible by 3
Answer A
Both the terms are multiple of 4,5 and 8. So the operation will result in a number divisible by 4,5 and 8. B,C,D are out
10^36 will result in a remainder of 1 when divided by 3
8240 will result in a remainder of 2 when divided by 3
The above operation will result in a number that cannot be divisible by 3
Answer A
Bunuel
30 May 2025, 13:47
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Bunuel
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.
