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Updated on: 06 Mar 2026, 19:35
Originally posted by MartyMurray on 05 Jan 2026, 17:56.
Last edited by MartyMurray on 06 Mar 2026, 19:35, edited 2 times in total.
Last edited by MartyMurray on 06 Mar 2026, 19:35, edited 2 times in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
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Question Stats:
72% (01:23) correct
28%
(01:37)
wrong
based on 75
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If \(n = 9! + 7 × 8!\), which of the following is the greatest possible integer \(k\) such that \(2^k\) is a factor of \(n\)?
(A) \(3\)
(B) \(4\)
(C) \(6\)
(D) \(7\)
(E) \(11\)
Source: Marty Murray Coaching
(A) \(3\)
(B) \(4\)
(C) \(6\)
(D) \(7\)
(E) \(11\)
Source: Marty Murray Coaching
Updated on: 05 Jan 2026, 19:57
Originally posted by sujoykrdatta on 05 Jan 2026, 19:12.
Last edited by sujoykrdatta on 05 Jan 2026, 19:57, edited 1 time in total.
Last edited by sujoykrdatta on 05 Jan 2026, 19:57, edited 1 time in total.
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9! + 7 × 8!
= 8! × (9+7)
= 8! × 16
Highest power of 2 in 8! is:
8/2 = 4
4/2 = 2
2/2 = 1
So 4+2+1=7
Highest power of 2 in 16 is: 4
So 7+4= 11 (D)
Edit: it is option (E)
= 8! × (9+7)
= 8! × 16
Highest power of 2 in 8! is:
8/2 = 4
4/2 = 2
2/2 = 1
So 4+2+1=7
Highest power of 2 in 16 is: 4
So 7+4= 11 (D)
Edit: it is option (E)
05 Jan 2026, 19:29
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If \(n = 9! + 7 × 8!\), which of the following is the greatest possible integer \(k\) such that \(2^k\) is a factor of \(n\)?
Factoring out 8!, we get the following:
\(n = (9 + 7) × 8!\)
\(n = 16 × 8!\)
Next, we can factor out all the \(2\)s:
\(n = 16 × (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)\)
\(n = 2^4 × (2^3 × 7 × (2 × 3) × 5 × 2^2 × 3 × 2 × 1)\)
\(n = 2^{11} × 7 × 5 × 3^2\)
So, the greatest possible value of \(k\) is \(11\).
(A) \(3\)
(B) \(4\)
(C) \(6\)
(D) \(7\)
(E) \(11\)
Correct answer: E
Factoring out 8!, we get the following:
\(n = (9 + 7) × 8!\)
\(n = 16 × 8!\)
Next, we can factor out all the \(2\)s:
\(n = 16 × (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)\)
\(n = 2^4 × (2^3 × 7 × (2 × 3) × 5 × 2^2 × 3 × 2 × 1)\)
\(n = 2^{11} × 7 × 5 × 3^2\)
So, the greatest possible value of \(k\) is \(11\).
(A) \(3\)
(B) \(4\)
(C) \(6\)
(D) \(7\)
(E) \(11\)
Correct answer: E
