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What is the highest index of ‘2’ that can divide (10! + 11! + 12!) wit

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Sajjad1994
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What is the highest index of ‘2’ that can divide (10! + 11! + 12!) wit [#permalink] New post   28 Oct 2020, 02:14
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What is the highest index of ‘2’ that can divide \((10! + 11! + 12!)\) without leaving any remainder?

(A) 8

(B) 9

(C) 12

(D) 16

(E) 25
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C
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Sumi1010
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Re: What is the highest index of ‘2’ that can divide (10! + 11! + 12!) wit [#permalink] New post   28 Oct 2020, 02:24
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(10!+11!+12!)= 10!(1+11+ 12x11) = 10!(144).
144 = 2^4 x 3^2
Thus , highest index of 2 in 144 = 4

Now, Highest power of 2 in 10!
10/2 Qt(5)
5/2 Qt(2)
2/2 Qt(1)
Thus, sum of quotients = 5+2+1 = 8.

Total powers of '2' = 8+4 = 12

Correct ans: C
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Re: What is the highest index of ‘2’ that can divide (10! + 11! + 12!) wit [#permalink] New post   28 Oct 2020, 08:48
Expert Reply
What is the source? You will certainly never see a question that asks you for the "index" of a divisor in a larger number -- that is advanced math terminology the GMAT does not expect test takers to know.

Sumi1010's solution is perfect, so I won't post the same thing all over again. :)
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Re: What is the highest index of ‘2’ that can divide (10! + 11! + 12!) wit [#permalink] New post   28 Oct 2020, 09:15
Asked: What is the highest index of ‘2’ that can divide \((10! + 11! + 12!)\) without leaving any remainder?

10! + 11! + 12! = 10! (1+11+132) = 10! *144 = 2^4*3^2*10!

Highest power of 2 that can divide 10! = 5 +2 + 1 = 8

Highest power of 2 that can divide 10! + 11! + 12! = 8+4 = 12

IMO C
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Re: What is the highest index of 2 that can divide (10! + 11! + 12!) wit [#permalink] New post   03 Aug 2023, 23:04
Index Means DIVISOR

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Re: What is the highest index of 2 that can divide (10! + 11! + 12!) wit [#permalink]
03 Aug 2023, 23:04
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