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# The product (8)(888...8), where the second factor has k digits, is an

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Senior Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 280
The product (8)(888...8), where the second factor has k digits, is an  [#permalink]

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18 Mar 2019, 22:01
00:00

Difficulty:

55% (hard)

Question Stats:

57% (03:15) correct 43% (01:45) wrong based on 14 sessions

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The product (8)(888...8), where the second factor has k digits, is an integer whose digits have a sum of 1000. What is k?

(A) 901
(B) 911
(C) 919
(D) 991
(E) 999
Manager
Joined: 31 Jul 2017
Posts: 87
Location: India
Schools: Anderson '21, LBS '21
Re: The product (8)(888...8), where the second factor has k digits, is an  [#permalink]

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18 Mar 2019, 23:03
1

8*8=64----- sum of numbers = 10
8*88=704---- sum of numbers= 11
Seems like a pattern a is developing..To confirm let's do 2 more rounds..
8*888=7104----- sum =12
8*8888=71104--- sum =13

So k+9= sum of numbers
991+9 =1000

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Re: The product (8)(888...8), where the second factor has k digits, is an   [#permalink] 18 Mar 2019, 23:03
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