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

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

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New post 18 Mar 2019, 22:01
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

44% (03:49) correct 56% (01:40) wrong based on 9 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
Spoiler: OA

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

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New post 18 Mar 2019, 23:03
1
Okay... So let's start with a simple multiplication

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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