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What is the smallest positive integer to plus

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ostrick5465
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What is the smallest positive integer to plus [#permalink] New post   28 Sep 2021, 01:15
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What is the smallest positive integer to plus to N to get a number that is divisible by 12? N is a 2014-digit positive integer that consists of 7s written next to each other.

A. 3
B. 5
C. 7
D. 11
E. 13
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Re: What is the smallest positive integer to plus [#permalink] New post   28 Sep 2021, 04:24
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ostrick5465 wrote:
What is the smallest positive integer to plus to N to get a number that is divisible by 12? N is a 2014-digit positive integer that consists of 7s written next to each other.

A. 3
B. 5
C. 7
D. 11
E. 13


Given:
(N+x)/12
what is x?
To be divisible by 12
the number should be divisible by both 3 and 4
for a number to be divisible by 3, the sum of its digits must be divisible by 3
for a number to be divisible by 4, the last two digits must be divisible by 4

About N
N is a 2014-digit positive integer that consists of 7s written next to each other
means 7777...7(2014 digits)

Consider just the last 2 digits
77
what we should add is that the last two digits are divisible by 4 and the entire number is divisible by 3

We can go by the options:
First, check the divisibility by 4
A. 3
77 + 3 =80
divisible by 4

B. 5
77 + 5 =82
not divisible by 4

C. 7
77 + 7 =84
divisible by 4

D. 11
77 + 11 =88
divisible by 4

E. 13
77 + 13 =90
not divisible by 4


Then check divisibility by 3
Note: after addition, The last two digits are changed from 77
A. 3
77 + 3 =80
7777...80(2014 digits)
(7*2012 + 8 +0) / 3
(14084 + 8+0) /3
not divisible

C. 7
77 + 7 =84
(7*2012 + 8 +4) / 3
(14084 + 8+4) /3
not divisible

D. 11
77 + 11 =88
divisible by 4
(7*2012 + 8 +8) / 3
(14084 + 8+8) /3
divisible

Answer D
GMAT Club Bot
gmatclubot
Re: What is the smallest positive integer to plus [#permalink]
28 Sep 2021, 04:24
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