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Senior Manager  P
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What is the remainder when 7 + 10n is divided by 3, if n is a single  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 72% (01:38) correct 28% (01:36) wrong based on 43 sessions

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What is the remainder when 7 + 10n is divided by 3, if n is a single digit positive integer?

(1) 10n+6 is divisible by 3

(2) n+6 = 12

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Re: What is the remainder when 7 + 10n is divided by 3, if n is a single  [#permalink]

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1
n can be 1 to 9

7 + 10n becomes 17,27,37,47,57,67,77,87,97

(7 + 10n)/3
--> Remainders will be 2,0,1 (cylicity 3 )

(1) 10n+6 is divisible by 3 --> 16,26,36,46,56,66,76,86,96 --> remainder will be 0 for n=3,6,9

for these remainders is 1 Sufficient

(2) n+6 = 12
n= 12-6
n=6

Remainder will be 1.Sufficent

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GMAT 1: 780 Q51 V45 GRE 1: Q170 V167 Re: What is the remainder when 7 + 10n is divided by 3, if n is a single  [#permalink]

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lnm87 wrote:
What is the remainder when 7 + 10n is divided by 3, if n is a single digit positive integer?

(1) 10n+6 is divisible by 3

(2) n+6 = 12

Statement 1:
Since 10n + 6 is divisible by 3, 10n + 7 divided by 3 will have a remainder of 1.

Statement 2:
n can be solved, sufficient.

Ans: D
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Re: What is the remainder when 7 + 10n is divided by 3, if n is a single  [#permalink]

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lnm87 wrote:
What is the remainder when 7 + 10n is divided by 3, if n is a single digit positive integer?

(1) 10n+6 is divisible by 3

(2) n+6 = 12

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Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
10n + 6 = 3a for some integer a.
10n = 3a - 6 = 3(a-2) and 10n is divisible by 3.
Since 3 is a prime number and 10 is not multiple, n must be divisible by 3.
We can put n = 3b for some integer b.
Then 7 + 10n = 7 + 10*3b = 30b + 7 = 3(10b+2) + 1 and it has a remainder 1 when it is divided by 3.

Since condition 1) yields a unique solution, it is sufficient

Condition 2)
We have n = 6 from the condition 2) n + 6 = 12.
7+10n = 67 = 3*22 + 1 and it has a remainder 1 when it is divided by 3.

Since condition 2) yields a unique solution, it is sufficient

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________ Re: What is the remainder when 7 + 10n is divided by 3, if n is a single   [#permalink] 29 Nov 2019, 23:45
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