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

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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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New post 27 Nov 2019, 23:42
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D
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Question Stats:

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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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New post 28 Nov 2019, 01:38
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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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Re: What is the remainder when 7 + 10n is divided by 3, if n is a single  [#permalink]

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New post 29 Nov 2019, 12:56
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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New post 29 Nov 2019, 23:45
1
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


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Therefore, D is the answer.

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.
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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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