What is the remainder when the positive integer N is divided by 12?

1) When N is divided by 6, the remainder is 1.

2) When N is divided by 12, the remainder is greater than 5.

Statement 1: N = 6A + 1

Integer A could be 0, 1, 2, 3, 4 etc

Plugging in for A, N could then be 1, 7, 13, 19, 25 etc

Dividing N by 12 yields different values. Insufficient

Statement 2: N = 12B + Integer > 5

For B, I tested 1 and added 6, 7, 8, and 9

N could be 18, 19, 30, or 31

Dividing N by 12 yields different values. Insufficient

1&2) The only overlap in the two lists is N = 19. So the OA is C. But how can I be sure that this is the only number that works without testing many more cases?

Thanks so much

## What is the remainder when the positive integer N is divided

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In DS questions, you have to be careful to pay attention to the question that is ASKED. Here, when you combine the two Facts, N=19 is NOT the only value that 'fits' (for example, N=7 and N=31 also fit). The question does NOT ask for the value of N though - it asks for the remainder when N is divided by 12. If you TEST each of these three options, you'll find that the remainder is ALWAYS 7 (and that pattern holds true, which is why the answer is C).

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Rich

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Rich is absolutely right.

But to your question "how can I be sure?", think conceptually: every 2nd multiple of 6 is also a multiple of 12. So in the set of numbers that had a remainder of 1 when divided by 6, [1, 7, 13, 19, 25...], notice that the remainders when divided by 12 are 1, 7, 1, 7, 1... This pattern will always hold. So once we knew statement 1, the only possibilities for the remainder were 1 or 7. Statement 2 gives us enough to narrow that down.

But to your question "how can I be sure?", think conceptually: every 2nd multiple of 6 is also a multiple of 12. So in the set of numbers that had a remainder of 1 when divided by 6, [1, 7, 13, 19, 25...], notice that the remainders when divided by 12 are 1, 7, 1, 7, 1... This pattern will always hold. So once we knew statement 1, the only possibilities for the remainder were 1 or 7. Statement 2 gives us enough to narrow that down.

Ceilidh Erickson

EdM in Mind, Brain, and Education

Harvard Graduate School of Education

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Hi Poisson,

Your approach is perfect.

To identify the pattern, probably this what I would do,

First value which satisfies both the statement condition is 7,

Probably to find the next value,

First value + LCM (6, 12) = 7 + 12 = 19.

So the next value could be,

19 + LCM (6, 12) = 19 + 12 = 31.

So the values which could match both the conditions would be 7, 19, 31, 43, 55...

So all these values when you divide by 12 the remainder is 7,

Here we can pretty much get convinced that we will get only one possible remainder.

Hope this is clear.

Your approach is perfect.

To identify the pattern, probably this what I would do,

First value which satisfies both the statement condition is 7,

Probably to find the next value,

First value + LCM (6, 12) = 7 + 12 = 19.

So the next value could be,

19 + LCM (6, 12) = 19 + 12 = 31.

So the values which could match both the conditions would be 7, 19, 31, 43, 55...

So all these values when you divide by 12 the remainder is 7,

Here we can pretty much get convinced that we will get only one possible remainder.

Hope this is clear.

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We need to determine the remainder when n is divided by 12.Poisson wrote:What is the remainder when the positive integer N is divided by 12?

1) When N is divided by 6, the remainder is 1.

2) When N is divided by 12, the remainder is greater than 5.

Statement One Alone:

When n is divided by 6, the remainder is 1.

The information in statement one is not sufficient to answer the question. We see that when n = 7, 7/12 has a remainder of 7; however when n = 13, 13/12 has a remainder of 1.

Statement Two Alone:

When n is divided by 12, the remainder is greater than 5.

The information in statement two is not sufficient to answer the question, since when n is divided by 12, it can be any one of these possible remainders: 6, 7, 8, 9, 10, and 11.

Statements One and Two Together:

Using the information from statements one, we see that n can be values such as:

7, 13, 19, 25, .....

We also see that when we divide these values by 12, we get a pattern of remainders:

7/12 has a remainder of 7

13/12 has a remainder of 1

19/12 has a reminder of 7

25/12 has a remainder of 1

Since we have found a pattern, we do not have to test any further numbers. Furthermore, since statement two tells us that the remainder when N is divided by 12 is greater than 5, the only possible remainder is 7.

Answer: C

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