When n divided by 3, the remainder is 2.

when n divided by 3, the remainder is 2.

This statement can be written as

n=3k+2 (where k is the quotient) ----1

similarly
when n is divided by 4, the remainder is 1

can be written as

n=4p+1 (here p is the quotient) ------2

from eq 1 and 2

3k+2=4p+1
or,
k=(4p-1)/3

substitute p= 1 , the result will give ----> k=1
substitute back in the equations
in both the cases we have n=5
dividing n by 12 will give remainder 5 !! so D

is there another step to find "n", as "n" should be 17, instead of 5

Is my approach correct?

3k+ 2 = n
4x+1 = n

so, 3k+2 = 4x+1
multiplying to make it 12
12k+8 = 12x+3
8-3=12x-12K
5=x-k

D

We can also just find a value for n that satisfies the conditions in the stem. Since the answer choices are numbers, any permissible value will lead to the answer.

I like to take conditions one at a time. Here are some values that have a remainder of 2 when they are divided by three (numbers that are two above a multiple of 3):

5, 8, 11, 14, 17....

Now we can look for one of these that has a remainder of 1 when divided by four (numbers that are one above a multiple of 4).

5 works. Now we just answer the question. 12 goes into zero evenly, and there are 5 left over. So the remainder when 5 is divided by 12 is 5. D is the answer.

And of course this would also work for 17 (12 goes into 12 evenly and there are 5 left over), and for 29, and 41 and any other number that satisfies the conditions.

Takeaway: If you identify an unknown in the stem that can't affect the answer (often the case when there are variables in the stem and values in the answer), plugging in a permissible value is often a good option for solving the question quickly.

Since we have to divide by 12 to get a remainder,
lets start from 13... does 13 satisfy the criteria of division by 3 and by 4 ->no
so next number which does satisfy the criteria given by 3 is 3 * (4+1) + 2 = 17,
does this satisfy the criteria of division by 4,
17 / 4 gives remainder 1. It does.
So 17 is the number to divide leading to remainder 5

case1
N=5,8,11,14,17,20

case 2
M=5,9,13,17,21

Therefore n=17

Remainder of 17/12 will be 5

D. 5 correct


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Least possible value is 5


5/3 = remainder is 2.
5/4 = remainder is 1.

No divide 5/12 , remainder is 5

Thats there in option (D), mark it as your answer ...
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when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 12

A 1
B 3
C 4
D 5
E 12

least value of n=5
5/12 leaves a remainder of 5
D

IMPORTANT: Many integer property questions can be found quickly by identifying values that satisfy the given information.

---------ASIDE------------------
When it comes to remainders, we have a nice rule that says:

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
---------ONTO THE QUESTION!-------------------------

1) When n divided by 3, the remainder is 2.
So, some possible values of n are: 2, 5, 8, 11, 14, 17, 20, . . . etc

2) When n divided by 4, the remainder is 1
So, some possible values of n are: 1, 5, 9, 13, 17, 21, . . . etc

As you can see, I listed more numbers than are necessary. We already have TWO values (n = 5, and n = 17 ) that satisfy both conditions.

What is the remainder when n is divided by 12?
If n = 5, then 5 divided by 12 equals 0 with remainder 5
So, the correct answer is D

If we had chosen a different possible value for n, the answer would be the same.
For example, if n = 17, then 17 divided by 12 equals 1 with remainder 5
So, the correct answer is still D

RELATED VIDEO FROM OUR COURSE

Since when n is divided by 3, the remainder is 2, n can be:

2, 5, 8, 11, ...

Since when n divided by 4, the remainder is 1, n can be:

1, 5, 9, 13, ...

We see that n could be 5: when 5 is divided by 12, we have 5/12 = 0 remainder 5.

Answer: D
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