divisibilty question

[manisha]

Hello FRiends,

I am solving question and answers of divisibility....
where i stop on this question.

Que==> when n is divided by 4, the remainder is 3. what is the remainder when 2n is divided by 4 ?

where i did the following work

Let n = 4q + 3.

Then 2n = 8q + 6
= 4(2q + 1 ) + 2

but here i am facing the problem , i am not able to get the answer ..

please explain me in detail, so that i could get

please write all the
....

Thanks ........
and 2 quest ion


A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is

Let x = 6q + 3.
Then, x² = (6q + 3)^{2
in the book they given = 36q2 + 36q + 9 as the next step but i dident understood how did they got this, which basic formula they used
please explain in detail......}

 

[wjm11]

Hello FRiends,

I am solving question and answers of divisibility....
where i stop on this question.

Que==> when n is divided by 4, the remainder is 3. what is the remainder when 2n is divided by 4 ?

where i did the following work

Let n = 4q + 3.

Then 2n = 8q + 6
= 4(2q + 1 ) + 2

but here i am facing the problem , i am not able to get the answer ..

please explain me in detail, so that i could get

please write all the steps....

Thanks ........

You have already solved your problem! Let's look at your work: "Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2 ".

We already know that "4(2q + 1)" is divisible by 4. Only the "+2" on the end is not divisible by 4. That is your remainder.

edit reason: correction

 

[mmm4444bot]

Hi manisha:

You edited your original post, after wmj11 replied.

Are the changes to your post a response to wjm11's reply?

When people change a post after someone has replied, most people will not notice the edits (nor even look for them because it's generally a waste of time for readers to try guess at what may have changed).

Once somebody has replied to a post, it is better to spell-out any changes or additions by adding a new post to the thread, instead. (You may even quote yourself, if that's handy.)

Cheers :cool:

 

[wjm11]

Manisha, when you edited, you posted a new problem. You should post new problems in a new thread. Otherwise, most tutors will not see the new problem.

A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is

Let x = 6q + 3.
Then, x² = (6q + 3)^{2
in the book they given = 36q2 + 36q + 9 as the next step but i dident understood how did they got this, which basic formula they used}

This is simply an expansion: x² = (6q + 3)² = (6q +3)(6q + 3) = 36q² + 18q + 18q + 9 = 36q² + 36q + 9.

 

[srmichael]

Hello FRiends,

I am solving question and answers of divisibility....
where i stop on this question.

Que==> when n is divided by 4, the remainder is 3. what is the remainder when 2n is divided by 4 ?

where i did the following work

Let n = 4q + 3.

Then 2n = 8q + 6
= 4(2q + 1 ) + 2

but here i am facing the problem , i am not able to get the answer ..

please explain me in detail, so that i could get

please write all the
....

Thanks ........
and 2 quest ion


A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is

Let x = 6q + 3.
Then, x² = (6q + 3)^{2
in the book they given = 36q2 + 36q + 9 as the next step but i dident understood how did they got this, which basic formula they used
please explain in detail......}

Your first question is a classic question asked on the SAT. Another way to approach this is to let n = 7 (divisor + remainder). Then 2n = 14. Thus 14/4 = 3 remainder 2. So your answer will be 2 for ANY n.

 

[soroban]

Hello, manisha!

A number divided by 6 leaves a remainder of 3.
When the square of the number is divided by 6, the remainder is __?

Let \(\displaystyle n\) = the number.

We are told that: .\(\displaystyle n \:=\:6q + 3\) for some integer \(\displaystyle q\)

Square the equation: .\(\displaystyle n^2 \:=\: (6q+3)^2\)

. . . . . . . . . . . . . . . . \(\displaystyle n^2 \:=\:36q^2 + 36q + 9\)

Divide by 6: .\(\displaystyle \dfrac{n^2}{6} \:=\:\dfrac{36q^2+36q+9}{6}\)

. . . . . . . . . .\(\displaystyle \dfrac{n^2}{6} \:=\:\dfrac{36q^2}{6} + \dfrac{36q}{6} + \dfrac{9}{6}\)

. . . . . . . . . .\(\displaystyle \dfrac{n^2}{6} \:=\:6q^2 + 6q + 1 + \dfrac{\color{red}{3}}{6}\)


Therefore, the remainder is \(\displaystyle 3.\)