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Comment on Remainder when Divided by 7
I set the equations equal to
That approach is solid!
That approach is solid!
I did not get the approach
Here's the longer version of
Here's the longer version of mtl1212's solution:
There's a nice rule that says:
If N divided by D equals Q with remainder R, then N = DQ + R
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
From the first sentence, we can write: x = 5q + 1
From the second sentence, we can write: x = 7k + 1
Since both equations are set equal to x, we can write:
5q + 1 = 7k + 1
Subtract 1 from both sides to get: 5q = 7k
Divide both sides by 5 to get: q = 7k/5
IMPORTANT: Notice that, in order for q to be an integer (which it is), 7k must be divisible by 5.
Since 7 is not divisible by 5, it MUST be the case that k is divisible by 5. Finally, if k is divisible by 5, then k/5 is an INTEGER, which means q = 7k/5 = 7(some integer)
Clearly 7(some integer) is a multiple of 7, which means q is a multiple of 7
The question asks, "What is the remainder when q is divided by 7?"
Since q is a multiple of 7, the remainder will be 0
If we give the value 10 to k
That's correct.
That's correct.
In fact, k can be ANY number that's divisible by 5 (e.g., 10, 35, 615, etc)
Cheers,
Brent
Thanks, Understood :) the
Good catch. I changed the
Good catch. I changed the last line to "Since q is a multiple of 7, the remainder will be 0"
At the very end of the video,
Think of it this way.
Think of it this way.
When we divide 17 by 5, we see that 5 divides into 17 THREE times (to make 15).
From the original 17, we have 2 left (after we subtract 15).
So, the remainder is 2.
Likewise, when we divide 1 by 5, we see that 5 divides into 1 ZERO times (to make 0).
From the original 1, we have 1 left.
So, the remainder is 1.
Alternatively, we can apply the formula for rebuilding the dividend.
It says:
If N divided by D equals Q with remainder R, then N = DQ + R
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
Likewise, since 1 divided by 5 equals 0 with remainder 1, then we can write 1 = (5)(0) + 1
Works!!
Now let's test out your answer.
You are suggesting that 1 divided by 5 equals 0 with remainder 5.
Applying the formula, then we can write: 1 = (5)(0) + 5
Doesn't work.
Does that help?
Cheers,
Brent
Brent, thank you for your
Hi Brent,
Can you give the solution of this question?
https://gre.myprepclub.com/forum/s-be-the-set-of-all-positive-integers-n-such-that-n-1760.html
Here's my solution: https:/
Here's my solution: https://gre.myprepclub.com/forum/s-be-the-set-of-all-positive-integers-n...
Cheers,
Brent
Yet again, just pick numbers
QA
QB: The remainder when 2^600 is divided by 7
For both these quantities I want to know if my approach is correct.
For QA I found the last digit is 1 and divided that by 4 so I got remainder 1
For QB I did the same approach and divided 6/7 but that gets me remainder 6. But that's not right
Unfortunately, knowing the
Unfortunately, knowing the unit's digit doesn't help us here.
For example, for QA, you determined that the unit's digit of 3^900 is 1.
However, knowing that the unit's digit is 1, doesn't help us determine the remainder when that number is divided by 4.
For example, 21 divided by 4 leaves remainder 1.
On the other hand, 31 divided by 4 leaves remainder 3.
The same applies to QB.
Unless I'm missing something basic, this question is beyond the scope of the GRE since it requires knowledge of modular arithmetic.