Hello, I joined GregMat+ today, I’m following the 2 Month plan.

I Completed the videos under day 1, but under things to do. I started solving Manhattan 5-lb chapter Divisibility and Primes.

I’m having a doubt regarding **Chapter 13, Q. 12.**, I referred to the solutions too. but In solutions, they mentioned, “*When dealing with remainder questions on the GRE, the best thing to do is test a few real numbers:*”

I would like to know if there is any other alternative / direct approach to solve this question?.

Also, I’m having 1 more naive question: what is the remainder of 10/6?

if it is 4? then my question is **why shouldn’t we 1st simplify it 1st and convert it to 5/3 and find remainder?** which results in ans as 2.

Pls refer Screenshot of Question below:

Can anyone help me here. Thanks.

Can you post the question image here?

This is because 10/6 means that you have to divide 10 with 6, and not divide 5 with 3

@zetakill Thanks for looking into my post. I have edited the post and attached the screenshot of the question.

Yeah, I do get it that 10/6 means we divide 10 into 6 parts. But I’m little stuck here. You do accept that 10/6 = 5/3, right? Then why shouldn’t we 1st simplify the fraction 10/6 and then find the remainder, which makes the calculations ease?

I mean to say that isn’t it recommended to simplify the fraction before we perform any calculations/comparison?

Thanks, I’m looking forward to your response.

You can directly select option b because of the fact that the remainder is an even number. You will always have 3 sitting in the denominator.

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@chitralpatil if you don’t mind could you please elaborate more? May be with an example or so?

Thanks.

You Can not fraction out further while finding remainder. It will always give you wrong answer.

remainder of 10/6 and remainder of 5/3 are two very different questions.

Thanks @shuchibshah27, Yeah I do get it that, if we fraction out before finding remainder we end up with wrong answers. But I’m specifically looking for answer **why.** I’m unable to reason out why is this behavior is seen while finding remainders.

According to my understanding if you see it in this way,

10/6 means , divide 1 pizza into 10 parts and take 6 of it. so you will have 4 pieces remained.

5/3 means divide 1 pizza into 5 parts and take 3 of it, you will have 2 pieces remained.

now these 4 pieces covers the same amount of pizza which 2 pieces covers. But still number pieces are different. I guess that is the reason you get different remainders every time.

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I guess @shuchibshah27 summed it up perfectly!

Another analogy would be like:

If you have 10 chocolates and gave 6 of them to @gregmat, you would be having 4 left right?

But if you had 5 chocolates and gave 3 of them to @gregmat, you’ll be left with 2 only. (Plus Greg won’t be too happy hahah)

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Thanks, @chitralpatil,

Sorry for the naive questions, Pls enlighten me here, I didn’t get the 3rd point. why did we choose 3? Even 4 is not divisible by 3, 11, 17 right. Then why we choose option B?

Thanks, @shuchibshah27 and @zetakill for the detailed explanation.

So from my understanding, can I put it like this: 10/6 is similar to 5/3 but not equal in quantity. So remainder 4 when we divide 10 over 6 is similar to remainder 2 when we divide 5 over 3. but the quantity/amount is different.

Pls, correct me if I’m wrong.

@zetakill, Also, could you pls make me understand the 1st part of my question? CH 13 Q12

Thanks

Make use of the formula (dividend/divisor) = quotient + (remainder/divisor)

Prime factorize the divisor and compare it with the prime factorization of the term in the remainder section.

If you see a number in the divisor which doesn’t divide the remainder (it’s prime factorized terms) then you can confidently conclude that the number is not divisible by that number.

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