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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
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manimgoindowndown
What is the remainder when positive integer x is divided by 3?
1) When x is divided by 6, the remainder is 2
2) When x is divided by 15, the remainder is 2



From F.S 1, we have that x = 6k+2, where k is a non-negative integer constant. Required to find x = 3p+r, where p= again a non-negative integer constant. We can see that for some value, 6k =\(3*(2k)\) = 3p. Thus, the remainder when divided by 3 will also be 2. Sufficient.

Similarly, from F.S 2 , we have that x = 15t+2. Just as above, for some integer, 15t = \(3*(5t)\) = 3p. Thus, the remainder is 2.Sufficient.

D.
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
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Bunuel
What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6, the remainder is 2 --> \(x=6q+2=3(2q)+2\) --> the remainder upon division x by 3 is 2. Sufficient.

(2) When x is divided by 15, the remainder is 2 --> \(x=15p+2=3(5p)+2\) --> the remainder upon division x by 3 is 2. Sufficient.

Answer: D.

For more on remainders check here: remainders-144665.html

Hope it helps.
Thanks even though it's my off day I'm going to run through that thread. Thanks for sorting the problems by difficulty. Your work and its contribution has been immense to my preparation Bunuel
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Re: What is the remainder when positive integer x is divided by 3? [#permalink]
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ronr34
What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6 remainder is 2
(2) When x is divided by 15, remainder is 2

I think it's D but can anyone else verify this?

What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6 remainder is 2 --> x = 6q + 2 = {multiple of 3} + 2, thus the remainder when x is divided by 3 is 2. Sufficient.

(2) When x is divided by 15, remainder is 2 --> x = 15p + 2 = {multiple of 3} + 2, thus the remainder when x is divided by 3 is 2. Sufficient.

Answer: D.

Hope it's clear.
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
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Quote:
(1) When x is divided by 6, the remainder is 2 --> x=6q+2=3(2q)+2 --> the remainder upon division x by 3 is 2. Sufficient.

(2) When x is divided by 15, the remainder is 2 --> x=15p+2=3(5p)+2 --> the remainder upon division x by 3 is 2. Sufficient.

Answer: D.

I am a little bit confused even though its just a simple problem.

My remainder formula is : x/y = x/y + r/y where R is the remainder ...

any one able to help me out ? Sorry !
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
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sauberheine1
Quote:
(1) When x is divided by 6, the remainder is 2 --> x=6q+2=3(2q)+2 --> the remainder upon division x by 3 is 2. Sufficient.

(2) When x is divided by 15, the remainder is 2 --> x=15p+2=3(5p)+2 --> the remainder upon division x by 3 is 2. Sufficient.

Answer: D.

I am a little bit confused even though its just a simple problem.

My remainder formula is : x/y = x/y + r/y where R is the remainder ...

any one able to help me out ? Sorry !

Check here: remainders-144665.html

If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).

For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since \(15 = 6*2 + 3\).

Notice that \(0\leq{r}<x\) means that remainder is a non-negative integer and always less than divisor.

This formula can also be written as \(\frac{y}{x} = q + \frac{r}{x}\).
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
EMPOWERgmatRichC niks18 chetan2u amanvermagmat gmatbusters KarishmaB

Do you have any strategy for picking numbers? I tried two random numbers when I got this Q in my mock and was lucky to get through.
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
adkikani
EMPOWERgmatRichC niks18 chetan2u amanvermagmat gmatbusters KarishmaB

Do you have any strategy for picking numbers? I tried two random numbers when I got this Q in my mock and was lucky to get through.

Hi adkikani

the algebraic approach has already been explained by Bunuel here

https://gmatclub.com/forum/what-is-the- ... l#p1192221
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
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adkikani
EMPOWERgmatRichC niks18 chetan2u amanvermagmat gmatbusters KarishmaB

Do you have any strategy for picking numbers? I tried two random numbers when I got this Q in my mock and was lucky to get through.


Number picking is not a good idea here. If you do want to use it, you need to find the repeating pattern.
Here, every number you take that satisfies either stmnt, you will get the same answer.

But say, stmnt 1 was
(1) When x is divided by 5, the remainder is 2.
So in case of 7, when you divide by 3, you will get 1.
In case of 12, when you divide by 3, you will get 0.
In case of 17, when you divide by 3, you will get 2.
In case of 22, when you divide by 3, you will get 1.
In case of 27, when you divide by 3, you will get 0.
so you see a pattern and all your cases are covered.

Much better would be to look at this from a holistic angle. Check here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... unraveled/
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
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adkikani
EMPOWERgmatRichC niks18 chetan2u amanvermagmat gmatbusters KarishmaB

Do you have any strategy for picking numbers? I tried two random numbers when I got this Q in my mock and was lucky to get through.


Number picking is not a good idea here. If you do want to use it, you need to find the repeating pattern.
Here, every number you take that satisfies either stmnt, you will get the same answer.

But say, stmnt 1 was
(1) When x is divided by 5, the remainder is 2.
So in case of 7, when you divide by 3, you will get 1.
In case of 12, when you divide by 3, you will get 0.
In case of 17, when you divide by 3, you will get 2.
In case of 22, when you divide by 3, you will get 1.
In case of 27, when you divide by 3, you will get 0.
so you see a pattern and all your cases are covered.

Much better would be to look at this from a holistic angle. Check here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... unraveled/

Hello KarishmaB, as a general rule or with practise, I don't even need to find a pattern, I would try to save as much time as possible. If the question would have been a little different suppose, I wanted remained when same number is divided by 11.

I can see when divided by 6 leaves a remainder of 2, when divided by 15 same remainder. i would just take LCM of both and add the remainder which will give me value of N.

LCM is 30 and N is 30+2. This came to me with practise. So coming back to divisibility by 3. Rem is 2 , by 7 it would be 4.

Pattern approach is important to come to understanding my approach. Kudos for explaining basics.
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
manimgoindowndown
What is the remainder when the positive integer x is divided by 3 ?

(1) When x is divided by 6, the remainder is 2.
(2) When x is divided by 15, the remainder is 2.

Asked: What is the remainder when the positive integer x is divided by 3 ?

(1) When x is divided by 6, the remainder is 2.
x= 3*2k+ 2 = 2 mod 3
SUFFICIENT

(2) When x is divided by 15, the remainder is 2.
x= 3*5k+2 = 2 mod 3
SUFFICIENT

IMO D

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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
Try calculating remainder using numbers of the given form in each statement:
Statement 1:
X = 2
2/3 => R= 2
X = 8
8/3 => R= 2
X = 14
14/3 => R= 2

Sufficient.

Statement 2:
X = 2
2/3 => R= 2
X = 17
17/3 => R= 2

Sufficient.

Hence D
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
In response to method explained by Bunuel (Any expert can answer!) - True or false - If statement two had said:

(2) When x is divided by 14, the remainder is 2.

^ This would be insufficient to answer the question: What is the remainder when the positive integer x is divided by 3, correct??
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
myhigheredmba
In response to method explained by Bunuel (Any expert can answer!) - True or false - If statement two had said:

(2) When x is divided by 14, the remainder is 2.

^ This would be insufficient to answer the question: What is the remainder when the positive integer x is divided by 3, correct??


Question: Remainder when x divided by 3?

Statement : (2) When x is divided by 14, the remainder is 2.

Firstly you are picking a composite number so it becomes tricky. I will ignore it for a moment.

2/14 works. 2/3 -> R=2

16/14 works. 16/15 -> R=1

So Not Sufficient.

myhigheredmba I don't see any reason why you should do this.?
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
Bunuel
What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6, the remainder is 2 --> \(x=6q+2=3(2q)+2\) --> the remainder upon division x by 3 is 2. Sufficient.

(2) When x is divided by 15, the remainder is 2 --> \(x=15p+2=3(5p)+2\) --> the remainder upon division x by 3 is 2. Sufficient.

Answer: D.

For more on remainders check here: https://gmatclub.com/forum/remainders-144665.html

Hope it helps.

Hi Bunuel,
I understand the reasoning, but I keep having the same reflex where I would write :
As we know that x = 6q + 2 then x / 3 = (6q + 2)/3 = 2q + 2/3
And I would assume that remainder is 2/3 where in fact it is 2.
Could you please advise me with what is wrong with that logic ?

Thank you for your help
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Re: What is the remainder when the positive integer x is divided by 3 ? [#permalink]
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chloe2m
Bunuel
What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6, the remainder is 2 --> \(x=6q+2=3(2q)+2\) --> the remainder upon division x by 3 is 2. Sufficient.

(2) When x is divided by 15, the remainder is 2 --> \(x=15p+2=3(5p)+2\) --> the remainder upon division x by 3 is 2. Sufficient.

Answer: D.

For more on remainders check here: https://gmatclub.com/forum/remainders-144665.html

Hope it helps.

Hi Bunuel,
I understand the reasoning, but I keep having the same reflex where I would write :
As we know that x = 6q + 2 then x / 3 = (6q + 2)/3 = 2q + 2/3
And I would assume that remainder is 2/3 where in fact it is 2.
Could you please advise me with what is wrong with that logic ?

Thank you for your help

Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

Thus, a remainder must be a non-negative integer; it cannot be a fraction.

6. Remainders



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