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If the remainder is 7 when positive integer n is divided by

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eybrj2
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If the remainder is 7 when positive integer n is divided by [#permalink] New post   06 Mar 2012, 23:28
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If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4
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B
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KarishmaB
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If the remainder is 7 when positive integer n is divided by [#permalink] New post   Updated on: 21 Dec 2023, 07:39
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eybrj2 wrote:
If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


Answer in less than 10 secs once you understand the theory of divisibility and remainders. Check out the theory on this link and then read the explanation given below:
https://youtu.be/A5abKfUBFSc
https://anaprep.com/number-properties-b ... isibility/

When you divide by 6, you further divide the groups of 18 in 3 groups. The last group of 7 will form another group of 6 and you will have 1 leftover. Answer should be (B)

Originally posted by KarishmaB on 08 Mar 2012, 05:39.
Last edited by KarishmaB on 21 Dec 2023, 07:39, edited 1 time in total.
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Re: PT #11 PS 3 Q 11 [#permalink] New post   07 Mar 2012, 01:02
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eybrj2 wrote:
If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


When positive integer n is dived by 18 the remainder is 7: \(n=18q+7=(18q+6)+1=6(3q+1)+1\) --> since first term \(6(3q+1)\) is divisible by 6 then the remainder will only be from the second term 1 --> 1 divided by 6 yields remainder of 1.

Answer: B.
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   13 Mar 2012, 13:58
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B) by taking numbers we can solve this easily

multiples of 18 are 18,36,54....etc

so to get a remainder of 7 we add 7 to multiples so the integer may be 25,43,61..etc

so if we divide these numbers with 6.. remainder is 1..
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   14 Mar 2012, 02:07
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the remainder is 7 when positive integer n is divided by 18
it means that n could be 7.

7/6; remainder=1
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   17 Nov 2013, 13:06
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If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4

According to the question,
Assume x is quotient here,

n=18x+7 ----------(1)
and n=16x+ ?

We can also write equation (1) as:
n=(18x+6)+1.

ie 6(3x+1)+1 ie the first term is perfectly divisible by 6.
So,the remainder left is 1.
So,answer (B) is right choice.
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   13 Jul 2014, 04:06
what if the question is reversed, example if 23 is the remainder when n is divided by 36, what is the remainder when n is divided by 72?
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   13 Jul 2014, 20:16
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Ritikadhir wrote:
what if the question is reversed, example if 23 is the remainder when n is divided by 36, what is the remainder when n is divided by 72?


When you divide n by 36, you have groups of 36 balls each and 23 balls leftover. If you want to divide by 72 now, you will join two groups of 36 to make groups of 72. You don't know whether you have even number of groups or odd number of groups of 36.
If the number of groups of 36 is even (quotient is even), you will be able to pair them all up to make groups of 72 such that remainder is 23 only.
If the number of groups of 36 is odd (quotient is odd), you will not be able to pair them all up. One group will be leftover and the remainder will be 36+23 = 59.
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If the remainder is 7 when positive integer n is divided by [#permalink] New post   05 Sep 2016, 12:17
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eybrj2 wrote:
If the remainder is 7 when positive integer n is divided by 18


Let possible value of n = 25

Check 25/18 will have quotient as 1and remainder 7

eybrj2 wrote:
what is the remainder when n is divided by 6?


25/6 will have quotient as 4 and remainder 1

Hence answer will be (B)
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   15 Jun 2018, 04:51
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Bunuel niks18 gmatbusters pushpitkc GMATPrepNow

Quote:
If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?


I understood approach by Abhishek009 but if I want to use alternate basic approach of rebuilding the dividend,
why am I faltering:

D: dividend
d: divisor
r: remainder
q: integer quotient

D = (q)*d + r
n = 18q + 7 . . .(1)

Question: r = ? n = 6.

I ended up with far too many variables in the approach.
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   15 Jun 2018, 05:01
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adkikani wrote:
Bunuel niks18 gmatbusters pushpitkc GMATPrepNow

Quote:
If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?


I understood approach by Abhishek009 but if I want to use alternate basic approach of rebuilding the dividend,
why am I faltering:

D: dividend
d: divisor
r: remainder
q: integer quotient

D = (q)*d + r
n = 18q + 7 . . .(1)

Question: r = ? n = 6.

I ended up with far too many variables in the approach.


Hi adkikani,

you did everything right there but you stopped before the finish line.

\(n=18q+7=18q+6+1=6(3q+1)+1\)

so, \(\frac{n}{6}=\frac{6(3q+1)}{6}+\frac{1}{6}\). Clearly the remainder here is 1
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   19 Dec 2020, 14:26
niks18 wrote:
adkikani wrote:
Bunuel niks18 gmatbusters pushpitkc GMATPrepNow

Quote:
If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?


I understood approach by Abhishek009 but if I want to use alternate basic approach of rebuilding the dividend,
why am I faltering:

D: dividend
d: divisor
r: remainder
q: integer quotient

D = (q)*d + r
n = 18q + 7 . . .(1)

Question: r = ? n = 6.

I ended up with far too many variables in the approach.


Hi adkikani,

you did everything right there but you stopped before the finish line.

\(n=18q+7=18q+6+1=6(3q+1)+1\)

so, \(\frac{n}{6}=\frac{6(3q+1)}{6}+\frac{1}{6}\). Clearly the remainder here is 1


chetansharma VeritasKarishma generis

Why are we grouping together multiples of 6 ? I mean 18q is the Divisor X Quotient so what does adding 6 to it mean ? I am trying to understand what this means/signifies.
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   19 Dec 2020, 19:28
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altairahmad wrote:
Why are we grouping together multiples of 6 ? I mean 18q is the Divisor X Quotient so what does adding 6 to it mean ? I am trying to understand what this means/signifies.


Hi

We are looking for remainder when divided by 6, so we got get all in terms of multiple of 6 as anything outside it will be a remainder.
Logically anything divisible by 18 has to be divisible by its factors , so by 6 also.
The remainder when divided by 18 is 7, but 7 is larger than 6. => 7=6+1
Hence 1 is the remainder
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post   31 Aug 2022, 01:50
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The remainder is 7 when positive integer n is divided by 18

Theory: Dividend = Divisor*Quotient + Remainder

n -> Dividend
18 -> Divisor
a -> Quotient (Assume)
7 -> Remainders
=> n = 18*a +7 = 18a+7 ...(1)

What is the remainder when n is divided by 6.

n = 18a + 7 (from 1)
=> n = 6*3a + 6 + 1
=> n = 6*(3a+1) + 1
=> n when divided by 6 gives 3a+1 as quotient and 1 as remainder

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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