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

Question

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

KarishmaB · Accepted Answer

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)

Bunuel · Answer

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.

BANON · Answer

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..

LalaB · Answer

the remainder is 7 when positive integer n is divided by 18  
it means that n could be 7.

7/6; remainder=1

sumit88 · Answer

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.

Ritikadhir · Answer

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?

KarishmaB · Answer

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.

Abhishek009 · Answer

Let possible value of n = 25

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

25/6 will have quotient as 4 and  remainder 1 
 
Hence answer will be (B)

adkikani · Answer

Bunuel   niks18   gmatbusters   pushpitkc   GMATPrepNow

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.

niks18 · Answer

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

altairahmad · Answer

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.

chetan2u · Answer

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

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

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

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