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Manager  Joined: 31 Oct 2011
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If the remainder is 7 when positive integer n is divided by  [#permalink]

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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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Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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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:
http://www.veritasprep.com/blog/2011/04 ... unraveled/

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)
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Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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1
4
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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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.

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GMAT 1: 690 Q47 V38 Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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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]

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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]

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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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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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Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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BANON wrote:
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..

If numerator is smaller than Denominator then the numerator could be a remainder also...example 7/18(here 7 is remainder),6/15(here 6 is remainder)
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If the remainder is 7 when positive integer n is divided by  [#permalink]

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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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GMAT 1: 540 Q38 V26 Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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Abhishek009 wrote:
eybrj2 wrote:
If the remainder is 7 when positive integer n is divided by 18

Least 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)

Thank you so much - why didn't I think earlier of simply Plugging-in?! :/
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GMAT 1: 540 Q38 V26 Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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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?

n=36x+23
n=72y+r2

In how far is this question (despite different numbers) different from the stated example?
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Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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I think easiest way to tackle this question is to find least possible value of n which 25 for 18 to get remainder 7 then check 25/6 remainder will be 1
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Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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Hi,

I solved this in equation form, not sure if this is the right approach but it helped me.

n= 18q +7 --> n = 6(3q) +7

n = 6q1 + r

6(3q) +7 = 6q1 +r

6(3q-q1) = r - 7

LHS(Multiple of 6) = RHS(has to be multiple of 6)

only the value which satisfies this is r= 1.
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GMAT 1: 710 Q49 V38 Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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It says the remainder is 7

we know by divisibility that if x is divided by y with remainder z then the equation will be x= ky +z where k is an integer. taking k as zero

ie- if we divide 7/18 the remainder will be 7 and the value of k will be zero. so 7 is a number which will give the remainder of 7 when divided by 18.

if we change values of k we will get more such numbers such as (18+7), (2*18 +7)...

so if we divide 7/6 the remainder is 1 ... it will be valid for other numbers as well.
so the answer is r=1
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Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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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]

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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.

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]

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n = 18a + 7
n/6 = 3a + 7/6
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Re: If the remainder is 7 when positive integer n is divided by  [#permalink]

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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 the question is asked such way, it means that any number satisfying to condition "If the remainder is 7 when positive integer n is divided by 18"
will be good for checking.
25:18 - remainder will be 7
25:6 - remainder will be 1

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