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

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

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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
Math Expert
Joined: 02 Sep 2009
Posts: 46035
Re: PT #11 PS 3 Q 11 [#permalink]

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07 Mar 2012, 01:02
8
6
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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Re: If the remainder is 7 when positive integer n is divided by [#permalink]

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08 Mar 2012, 05:39
18
5
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 20 Feb 2012 Posts: 41 Re: If the remainder is 7 when positive integer n is divided by [#permalink] ### Show Tags 13 Mar 2012, 13:58 3 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.. Senior Manager Joined: 23 Oct 2010 Posts: 364 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: If the remainder is 7 when positive integer n is divided by [#permalink] ### Show Tags 14 Mar 2012, 02:07 3 the remainder is 7 when positive integer n is divided by 18 it means that n could be 7. 7/6; remainder=1 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Intern Joined: 31 Aug 2013 Posts: 15 Re: If the remainder is 7 when positive integer n is divided by [#permalink] ### Show Tags 17 Nov 2013, 13:06 1 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. Intern Joined: 02 Jul 2013 Posts: 1 Concentration: Human Resources, General Management GMAT Date: 08-14-2014 Re: If the remainder is 7 when positive integer n is divided by [#permalink] ### Show Tags 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? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8097 Location: Pune, India Re: If the remainder is 7 when positive integer n is divided by [#permalink] ### Show Tags 13 Jul 2014, 20:16 3 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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01 Sep 2015, 01:52
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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Re: If the remainder is 7 when positive integer n is divided by [#permalink]

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05 Sep 2016, 12:17
1
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

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

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25 Jan 2017, 07:59
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

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

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25 Jan 2017, 08:01
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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19 Feb 2017, 23:05
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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23 Sep 2017, 07:34
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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Re: If the remainder is 7 when positive integer n is divided by [#permalink]

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19 May 2018, 13:46
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.
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Re: If the remainder is 7 when positive integer n is divided by [#permalink]

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15 Jun 2018, 04:51
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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15 Jun 2018, 05:01
1
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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15 Jun 2018, 15:16
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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17 Jun 2018, 14:14
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

B
Re: If the remainder is 7 when positive integer n is divided by   [#permalink] 17 Jun 2018, 14:14
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