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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] New post 06 Mar 2012, 22:28
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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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Re: PT #11 PS 3 Q 11 [#permalink] New post 07 Mar 2012, 00:02
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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 08 Mar 2012, 04:39
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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:
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] New post 13 Mar 2012, 12:58
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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, 01:07
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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 30 Sep 2013, 06:19
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Re: If the remainder is 7 when positive integer n is divided by [#permalink] New post 17 Nov 2013, 12:06
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, 03:06
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, 19:16
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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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Re: If the remainder is 7 when positive integer n is divided by   [#permalink] 13 Jul 2014, 19:16
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