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# When N is divided by 10 the remainder is 1 and when N is div

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Intern
Joined: 28 Jan 2011
Posts: 21
When N is divided by 10 the remainder is 1 and when N is div  [#permalink]

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06 Sep 2013, 11:44
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Difficulty:

15% (low)

Question Stats:

83% (01:28) correct 17% (01:56) wrong based on 105 sessions

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When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

(a) 4
(b) 7
(c) 11
(d) 13
(e) 17

How would you go about solving this problem?
Math Expert
Joined: 02 Sep 2009
Posts: 61283
Re: When N is divided by 10 the remainder is 1 and when N is div  [#permalink]

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06 Sep 2013, 13:48
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salsal wrote:
When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

(a) 4
(b) 7
(c) 11
(d) 13
(e) 17

How would you go about solving this problem?

When N is divided by 10 the remainder is 1 --> N = 10q + 1 --> N can be 1, 11, 21, 31, 41, ....
When N is divided by 3 the remainder is 2 --> N= 3p +2 --> N can be 2, 5, 8, 11, 14, 17, 20, 23, ...

Notice that N can be 11. Now, since we cannot have more than 1 correct answer in PS, then the remainder must be the same for any possible value of N. If N is 11, then the remainder when N is divided by 30 is 11.

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Director
Joined: 17 Dec 2012
Posts: 620
Location: India
Re: When N is divided by 10 the remainder is 1 and when N is div  [#permalink]

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06 Sep 2013, 17:07
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1
salsal wrote:
When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

(a) 4
(b) 7
(c) 11
(d) 13
(e) 17

How would you go about solving this problem?

N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.
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Srinivasan Vaidyaraman
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Re: When N is divided by 10 the remainder is 1 and when N is div  [#permalink]

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06 Jan 2020, 09:48
salsal wrote:
When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

(a) 4
(b) 7
(c) 11
(d) 13
(e) 17

How would you go about solving this problem?

$$N_{10}$$ = { 11 , 21 , ................}
$$N_3$$ = { 2 , 5 , 8 , 11...........}

Thus, $$\frac{N}{N_{30}} = \frac{11}{30}$$ Remainder will be (C) 11 , Answer
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Abhishek....

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Re: When N is divided by 10 the remainder is 1 and when N is div   [#permalink] 06 Jan 2020, 09:48
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