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N is a positive integer which can be expressed as 57 x 10p, where p...

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N is a positive integer which can be expressed as 57 x 10p, where p...  [#permalink]

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New post Updated on: 21 Nov 2018, 04:44
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A
B
C
D
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Question Stats:

87% (01:05) correct 13% (01:21) wrong based on 112 sessions

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Interesting Applications of Remainders – Practice question 3

N is a positive integer which can be expressed as 57 x \(10^p\), where p is a positive integer. What is the remainder when N is divided by 9?

    A. 0
    B. 3
    C. 4
    D. 6
    E. 7


To read the article: Interesting Applications of Remainders

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Originally posted by EgmatQuantExpert on 21 Nov 2018, 04:03.
Last edited by EgmatQuantExpert on 21 Nov 2018, 04:44, edited 1 time in total.
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Re: N is a positive integer which can be expressed as 57 x 10p, where p...  [#permalink]

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New post 21 Nov 2018, 04:34
1
\(N = 57*10^P\)

When N is divided by 9, 10^P will always give a remainder of 1.
Hence, N becomes 57*1 = 57/9 = 3.

B is the answer.
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N is a positive integer which can be expressed as 57 x 10p, where p...  [#permalink]

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New post 25 Nov 2018, 17:51

Solution



Given:
    • N= \(57* 10^p\)
    • p is a positive integer.

To find:
    • The remainder when N is divided by 9.

Approach and Working:
    • N= \(57* 10^p\)
    • \((\frac{N}{9})_R = (\frac{{57* 10^P}}{9})_R\)
    • = \((\frac{57}{9})_R * (\frac{{10^p}}{9})_R\)
    • = 3 *1=3

Hence, the correct answer is option B.

Answer: B
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N is a positive integer which can be expressed as 57 x 10p, where p...   [#permalink] 25 Nov 2018, 17:51
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