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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
N is a positive integer which can be expressed as 57 x 10p, where p...  [#permalink]

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Updated on: 21 Nov 2018, 04:44
1
00:00

Difficulty:

5% (low)

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.
NUS School Moderator
Joined: 18 Jul 2018
Posts: 981
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: N is a positive integer which can be expressed as 57 x 10p, where p...  [#permalink]

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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.

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
N is a positive integer which can be expressed as 57 x 10p, where p...  [#permalink]

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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.

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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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