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While shifting his departmental store, Mr. Trump found the

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While shifting his departmental store, Mr. Trump found the  [#permalink]

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New post 27 Nov 2019, 23:59
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Question Stats:

79% (02:01) correct 21% (01:51) wrong based on 34 sessions

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While shifting his departmental store, Mr. Trump found the number of articles in his store to be 7^10. He had 8 rooms each of equal capacity to store these articles. If at the end he was left with n articles for which he had no space, which of the following could the minimum possible value of n?
A) 0
B) 1
C) 2
D) 3
E) 4

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Re: While shifting his departmental store, Mr. Trump found the  [#permalink]

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New post 28 Nov 2019, 03:15
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the question is simply asking about the remainder of \(\frac{7^{10}}{8}\)

\(7^{10}\) can be rewritten as \((8-1)^{10}\), which can be simplified to \((-1)^{10}\) , which is equal to 1 --> B

(as I know: source of question is Jamboree)
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New post 28 Nov 2019, 22:27
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last digit of 7^10 will be 9
and as per question
8*x=n = 7^10
the nearest values of n can be 1
hence B
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Re: While shifting his departmental store, Mr. Trump found the  [#permalink]

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New post 28 Nov 2019, 22:59
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This question tests our knowledge about recognizing pattern. 7^1/8 gives us a remainder of 7, 7^2/8 gives us a remainder of 1, and so on we get a pattern of 7 1 7 1. for every even digit of the exponent we get a 1, hence the minimum value should be 1
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New post 01 Dec 2019, 03:46
You can think of this logically rather than mathematically:
if you have 7^10 articles and they need to be divided equally in 8 rooms.... you can think as 7^8 articles were equally divided in 8 rooms. The remaining 7^2 i.e. 49 still remain... with a remainder of 1, 48 (6*8= 48) articles can still be divided equally among the 8 rooms . Hence B
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New post 01 Dec 2019, 11:24
Solved it with divisibility, cycle of 7 is:

7
49
343
2401

Possible Remainders when divided by 8 are either 7 or 1, as 1 is the only answer choice available -> 1
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New post 01 Dec 2019, 18:22
The question is what is the remainder when 7^10 is divided by 8.

7^1 is 7 and 7/8 leaves a remainder of 7.
7^2 is 49 and 49/8 leaves a remainder of 1
7^3 is 343 and 343/8 leaves a remainder of 7

continuing so on.... when 7 is raised to an even number and divided by 8; the remainder is 1 and when 7 is raised to an odd number and divided by 8 the remainder is 7. Hence the correct answer is the remainder of 1 as 7 is raised to power 10.

The correct answer is option B
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New post 04 Dec 2019, 04:51
use the cyclicity of 7 :
(7,9,3,1)

7^1 = 7
7^2 = 49
7^3 = 693
7^1 = 4851
i.e. take the last digits until the cycle repeats again with starting number.

Now we have 8 rooms so start counting from the cyclicity in (7,9,3,1) till 8 (startover the counting from begining) and we will have the answer 1 which is the remainder.
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Re: While shifting his departmental store, Mr. Trump found the   [#permalink] 04 Dec 2019, 04:51
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