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Joined: 03 Nov 2019
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While shifting his departmental store, Mr. Trump found the
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27 Nov 2019, 23:59
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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 Posted from my mobile device
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Re: While shifting his departmental store, Mr. Trump found the
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28 Nov 2019, 03:15
the question is simply asking about the remainder of \(\frac{7^{10}}{8}\)
\(7^{10}\) can be rewritten as \((81)^{10}\), 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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28 Nov 2019, 22:27
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
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28 Nov 2019, 22:59
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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Joined: 31 Aug 2019
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Re: While shifting his departmental store, Mr. Trump found the
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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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Re: While shifting his departmental store, Mr. Trump found the
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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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Re: While shifting his departmental store, Mr. Trump found the
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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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Re: While shifting his departmental store, Mr. Trump found the
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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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