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Find the remainder when 71234 is divided by 10

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Joined: 04 Jan 2015
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Find the remainder when 71234 is divided by 10  [#permalink]

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New post Updated on: 21 Nov 2018, 03:44
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

66% (00:51) correct 34% (00:55) wrong based on 62 sessions

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Interesting Applications of Remainders – Practice question 1

Find the remainder when \(7^{1234}\) is divided by 10?

    A. 1
    B. 3
    C. 4
    D. 7
    E. 9

To solve question 2: Question 2

To read the article: Interesting Applications of Remainders

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Originally posted by EgmatQuantExpert on 21 Nov 2018, 02:55.
Last edited by EgmatQuantExpert on 21 Nov 2018, 03:44, edited 3 times in total.
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Re: Find the remainder when 71234 is divided by 10  [#permalink]

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New post 21 Nov 2018, 03:24
2
Numbers 2, 3, 7 and 8 have a cyclicity of 4.
Numbers 4 and 9 have a cyclicity of 2.
Numbers 0, 1, 5 and 6 have a cyclicity of 1.


The remainder when 1234 is divided by 4 is 2.
hence \(7^{1234} = 7^2\)

So the remainder when 49 is divided by 10 is 9.

E is the answer.
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Re: Find the remainder when 71234 is divided by 10  [#permalink]

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New post 25 Nov 2018, 16:35
1

Solution



To find:
    • The remainder, when \(7^{1234}\) is divided by 10

Approach and Working:
We know that if we divide a number by 10, then the remainder is same as the units digit of the given number.
    • Hence, we need to determine the units digit of \(7^{1234}\).

As per our conceptual understanding, the units digit cycle of 7 is as follows:
    • \(7^1 = 7^5 = 7^{4k+1} = 7\)
    • \(7^2 = 7^6 = 7^{4k+2} = 9\)
    • \(7^3 = 7^7 = 7^{4k+3} = 3\)
    • \(7^4 = 7^8 = 7^{4k+4} = 1\)

As we can write \(7^{1234}\) as \(7^{4k+2}\), the unit digit of the number is 9.

Hence, the correct answer is option E.

Answer: E
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Articles and Question to reach Q51 | Question of the week

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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



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Re: Find the remainder when 71234 is divided by 10 &nbs [#permalink] 25 Nov 2018, 16:35
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