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What is the unit's digit in the numerical value of (2)^{37} * (3)^{47}

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What is the unit's digit in the numerical value of (2)^{37} * (3)^{47}  [#permalink]

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New post 09 Aug 2018, 05:10
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:36) correct 36% (02:11) wrong based on 39 sessions

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What is the unit's digit in the numerical value of \((2)^{37} * (3)^{47} * (7)^{79} * (13)^{26}\)?

A. 2
B. 4
C. 6
D. 8
E. 9

Source: Experts Global

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What is the unit's digit in the numerical value of (2)^{37} * (3)^{47}  [#permalink]

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New post 09 Aug 2018, 05:27
pushpitkc wrote:
What is the unit's digit in the numerical value of \((2)^{37} * (3)^{47} * (7)^{79} * (13)^{26}\)?

A. 2
B. 4
C. 6
D. 8
E. 9

Source: Experts Global


OA:D

2,3,7 have cyclicity of 4
Unit digit of \(2^{37} =2\)
Unit digit of \(3^{47}= 7\)
Unit digit of\(7^{79} =3\)
Unit digit of \(13^{26} =9\)
Unit digit of \(2*7*3*9= 8\)
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Re: What is the unit's digit in the numerical value of (2)^{37} * (3)^{47}  [#permalink]

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New post 09 Aug 2018, 05:29
pushpitkc wrote:
What is the unit's digit in the numerical value of \((2)^{37} * (3)^{47} * (7)^{79} * (13)^{26}\)?

A. 2
B. 4
C. 6
D. 8
E. 9

Source: Experts Global


Cyclicity of 2,3, and 7 is 4
Cyclicity of 13: 3-9-7-1-3-9-7-1-3

So, unit's digit in the numerical value of \((2)^{37} * (3)^{47} * (7)^{79} * (13)^{26}\)=2*7*3*9=378

Ans. (D)
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Re: What is the unit's digit in the numerical value of (2)^{37} * (3)^{47}  [#permalink]

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New post 09 Aug 2018, 08:02
pushpitkc wrote:
What is the unit's digit in the numerical value of \((2)^{37} * (3)^{47} * (7)^{79} * (13)^{26}\)?

A. 2
B. 4
C. 6
D. 8
E. 9

Source: Experts Global


\((2)^{37} = (2)^{4*9+1}\) = Units Digit \(2\) ; As \(2^4 = 6\) and \(2^1 = 2\)

\((3)^{47} = (3)^{4*11+3}\) = Units Digit \(7\) ; As \(3^4 = 1\) and \(3^3 = 7\)

\((7)^{79} = (7)^{4*19 + 3}\) = Units Digit \(3\) ; As \(7^4 = 1\) and \(7^3 = 3\)

(13)^{26} = (13)^{4*6 +2 } = Units Digit \(9\) ; As \(3^4 = 1\) and \(3^2 = 9\)

Thus, the units digit is \(2*7*3*9 = xx8\), Answer must be (D)
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