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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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09 Aug 2018, 06:10
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Difficulty:

45% (medium)

Question Stats:

63% (01:52) correct 38% (02:15) wrong based on 45 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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Joined: 18 Jun 2018
Posts: 263
What is the unit's digit in the numerical value of (2)^{37} * (3)^{47}  [#permalink]

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09 Aug 2018, 06:27
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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09 Aug 2018, 06:29
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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09 Aug 2018, 09:02
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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Re: What is the unit's digit in the numerical value of (2)^{37} * (3)^{47}   [#permalink] 09 Aug 2018, 09:02
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