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Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B)

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GMATinsight
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Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink] New post   Updated on: 25 Feb 2020, 08:04
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Question Stats:

63% (02:23) correct 37% (02:19) wrong based on 83 sessions
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Find the unit digit of

\(72^{72}*73^{73}*74^{74}*76^{76}*77^{77}*78^{78}\)

A) 2
B) 4
c) 6
D) 8
E) None of these

Source: https://www.GMATinsight.com
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B

Originally posted by GMATinsight on 23 Feb 2020, 05:11.
Last edited by GMATinsight on 25 Feb 2020, 08:04, edited 1 time in total.
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Fightingspirit
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Re: Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink] New post   23 Feb 2020, 15:16
Applying Cyclicity logic for 2,3,4,6,7 and 8.

so the unit digit is 4

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Re: Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink] New post   Updated on: 23 Feb 2020, 19:34
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Originally posted by ajaymahadev on 23 Feb 2020, 18:31.
Last edited by ajaymahadev on 23 Feb 2020, 19:34, edited 1 time in total.
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firas92
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Re: Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink] New post   23 Feb 2020, 19:12
ajaymahadev wrote:
Kudos will be highly appreciated.


Hi ajaymahadev

What do you mean by \(R(\frac{78}{4})=0\)?

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ajaymahadev
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Re: Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink] New post   23 Feb 2020, 19:35
firas92 wrote:
ajaymahadev wrote:
Kudos will be highly appreciated.


Hi ajaymahadev

What do you mean by \(R(\frac{78}{4})=0\)?

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Careless mistake from my part. Sorry. The remainder of 78/4 is 2. Edited the answer. The answer is 4.
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ajaymahadev
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Re: Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink] New post   23 Feb 2020, 19:39
The official answer is wrong. The answer is 4.

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Re: Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink] New post   25 Feb 2020, 07:55
GMATinsight wrote:
Find the unit digit of

\(72^{72}*73^{73}*74^{74}*76^{76}*77^{77}*78^{78}\)

A) 2
B) 4
c) 6
D) 8
E) None of these

Source: https://www.GMATinsight.com


\(72^{4*18}*73^{18*4+1}*74^{2*37}*76^{76}*77^{4*19+1}*78^{4*19+2}\)

72^4k = Will have units digit as 6
73^4k will have units digit 1 * 73 = Units digit 3
74^2k will have units digit as 6
76^k will have units digit as 6
77^4k will have units digit as 1 * 7 = Units digit 7
78^4k will have units digit as 6 * 4 = units 4

Multiply all 6*3*6*6*7*4 = 4 Units digit, Answer must be (B)
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Re: Find the unit digit of 72^72*73^73*74^74*76^76*77^77*78^78 A) 2 B) [#permalink]
25 Feb 2020, 07:55
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