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Bunuel
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<x> denotes the unit digit of x. For example, <123> = 3. What is <7^{1 25 Jan 2024, 02:30
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\(<x>\) denotes the unit digit of x. For example, \(<123> = 3\). What is \(<7^{19}+7^{89}>\)?

A. 0
B. 1
C. 3
D. 8
E. 9

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Bunuel
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<x> denotes the unit digit of x. For example, <123> = 3. What is <7^{1 25 Jan 2024, 04:18
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Rucha.Shukla
D?

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Nope. It's not D. Also, can you please provide complete solutions instead of single letters? Solutions benefit users, while single-letter posts are basically spam. Thank you for your cooperation!
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<x> denotes the unit digit of x. For example, <123> = 3. What is <7^{1 25 Jan 2024, 04:25
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[quote="Bunuel"][quote="Rucha.Shukla"]D?

[size=80][b][i]Posted from my mobile device[/i][/b][/size][/quote]

Nope. It's not D. Also, can you please provide complete solutions instead of single letters? Solutions benefit users, while single-letter posts are basically spam. Thank you for your cooperation![/quote]

Hi, sure. I would love to expand IF the answer is correct but if it's not it'll just be a wrong logic which many times people might confuse as right logic if they don't pay attention hence I did not expand. Sorry.
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<x> denotes the unit digit of x. For example, <123> = 3. What is <7^{1 25 Jan 2024, 04:47
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A. 0 ?

Cyclicity of 7 is 4 (7,9,3,1)

19/4 gives remainder 3 = units digit at 3rd power = 3

89/4 gives remainder 1 = units digit at 1st power= 7

7 + 3 = 1(0)

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<x> denotes the unit digit of x. For example, <123> = 3. What is <7^{1 25 Jan 2024, 05:08
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We need to find the trend when 7 is multiplied by 7 multiple times

7*7=49
7^3=343 ends with 3
7^4= ends with 1

7,9,3,1 and this pattern keeps on repeating.

So 7^19 can be re written as (7)^16+3 = (7^4)^4*7^3 which means 7^3 will define the end number =3

Same exercise we have to do for 7^89, end digit wil be 7

So total of 7+3=10

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<x> denotes the unit digit of x. For example, <123> = 3. What is <7^{1 25 Jan 2024, 22:43
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\(<x>\) denotes the unit digit of x. For example, \(<123> = 3\). What is \(<7^{19}+7^{89}>\)?

A. 0
B. 1
C. 3
D. 8
E. 9

This is a PS Butler Question


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