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What is the units digit of (1337)^124(13)^27(9)^5?
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04 Jul 2023, 04:31
04 Jul 2023, 04:31
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Question Stats:
66% (01:18) correct
33% (01:09) wrong based on 18 sessions
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What is the unit’s digit of \((1337)^{124}(13)^{27}(9)^5\)?
A. 1
B. 3
C. 5
D. 7
E. 9
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
A. 1
B. 3
C. 5
D. 7
E. 9
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
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Re: What is the units digit of (1337)^124(13)^27(9)^5?
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04 Jul 2023, 10:13
04 Jul 2023, 10:13
3
Expert Reply
To determine the unit's digit of the given expression, we can focus on the unit's digit of each individual term and then find the unit's digit of their product.
Let's analyze the unit's digits of each term:
(1337)^124: The unit's digit of 1337 is 7. Since the unit's digit of 7 raised to any positive power follows a pattern of 7, 9, 3, 1, repeating, the unit's digit of (1337)^124 will be 1.
(13)^27: The unit's digit of 13 is 3. When 3 is raised to any positive power, the unit's digit follows a pattern of 3, 9, 7, 1, repeating. Therefore, the unit's digit of (13)^27 will be 7.
(9)^5: The unit's digit of 9 raised to any positive power is always 9.
Now, let's find the unit's digit of their product:
Unit's digit of (1337)^124(13)^27(9)^5 = (1)(7)(9) = 63.
Therefore, the unit's digit of the expression (1337)^124(13)^27(9)^5 is 3.
Answer: B
Let's analyze the unit's digits of each term:
(1337)^124: The unit's digit of 1337 is 7. Since the unit's digit of 7 raised to any positive power follows a pattern of 7, 9, 3, 1, repeating, the unit's digit of (1337)^124 will be 1.
(13)^27: The unit's digit of 13 is 3. When 3 is raised to any positive power, the unit's digit follows a pattern of 3, 9, 7, 1, repeating. Therefore, the unit's digit of (13)^27 will be 7.
(9)^5: The unit's digit of 9 raised to any positive power is always 9.
Now, let's find the unit's digit of their product:
Unit's digit of (1337)^124(13)^27(9)^5 = (1)(7)(9) = 63.
Therefore, the unit's digit of the expression (1337)^124(13)^27(9)^5 is 3.
Answer: B
gmatclubot
Re: What is the units digit of (1337)^124(13)^27(9)^5? [#permalink]
04 Jul 2023, 10:13
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