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# What is the units digit of (16^8)(44^x)(37^5)?

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Intern
Joined: 07 Jun 2018
Posts: 16
What is the units digit of (16^8)(44^x)(37^5)?  [#permalink]

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25 Oct 2018, 11:51
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Difficulty:

35% (medium)

Question Stats:

60% (01:05) correct 40% (01:01) wrong based on 47 sessions

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What is the units digit of $$(16^{8})(44^{x})(37^{5})$$?

(1) x=2y where y is a positive integer.
(2) y=2
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Re: What is the units digit of (16^8)(44^x)(37^5)?  [#permalink]

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25 Oct 2018, 11:58
The query is basically banks on cyclicity 4.
Cyclicity of 4 is 2. for all even cycles the value is 6 and for all odds the value is 4.

(1) sufficient ...... as by defn x is even
(2) not-sufficient ...... no info for x.
Ans A.
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Re: What is the units digit of (16^8)(44^x)(37^5)?  [#permalink]

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25 Oct 2018, 14:45
Jazzmin wrote:
What is the units digit of $$(16^{8})(44^{x})(37^{5})$$?

(1) x=2y where y is a positive integer.
(2) y=2

6 to any positive integer power will have a units digit of 6

5 to any positive integer power will have a units digit of 5.

4 has cycles of 4,6,4,6

Regardles so of the value of y we know the power will be even meaning it is a unit of 6.

Statement 2) is not in any means needed to find the answer

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Re: What is the units digit of (16^8)(44^x)(37^5)?  [#permalink]

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25 Oct 2018, 22:35
1
Jazzmin wrote:
What is the units digit of $$(16^{8})(44^{x})(37^{5})$$?

(1) x=2y where y is a positive integer.
(2) y=2

Time needed: 1 min 20s

To answer, we need to know the units digit of $$44^x$$.
Note that powers of 4 elevated to an integer can take 2 values: 4 if the exponent is odd, 6 if the exponent is even. Thus, we just need to know if x is even or odd.

Process of elimination:
1) We know x is gonna be a positive, even number. Sufficient. Eliminate C,E
2) Doesn't provide any useful information. Insufficient. Eliminate B,D.

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Re: What is the units digit of (16^8)(44^x)(37^5)? &nbs [#permalink] 25 Oct 2018, 22:35
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