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

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

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25 Oct 2018, 12:51
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35% (medium)

Question Stats:

60% (01:16) correct 40% (01:22) wrong based on 96 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, 12:58
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, 15:45
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, 23:35
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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)?  [#permalink]

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16 Apr 2019, 19:19
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

$$(16^{8})(44^{x})(37^{5})$$

for 16^8 = 6 always
37^5= 7
for 44^x
x=even = 6 and x odd= 4
#1
x=2y where y is a positive integer.
x will always be even
so 44^x= 4 always
sufficient

#2
insufficient
IMO A
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Re: What is the units digit of (16^8)(44^x)(37^5)?  [#permalink]

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16 Apr 2019, 19:53
Time taken: 31 sec

a) For x=2y
We know that the power is going to be even. We can find out that even power of 4 will give units digit of 4.
With this, we can find the units digit of the entire question, we CAN but don't HAVE TO.
That is all we need to know since this is DS. Hence, the statement is sufficient.

b) y=2
Statement is insufficient.

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Re: What is the units digit of (16^8)(44^x)(37^5)?   [#permalink] 16 Apr 2019, 19:53
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