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# What is the units digit of a^18?

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Intern
Joined: 30 Jun 2012
Posts: 13
What is the units digit of a^18? [#permalink]

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09 Dec 2012, 07:56
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Difficulty:

75% (hard)

Question Stats:

34% (01:56) correct 66% (00:58) wrong based on 59 sessions

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What is the units digit of a^18?

(1) a^2 has a units digit of 9
(2) a^7 has a units digit of 3
[Reveal] Spoiler: OA
VP
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Re: What is the units digit of a^18? [#permalink]

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09 Dec 2012, 19:45
Statement 1 tells us that the number may be either 3 or 7. In either case we will get 9 as the answer. Sufficient.
Statement 2 confirms that the number is 7. So last digit of 7^18 is the same as the last digit of 7^2 , which is 9.
Hence sufficient.
+1 D
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Last edited by Marcab on 10 Dec 2012, 05:40, edited 1 time in total.
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 01:01

According to me the number should be 7 and not 3.
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 01:04
Yes its actually 7 only. I mistook it for a^5.
thanks for pointing that out.
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 04:45
Ans: we need to find the value of a to get the unit digit, looking at (1) we find that a could be 3 or 7, looking at (2) we find that a is 7 ( the units digit cyclicity is 2 or 4) and only 7 gives a units digit as 3 at raised to power 7. So the answer is (B)
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Intern
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 05:14
1
KUDOS
Marcab wrote:
Statement 1 tells us that the number may be either 3 or 7. Insufficient.
Statement 2 confirms that the number is 3. So last digit of 3^18 is the same as the last digit of 3^2 , which is 9.
Hence sufficient.
+1 B

Hi Marcab

I have a question and I could be wrong but

lets take A
a^2 has a units digit of 9
As you pointed out that the unit digit of a can be 3 or 7 but the question is asking for unit's digit of a^18. Lets take 3 and 7 seperately
3 units digit - 3, 9, 7, 1, 3, ..... therefore, the units digit for 3^18 is 9
7 units digit - 7, 9, 3, 1, 7, ... therefore, the units digit for 7^18 is 9 too. Thus, SUFFICIENT

2nd statement is clearly sufficient. Therefore, correct answer should be D.

Please let me know if the above explanation is wrong.

Thanks
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 05:43
Hii sjai.
Kudos to you.
I am not at all a morning guy and this question is simply restates the fact.
Sorry for the confusion and thanks.
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 06:05
Answer is D , but why is the official answer B ?
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 06:08
Marcab wrote:
Hii sjai.
Kudos to you.
I am not at all a morning guy and this question is simply restates the fact.
Sorry for the confusion and thanks.

Thanks Marcab. My first Kudos

Posted from my mobile device
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 06:42
deepri0812 wrote:
Answer is D , but why is the official answer B ?

D => if each answer is sufficient
answer <1> is not sufficient, as there are two answers 3 and 7. it needs to have one answer to be sufficient, hence =>B
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 06:49
NikRu- question is asking what is the units digit of a^18, which comes as one answer - 9 for both the options .

It does not ask what is the value of a - if that was the case your explanation would have been true.
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Re: What is the units digit of a^18? [#permalink]

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10 Dec 2012, 07:50
1
KUDOS
deepri0812 wrote:
NikRu- question is asking what is the units digit of a^18, which comes as one answer - 9 for both the options .

It does not ask what is the value of a - if that was the case your explanation would have been true.

Ok, another reason why A is not sufficient => it does not say that a is an integer

3.1^2 = > 9

3.1 ^18 => 0 thus not sufficient, answer B
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Re: What is the units digit of a^18? [#permalink]

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11 Dec 2012, 05:37
apoorvarora wrote:
What is the units digit of a^18?

(1) a^2 has a units digit of 9
(2) a^7 has a units digit of 3

Ans: : We need to find a to find the units digit. From statement 1 we get a to be either 3 or 7.
From statement 2 we get a to be 7( checking the cyclicity of numbers we find that only 7 has unit digit 3 at power 7). Therefore the answer is (B).
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Re: What is the units digit of a^18? [#permalink]

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11 Dec 2012, 05:42
priyamne wrote:
apoorvarora wrote:
What is the units digit of a^18?

(1) a^2 has a units digit of 9
(2) a^7 has a units digit of 3

Ans: : We need to find a to find the units digit. From statement 1 we get a to be either 3 or 7.
From statement 2 we get a to be 7( checking the cyclicity of numbers we find that only 7 has unit digit 3 at power 7). Therefore the answer is (B).

Units digit of 3^18 and units digit of 7^18 are the same.
Both statements are sufficient.
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Re: What is the units digit of a^18? [#permalink]

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11 May 2013, 08:19
NikRu wrote:
.... it does not say that a is an integer

That's the main problem with this question making it a "not-GMAT-like" question.

if a = 4.393

the units digit of a^2 is 9
the units digit of a^7 is 3

but

the units digit of a^18 is 6

Although the answer is E, I believe it's not a GMAT question
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Re: What is the units digit of a^18?   [#permalink] 11 May 2013, 08:19
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