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What is the units digit of a^18? [#permalink]
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09 Dec 2012, 07:56
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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
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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
Can you please elaborate??
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



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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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Re: What is the units digit of a^18? [#permalink]
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10 Dec 2012, 05:14
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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
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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 "notGMATlike" 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?
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