What is the units digit of a^18?

Question

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

Marcab · Answer

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

apoorvarora · Answer

Can you please elaborate??

According to me the number should be 7 and not 3.

Marcab · Answer

Yes its actually 7 only. I mistook it for a^5.
thanks for pointing that out.

priyamne · Answer

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)

sjai8 · Answer

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

Marcab · Answer

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.

deepri0812 · Answer

Answer is D , but why is the official answer B ?

sjai8 · Answer

Thanks Marcab. My first Kudos

Posted from my mobile device

NikRu · Answer

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

deepri0812 · Answer

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.

NikRu · Answer

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

priyamne · Answer

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).

Marcab · Answer

Units digit of 3^18 and units digit of 7^18 are the same.
Both statements are sufficient.

walker · Answer

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

What is the units digit of a^18?

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GMAT Data Sufficiency (DS) Questions

What is the units digit of a^18?

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