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Re: What is the units digit of a^18? [#permalink]
09 Dec 2012, 18:45

Expert's post

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

Re: What is the units digit of a^18? [#permalink]
10 Dec 2012, 03:45

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)

Re: What is the units digit of a^18? [#permalink]
10 Dec 2012, 04:14

1

This post received 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.

Re: What is the units digit of a^18? [#permalink]
10 Dec 2012, 05:42

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

Re: What is the units digit of a^18? [#permalink]
11 Dec 2012, 04:37

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).

Re: What is the units digit of a^18? [#permalink]
11 Dec 2012, 04:42

Expert's post

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.