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If the units digit of integer n is greater than 2, what is the units digit of n ?

(1) The units digit of n is the same as the units digit of n^2 --> since the units digit of n is greater than 2, then its units digit could be 5 or 6 (if we were not told that the units digit of n is greater than 2, then it cold also be 0 and 1). For example, both 45 and 45^2 have the units digit of 5, similarly both 26 and 26^2 have the units digit of 6. Not sufficient.

(2) The units digit of n is the same as the units digit of n^3 --> the units digit of n could be 4, 5, 6, or 9. Not sufficient.

(1)+(2) The units digit of n could still be 5 or 6. Not sufficient.

Answer: E.

Difficulty level changed to 600. _________________

Re: If the units digit of integer n is greater than 2, what is [#permalink]

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14 Jun 2012, 07:24

1

This post received KUDOS

Hi there,

I'd approach this question by essentially "brute-forcing" it with a couple of quick number substitutions. The multiplication table for each integer should come very easily to anyone taking the GMAT. This allows us to run through the entire set of integers very quickly, and should not take more than a minute or so.

xxx5^2 = yyy5, xxx5^3 = yyy5

Similarly, integers ending with 6, when squared or cubed, result in integers still ending in 6.

Neither of these statements is sufficient, either alone or in combination with the other.

With regard to the question difficulty - 650 seems like it might be about right, although a lower score could work, too. As noted above, brute-forcing it works well enough and is not even particularly time-consuming. This is, I feel, an indication that the question is not very difficult.

I'd approach this question by essentially "brute-forcing" it with a couple of quick number substitutions. The multiplication table for each integer should come very easily to anyone taking the GMAT. This allows us to run through the entire set of integers very quickly, and should not take more than a minute or so.

xxx5^2 = yyy5, xxx5^3 = yyy5

Similarly, integers ending with 6, when squared or cubed, result in integers still ending in 6.

Neither of these statements is sufficient, either alone or in combination with the other.

With regard to the question difficulty - 650 seems like it might be about right, although a lower score could work, too. As noted above, brute-forcing it works well enough and is not even particularly time-consuming. This is, I feel, an indication that the question is not very difficult.

- MrFong

Thank you. I also thought that it was not a hard problem. Though I'll wait for other comments and then might change difficulty to 600.
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Its E bunuel??

Take 6 .. its square unit digit is 6..and cube unit digit is 6.. Take 5 ..again its square and cube unit digit is 5..

So i think E is the answer..
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Re: If the units digit of integer n is greater than 2, what is [#permalink]

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14 Jun 2012, 23:09

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Hi,

Difficulty level: 600

Since, unit digit is greater than 2, then, possible digits at unit place would be: 3: Unit digit of \(3^2=9, 3^3=7\) 4: Unit digit of \(4^2=6, 4^3=4\) 5: Unit digit of \(5^2=5, 5^3=5\) 6: Unit digit of \(6^2=6, 6^3=6\) 7: Unit digit of \(7^2=9, 7^3=3\) 8: Unit digit of \(8^2=4, 8^3=2\) 9: Unit digit of \(9^2=1, 9^3=9\)

Using (1), Unit digit can be: 5: Unit digit of \(5^2=5\) 6: Unit digit of \(6^2=6\). Insufficient.

Using (2), Unit digit can be: 4: Unit digit of \(4^3=4\) 5: Unit digit of \(5^3=5\) 6: Unit digit of \(6^3=6\). Insufficient.

Combining both the statements: Unit digit can either be 5 or 6. Insufficient.

If the units digit of integer n is greater than 2, what is the units digit of n ?

(1) The units digit of n is the same as the units digit of n^2 --> since the units digit of n is greater than 2, then its units digit could be 5 or 6 (if we were not told that the units digit of n is greater than 2, then it cold also be 0 and 1). For example, both 45 and 45^2 have the units digit of 5, similarly both 26 and 26^2 have the units digit of 6. Not sufficient.

(2) The units digit of n is the same as the units digit of n^3 --> the units digit of n could be 4, 5, 6, or 9. Not sufficient.

(1)+(2) The units digit of n could still be 5 or 6. Not sufficient.

Answer: E.

Difficulty level changed to 600. _________________

Re: If the units digit of integer n is greater than 2, what is [#permalink]

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23 Jul 2012, 07:36

If the units digit of integer n is greater than 2, what is the units digit of n ?

(1) The units digit of n is the same as the units digit of n^2. n=5,6 both greater than 2 5^2=25 6^2=36 not sufficient (2) The units digit of n is the same as the units digit of n^3. n=4,5,6,9 4^3=64 5^3=125 6^3=216 9^3=729 not sufficient from (i) and (ii) 5 & 6 not sufficient (E)
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Re: If the units digit of integer n is greater than 2, what is [#permalink]

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19 Oct 2014, 21:16

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Re: If the units digit of integer n is greater than 2, what is [#permalink]

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15 Dec 2015, 16:38

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If the units digit of integer n is greater than 2, what is [#permalink]

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03 Dec 2016, 22:19

Here is my solution -> Units digit of n>2 so the unit digit of n can be => {3,4,...9} we need the unit digit of n Lets dive into statements Statement 1 Unit digit of n = units digit of n^2 so the units digits of n can be 5 or 6 Not sufficient Statement 2 Units digit of n =units digit of n^3 so the units digit of n^3 can be {4,5,6,9} Hence not sufficient Statement 1 and statement 2 units digit of n can be 5 or 6 Hence insufficient Hence E

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