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

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

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14 Jun 2012, 03:00
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Difficulty:

5% (low)

Question Stats:

77% (02:05) correct 23% (00:56) wrong based on 847 sessions

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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.
(2) The units digit of n is the same as the units digit of n^3.

Diagnostic Test
Question: 25
Page: 25
Difficulty: 600
[Reveal] Spoiler: OA

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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, 03:00
1
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SOLUTION

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.

Difficulty level changed to 600.
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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, 07:24
1
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.

- MrFong
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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, 07:32
MrFong wrote:
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.

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

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14 Jun 2012, 12:17
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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.
(2) The units digit of n is the same as the units digit of n^3.

Diagnostic Test
Question: 25
Page: 25
Difficulty: 650

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Explanations (OE) to them along with an alternate approaches if necessary.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button (the best solution we'll be put along the OE in the second post);
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

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
2
KUDOS
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.

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

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16 Jun 2012, 04:18
Difficulty level: 600+

I simply noted down numbers from 3 to 9 and checked square and cube values. Found 5 and 6 given similar answers.

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

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22 Jun 2012, 03:14
SOLUTION

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.

Difficulty level changed to 600.
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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
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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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Re: If the units digit of integer n is greater than 2, what is   [#permalink] 03 Dec 2016, 22:19
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