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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] New post 14 Jun 2012, 02:00
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71% (01:00) correct 29% (00:41) wrong based on 232 sessions
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] New post 14 Jun 2012, 02:00
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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.

Answer: E.

Difficulty level changed to 600.
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Re: If the units digit of integer n is greater than 2, what is [#permalink] New post 14 Jun 2012, 06:24
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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.

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Re: If the units digit of integer n is greater than 2, what is [#permalink] New post 14 Jun 2012, 06:32
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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] New post 14 Jun 2012, 11:17
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


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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] New post 14 Jun 2012, 22:09
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.

Thus, Answer is (E)

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Re: If the units digit of integer n is greater than 2, what is [#permalink] New post 16 Jun 2012, 03:18
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] New post 22 Jun 2012, 02:14
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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.

Answer: E.

Difficulty level changed to 600.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If the units digit of integer n is greater than 2, what is [#permalink] New post 23 Jul 2012, 06:36
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] 23 Jul 2012, 06:36
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