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

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.
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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.

- 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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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)

Regards,

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

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)

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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Theory:
unit-digit^p = unit-digit, when unit-digit is 0,1,5,6. p may be odd or even

(--4)^odd=4
(--9)^odd=9

Statement 1.
5,6 (not, 4 and 9 because the power is square(even)). Insufficient

statement 2.
5,6, and 4,9. Insufficient

Statement 1 and 2.
5,6. Two values so insufficient

Hence, Ans is E

We are given that the units digit of integer n is greater than 2 and we need to determine that units digit.

Statement One Alone:

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

If the units digit of n is the same as the units digit of n^2, then the units digit can be 0, 1, 5, or 6 (since 0^2 = 0, 1^2 = 1, 5^2 = 25 and 6^2 = 36). However, we are given that the units digits is greater than 2, so n can be either 5 or 6. Since we can’t determine exactly which digit it is, statement one alone is not sufficient to answer the question.

Statement Two Alone:

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

If the units digit of n is the same as the units digit of n^2, then the units digit can be 0, 1, 4, 5, 6, or 9. (since 0^3 = 0, 1^3 = 1, 4^3 = 64, 5^3 = 125, 6^3 = 216 and 9^3 = 729). However, we are given that the units digits is greater than 2, so n can be 4, 5, 6 or 9. Since we can’t determine exactly which digit it is, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

With two statements together, the units digit of n can still be either 5 or 6. Since we can’t determine which one it is, the two statements together are still not sufficient to answer the question.

Answer: E
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So, n can be 3, 4 ,5,6,7,8 and 9.

So let's find squares and cubes of these numbers.

3^2 = 9 so last digit is not 3. Similarly for 4 , 7,8 and 9, when we square or cube them units digit changes. For 5 and 6 units digit doesn't not change for square or cube. So we have 2 choices. Don't know which one is the one.

So the answer is E

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For the given statement n ; Lets xy be the number where y>2 and we need n=?

1. n unit digit = n^2 unit digit
5 , 25 and 6,36 -- not sufficient
2. n unit digit = n^3 unit digit
5,125 , 6,216 rest we dont need. -- not sufficient

we have taken example above which shows we still don't have one value combined

Ans E.

Nice one, I think we can bump this to 600+

n= An integer, say for the sake of simplicity:

\(n= _ _\)

(1) The units digit of n is the same as the units' digit of \(n^2\).

let say, \(n= 6\), we can write 6 as two-digit integer = \(06\) and \(n^2 = 36\) ( Same units digit 6)

let say, \(n= 5\), then \(n^2= 25\) (say units digit of 5)

we have two possible values, not sufficient.

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

again, let's say \(n= 06\), \(n^3= 216\) ( same units digit, 6)

Say, \(n=9\) , \(n^3= 729\) (same units digit, 9)

Two possible values, insufficient.

1+2

We can re-use the same values, for simplicity,

n has the same values for Unit digit as n^2 and n^3, Cool : what if n= 6 and n= 11...? both \(n^2 \) and \(n^3 \)for 11 and 6 will have the same unit's digit. hence, we can't find n based on the provided info.

E. is the answer

"since the units digit of n is greater than 2, then its units digit could be 5 or 6"

but the units digit could also be 7 and 9, e.g.: 7, 7'2=49

What don't I understand here?

"since the units digit of n is greater than 2, then its units digit could be 5 or 6"

but the units digit could also be 7 and 9, e.g.: 7, 7'2=49

What don't I understand here?


Okay I got it, unit digits of n has to equal units digit of n'2...

(1) Why can the units digit only be 5 or 6? 7'2=49, so the units digit here is 9

(1) says: The units digit of n is the same as the units digit of n^2. Does ..7 or ..9 satisfy this?
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