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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]  12 Jun 2009, 20:25
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-units-digit-of-integer-n-is-greater-than-2-what-is-134501.html
[Reveal] Spoiler: OA
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Re: units digit [#permalink]  13 Jun 2011, 09:42
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the numbers greater than 2 are: 3,4,5,6,8,9
1) 5^2 = 25 and 6^2 = 6, so 5 and 6 insufficient.
2) 4, 5, 6 so insufficient.

For C 5 and 6 insufficient.
Ans. E
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Re: If the units digit of integer n is greater than 2, what is [#permalink]  14 Apr 2012, 10:48
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Expert's post
priyalr wrote:
Hi all,

I marked the qorng ans, because I took units digit of n to assume that the no. n is a two digit or more no. In this question why can;t we consider n=13, 24, 104 etc, as each no. has units digit more than 2. Why should we consider in the given problem n as only single digit no. ?

Pls explain.

We cannot assume that $$n$$ has two or more digits, it can have any number of digits: 1, 2, ..., 1,000,000, ... Now, the point is that we don't really care how many digits it has. That's because the units digit of some integer $$(x...z)^a$$ is the same as the units digit of $$z^a$$, so we are only interested in the units digit of $$n$$.

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 can 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 $$n$$ can be 4, 5, 6, or 9. Not sufficient.

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

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Re: units digit [#permalink]  12 Jun 2009, 20:38
This is what I think. You just need to find out 2 numbers which fit the criteria to say that the answer is E.

Numbers can be from 3 through 9.

1. Say the number is 6, n^2 = 36. Also if u take 16, n^2 = 256. Hence, for different numbers, N^2 has the same unit digit as the unit digit of the number N.

2. Same way for St. 2. N= 4, N^3 = 64. Also, N=5, N^3 = 125. 2 numbers so can't decide on a particular number here.

Hence E.
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Re: units digit [#permalink]  15 Jun 2009, 10:35
(i) n=n^2

5, 6, 10, 11......
25, 36, 100, 121...... satisfy this condition
Insufficient

(ii) n=n^3

5, 6, 10....
125, 196, 1000.....satify this condtion
Insufficient

(i) and (ii) together

n=5, 10 .....
n2=25, 100..
n3=125, 1000....

So, E is the best option
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Re: units digit [#permalink]  15 Jun 2009, 11:40
hasham222, your answer is right. Just remember that 10 & 11 aren't units, so they shouldn't be included in the explanation.
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Re: units digit [#permalink]  19 Jun 2009, 19:42
(1) The units digit of n is the same as the units digit of n^2

5 & 6 meet the requirement. So (1) is insufficient.

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

4,5,6 & 9 meet the requirement. So (2) is insufficient,too.

Consider (1) & (2) together, we'll find that 5 & 6 still meet both requirements. Hence answer (E).
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Re: units digit [#permalink]  19 Jun 2009, 22:35
yes.. same explanation as above. E for me too
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Re: units digit [#permalink]  24 Jun 2009, 13:51
frolixwithdanger,

10 and 11 do have units in them, 10's units is 0 and 11's units is 1. They are valid numbers > 2 and can be used to solve the DS.
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Re: units digit [#permalink]  05 Jul 2011, 06:45
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Re: units digit [#permalink]  05 Jul 2011, 07:16
I am new to GMAT and I was completely helpless because of this question. However, GMAT official explanation satisfied me. Thanks to OG guide. My understanding to the problem:

The Question says units digit of n is greater than 2 so lets assume the number be 3,4,5,6,7,8,9.

Now statement 1 says digit n should equal to n^2's units digit

Lets try with 5 and 6
n^2=5^2=25 where digit 5 is equal to its squared units digit 5.
n^2=6^36 where digit 6 is to its squared units digit 6
HOWEVER, there is no actual answer i.e. whether to choose 5 or 6. So, it is insufficient.

Similarly, Statement 2 says n should equal to n^3's unit digit
Lets try with 4 and 5
n^3=4^3=64 where digit 4 is equal to its cube units digit 4.
n^3=5^3=125 where digit 5 is equal to its cube units digit 5
HOWEVER, there is no actual answer i.e. whether to choose 4 or 5. So, it is insufficient.

If we take two statements together then we still don't find correct answer i.e. whether to choose 4,5 or 6. So, they are INSUFFICIENT together.

So the Answer is E. They together are also not sufficient.
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Re: units digit [#permalink]  20 Jul 2011, 06:15
Guys, I don't understand why the OG and everyone keep saying that 5 and 6 are the only numbers which, when cubed, will both have a 5 or 6 in their units digit (2). Isn't it also true for numbers 4 and 9? I know it won't change the answer, but just curious.
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Re: If the units digit of integer n is greater than 2, what is [#permalink]  14 Apr 2012, 06:04
Hi all,

I marked the qorng ans, because I took units digit of n to assume that the no. n is a two digit or more no. In this question why can;t we consider n=13, 24, 104 etc, as each no. has units digit more than 2. Why should we consider in the given problem n as only single digit no. ?

Pls explain.
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Re: If the units digit of integer n is greater than 2, what is [#permalink]  14 Apr 2012, 22:41
Jozu wrote:
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

Official Guide 12 Question

 Question: 25 Page: 25 Difficulty: 750

Find All Official Guide Questions

Video Explanations:

1: INSUFFICIENT as we have many Ns which will have same unit digit as N2
2: INSUFFICIENT as we have many Ns which will have same unit digit as N3

hence options A, B & D are out of question.

hence answer should be either C or E

but there are many numbers which satisfy both the above conditions

hence E
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Re: units digit [#permalink]  09 Aug 2013, 00:19
gmatprep09 wrote:
This is what I think. You just need to find out 2 numbers which fit the criteria to say that the answer is E.

Numbers can be from 3 through 9.

1. Say the number is 6, n^2 = 36. Also if u take 16, n^2 = 256. Hence, for different numbers, N^2 has the same unit digit as the unit digit of the number N.

2. Same way for St. 2. N= 4, N^3 = 64. Also, N=5, N^3 = 125. 2 numbers so can't decide on a particular number here.

Hence E.

Hey, I find B as the answer of this question because statement 2 alone is sufficient to find the unique answer of this question.
Because as per statement 2 If we take a number say 23479 then the cube of this number will also end at 9.

Please tell me if I am wrong and where ?
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Re: units digit [#permalink]  09 Aug 2013, 02:51
Expert's post
dheeraj787 wrote:
gmatprep09 wrote:
This is what I think. You just need to find out 2 numbers which fit the criteria to say that the answer is E.

Numbers can be from 3 through 9.

1. Say the number is 6, n^2 = 36. Also if u take 16, n^2 = 256. Hence, for different numbers, N^2 has the same unit digit as the unit digit of the number N.

2. Same way for St. 2. N= 4, N^3 = 64. Also, N=5, N^3 = 125. 2 numbers so can't decide on a particular number here.

Hence E.

Hey, I find B as the answer of this question because statement 2 alone is sufficient to find the unique answer of this question.
Because as per statement 2 If we take a number say 23479 then the cube of this number will also end at 9.

Please tell me if I am wrong and where ?

Check here: if-the-units-digit-of-integer-n-is-greater-than-2-what-is-134501.html#p1096557

Hope it helps.
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Re: units digit   [#permalink] 09 Aug 2013, 02:51
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