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# If x is a positive integer, what is the units digit of x^2?

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Manager
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If x is a positive integer, what is the units digit of x^2?  [#permalink]

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Updated on: 14 Sep 2013, 15:23
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25% (medium)

Question Stats:

74% (01:14) correct 26% (01:23) wrong based on 311 sessions

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If x is a positive integer, what is the units digit of x^2?

(1) The units digit of x^4 is 1.
(2) The units digit of x is 3.

Originally posted by marcusaurelius on 17 May 2010, 15:52.
Last edited by Bunuel on 14 Sep 2013, 15:23, edited 1 time in total.
Edited the question and added the OA.
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Re: If x is a positive integer, what is the units digit of x^2?  [#permalink]

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14 Sep 2013, 15:25
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##### General Discussion
Manager
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17 May 2010, 16:06
2
marcusaurelius wrote:
If x is a positive integer, what is the units digit of x^2?

(1) The units digit of x^4 is 1.

(2) The units digit of x is 3.

oa is B

OA is B

As from the statement 1
You won't be able to find single answer for unit digit. If we'll calculate x^2 it will come as +1 or -1.

From Statement 2
It's given that x = 3 and whenever we will square this we will always get 9 as a unit digit. Try this for 13^2 = 169 or 33^2 = 1089

I think I haven't made any mistake
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17 May 2010, 16:07
I realized how absurdly easy this was after I posted it, but thank you for writing it out.
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18 May 2010, 06:17
2
pardeepattri wrote:
marcusaurelius wrote:
If x is a positive integer, what is the units digit of x^2?

(1) The units digit of x^4 is 1.

(2) The units digit of x is 3.

oa is B

OA is B

As from the statement 1
You won't be able to find single answer for unit digit. If we'll calculate x^2 it will come as +1 or -1.

From Statement 2
It's given that x = 3 and whenever we will square this we will always get 9 as a unit digit. Try this for 13^2 = 169 or 33^2 = 1089

I think I haven't made any mistake

OA is b but your reasoning is not correct,
First the question clearly says that x is positive and hence there is no question for x being -ve or + ve

Secondly the reason St 1 is no sufficient is that St says the unti digit of$$x^4$$ is 1, now if number x has 3 its unit digit then $$x^4$$ will have unit digit as $$1 ( 3^4 =81)$$ and also when x has unit digit has 7 then also the $$x^4$$ will have unit digit as 1

at least two options hence not sufficient
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Re: If x is a positive integer, what is the units digit of x^2?  [#permalink]

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14 Sep 2013, 15:05
Not sure what your guys are talking about.. None of you picked contradictory numbers. To show (1) is insufficient.
So 3^4=81 , 3^2=9
7^4=2401, 7^2=49

Still nothing to show (1) is insuff.

Then you try 11^4= ends in 1. 11^=ends in 1.
Now insuff
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Re: If x is a positive integer, what is the units digit of x^2?  [#permalink]

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26 Nov 2014, 14:10
cipher wrote:
pardeepattri wrote:
marcusaurelius wrote:
If x is a positive integer, what is the units digit of x^2?

(1) The units digit of x^4 is 1.

(2) The units digit of x is 3.

oa is B

OA is B

As from the statement 1
You won't be able to find single answer for unit digit. If we'll calculate x^2 it will come as +1 or -1.

From Statement 2
It's given that x = 3 and whenever we will square this we will always get 9 as a unit digit. Try this for 13^2 = 169 or 33^2 = 1089

I think I haven't made any mistake

OA is b but your reasoning is not correct,
First the question clearly says that x is positive and hence there is no question for x being -ve or + ve

Secondly the reason St 1 is no sufficient is that St says the unti digit of$$x^4$$ is 1, now if number x has 3 its unit digit then $$x^4$$ will have unit digit as $$1 ( 3^4 =81)$$ and also when x has unit digit has 7 then also the $$x^4$$ will have unit digit as 1

at least two options hence not sufficient

x= 9 also gives 1 at the fourth power. Since the question asks for the units digit of x^2, even if x had been 3 or 7, they both would have given a units digit on 9 when squared. if x=9, however, then we get a different units digit (1) for x^2
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Re: If x is a positive integer, what is the units digit of x^2?  [#permalink]

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05 Oct 2018, 09:43
marcusaurelius wrote:
If x is a positive integer, what is the units digit of x^2?

(1) The units digit of x^4 is 1.
(2) The units digit of x is 3.

1) $$x^4 = 1$$means x could be 1,3,7,9,11 etc..

Insufficient

2) units digit of x is 3

33, 333, 343, 3, etc.. as long as the units digit is 3 it is enough to find out the units digit for x^2

Sufficient.

B
Re: If x is a positive integer, what is the units digit of x^2?   [#permalink] 05 Oct 2018, 09:43
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