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

Question

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

Bunuel · Accepted Answer

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pardeepattri · Answer

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

marcusaurelius · Answer

I realized how absurdly easy this was after I posted it, but thank you for writing it out.

cipher · Answer

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

alphabeta1234 · Answer

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

usre123 · Answer

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

Salsanousi · Answer

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

yazadsarkari · Answer

This question is pretty easy it goes like this 
St 1 : If x4 is 3^4 or 7^4 the units digit will be 1 so not suff
St 2 : SUFF because it gives the value of X

Tip : do not try to solve these sums instead try to imagine the numbers that can be formed

TDTGiang · Answer

IMO:
1. If the UD of x^4 = 1 => the UD of x will be 1, 4, 7 or 9
But this does not help to clearly determine the UD of x^2. 1) is not enough
2. If the UD of x = 3 => the Cyclicity of 3 is 4 (3-9-7-1)
This will determine the UD of x^2 = 9 => 2 is enough => B

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

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GMAT Data Sufficiency (DS) Questions

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

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