What is the units digit of positive integer x? (1) Units digit of x^2

Question

What is the units digit of positive integer x?

(1) Units digit of x^2 = 4

(2) Units digit of (x+1)^2 = 1

Anurocks1233 · Answer

What is the units digit of positive integer x?

(1) Units digit of x^2 = 4
Only 2*2 result in 4 so this statement is sufficient

(2) Units digit of (x+1)^2 = 1
1 can be a result of 9*9 or 1*1 
So insufficient

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gmatophobia · Answer

(1) Units digit of x^2 = 4

The unit digit of  x^2  will be obtained by multiplying the unit digit of x and x, hence we know that the unit digit of x is 2 in this case.

(2) Units digit of (x+1)^2 = 1

When expanded, we get  x^2 + 2x +1

The unit digit of 1 will be contributed by the unit digit of all the elements in the expanded form.

We don't have enough information to conclude the same.

IMO A

Isa1989 · Answer

From the 1st statement:-
The units digit of x^2=4 which implies that the units digit of x could be either 2 or 8.
Let's assume x=12, then 1 2 *1 2 =14 4  ; 
Let's assume x=28 then, 2 8 *2 8 =78 4 
Since this presents two different values for the units digit of x, this is insufficient.

From the 2nd statement:-
The units digit of (x+1)^2=1 which implies that the units digit of x+1 could be either 1 or 9.
Let's assume (x+1)=11, then 1 1 *1 1 =12 1  ; 
Let's assume (x+1)=19 then, 1 9 *1 9 =36 1 .
If the units digit of (x+1) is 1 then the units digit of x=0; For e.g 1 1 -1=1 0  ; 
If the units digit of (x+1) is 9 then the units digit of x=8 ; For e.g 1 9 -1=1 8 .
Since we have two different values for the units digit of x, this is insufficient.

Now if we combine both statements, the only value for the units digit of x that satisfies both is  8 .Therefore,both statements combined are sufficient to determine the units digit of x.

IMO C.

ElninoEffect · Answer

(1) Units digit of x^2 = 4
Unit digit of X can be 2 or 8
 Not Sufficient.

(2) Units digit of (x+1)^2 = 1
We can get square of a unit digit 1 in only two cases 1 and 9
& for (x+1)^2 x has to be 0 or 8  but  x cannot be 0 since x is +ve.
So x has to be 8.
 Sufficient.

B is the answer.

stne · Answer

(1) Units digit of  x^2 = 4

x   could be of the form _ _ 2 i.e. ending with  2  
 x   could be of the form _ _ 8 i.e. ending with  8

INSUFF.

(2) Units digit of  (x+1)^2 = 1

x   could be of the form _ _  0  i.e. ending with  0 
 x  could be of the form _ _  8  i.e. ending with  8

INSUFF.

1+2

x  is of the form _ _  8

SUFF.

Ans C

Hope it's clear.

CrackverbalGMAT · Answer

Lets try to get a definite answer to the question stem by using these statements given.

(1) Units digit of   x^2  = 4
 
From St 1. we can conclude that unit digit of x could be either 2 or 8.

Since we have 2 possible answers, St 1 alone is not sufficient.

(2) Units digit of  (x+1)^2  = 1

From St 2, we can conclude that the unit digit of x+1 should be either 1 or 9 . i.e the unit digit of x should be either 0 or 8.

Since there are 2 possible answers, Statement 2 alone is not sufficient .

Combining St 1 and St 2 , only possible unit digit of x that satisfies both the statements is 8.

Since we get a unique answer to the question stem, Option C is the correct answer.

Thanks,
Clifin J Francis.

What is the units digit of positive integer x? (1) Units digit of x^2

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