What is the units digit of y?

Question

(1) The units digit of y^2 = 9.
(2) The units digit of y^4 = 1.

chetan2u · Answer

the power of numbers repeat in foursteps..
here since we have these sequence of odd numbers 9 and 1..
lets see each statement..
1) y^2=9... 3 follows last digit as 3,9,7,1... also 7 follows sequence 7,9,3,1... ans can be 3 ,7 .. insuff
2)y^4=1.. same as above ans can be 1 or 3 or 7or 9.. insuff

combined ans can be 3 or 7.. insuff
ans E

shriramvelamuri · Answer

3 and 7 both possible and hence E.

vishwaprakash · Answer

My attempt :

This question basically test power cycle concept.

Statement 1 :
The units digit of y^2 = 9.
hence Unit digit of Y can be 3 or 7

statement 1 is Not sufficient

Statement 2 :
The units digit of y^4 = 1.
Hence unit digit of Y can 1,3 or 7

statement 2 is Not sufficient

Combine statement 1 & 2
Unit digit of Y can be either 3 or 7
Because
3^2 = 9, 7^2 = 9
Unit Digit of(3^4) = 1 and Unit Digit (7^4) = 1

Hence Option E

karant · Answer

1) Y^2 = 9

Then Y can be either 3 or 7. Insufficient

2) Y^4 = 1

Then Y can be 1,3,7 ,or 9 . Insufficient

Combining 1 and 2.

So, we have two possible values of Y as 3 or 7 satisfying statement 1 and 2.

Thus, given information fails to provide unique value of Y. Hence, Insufficient

adityadon · Answer

Using only statement 1 , we can have 7 or 3 at unit place
Using only statement 2 , we can have 1 or 3 or 7 at unit place.

Combining both , 
3^4 = 81 and 7^4=3301
so again we have two different asnwers 3 or 7
So answer is E.

chetan2u · Answer

hi, 
although the answer is correct and inference sufficient, statement 2 would also give 9 as an option...

bluesquare · Answer

1: 3*3=9, 7*7=49. So y can end in either 3 or 7, insufficient.
2: 3^4 = 81, 7^4=49*49, which has a units digit of 1 again. So also insufficient.  
Together the units digit can still be either 3 or 7, so it is insufficient. Answer is E.

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

We can see that Statement 1 is INSUFFICIENT— both 3 and 7 yield a units digit of 9 when raised to the 2nd power. (Notice that you would only need to check odd numbers for this statement, as even numbers to any power cannot end in a 9.)

Statement 2 is also INSUFFICIENT, as 1, 3, 7 and 9 yield a units digit of 1 when raised to the 4th power. (Once again, only odd numbers need to be checked.)

Combining these two statements, y could end in a 3 or a 7. INSUFFICIENT.

The correct answer is (E): The two statements COMBINED are not sufficient.

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What is the units digit of y?

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