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The question stem DOES NOT tell us that Y is either a Single Digit No. or a two digit number..
(1) The unit digit of y^2 = 1 ... Y therefore could be any one of the following numbers:
1, 9, 11 (11 x 11 = 121 , unit digit of 121 is one), 19, 21, 29....
So statement One is not suff.
(2) The units digit of Y does not equal 1.
Taking 1 and 2 together we can remove the following numbers from the list :
1,11,21,31 etc ..
This still leaves, 9 , 19, 29, 39..The squares of all result in a NUMBER whose UNIT digit is 1 ..
Why is the official answer ASSUMING that Y has only one digit when it is not mentioned?
Read the question carefully. They are asking the units digit of Y. Not the number Y itself. 9, 19, 29, 39,..... are all values of Y; agreed. But the units digit will always remain 9. Thus, answer is C. _________________
Agree with TH03 response, we need to concentrate on the unit digit as the questions ask for its value in the question.
(1) The unit digit of y^2 = 1 .
This comes down to either to 1 or 9 as unit digit (the number could be 1,11,21 or 9,19,29 etc) Not sufficient (2) The units digit of Y does not equal 1. This could be anything from 0, 9 except 1 Not suff.
Combining both of them we reach the answer is (C) as 9 is the last digit.