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If n is a positive integer, what is the units digit of n?

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If n is a positive integer, what is the units digit of n?

(1) the units digit of (n+4)^2  is 4
(2) the units digit of (n+3)^2 is 1

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Ans is C ; means both statements are reqd to answer the question.
for statement 1:  Unit digit of (n+4) can be 2 or 8 ( e.g. 2*2=4, 8*8=64 )
so only 1 is not sufficient.
For statement 2: Unit digit of (n+3) can be 1 or 9 ( e.g. 11*11=121, 9*9=81 )
so only 2 is also not sufficient.
But 1 and 2 together implis that  (n+4) ends with 2 and (n+3) ends with 1. So we can have an answer for unit digit of n (8).
answered Jan 6, 2015 by Student (31 points)
selected Jan 8, 2015 by
GMAX Online
In thinking about answer choice (1), first decide which numbers, when squared, will give a unit's digit of 4. The numbers 2, 8, and 12 meet this condition. Now subtract 4 from each of them, to get  the value of n. So we are left with 8 and 12 as possible answers. Since there are 2 possible solutions, answer choice (1) by itself is not enough. To understand answer choice (2), look for numbers that, when squared, have a unit's digit of 1. The possibilities are 1, 9, and 11. Now subtract 3 and we get 6 and 8. Since 8 is the answer in both (1) and (2), it is the only solution to the problem, and we need both statements to solve the question.
answered Jan 5, 2015 by Beginner (11 points)
Statement 1 is individually not sufficient to answer the question . However Statement 2 is alone sufficent to answer the question
Statement 1 Insufficient - Only the squares of 2 and 8 have unit digits as 4 ( 4 and 64 ) . Statement 1 has n+4 which can be any number for eg can be 12 or 18 which means n can be either 8 or 14 . Hence we can not determine the exact unit digit of n .
Statement 2 Sufficient  - Only the square of 9 ends with 1 (81 ) . Hence n+3 has to end with 9 which means the unit digit of original number n has to be 6 .
answered Jan 5, 2015 by Beginner (3 points)
11 squared is 121
commented Jan 6, 2015 by Beginner (1 point)
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