# Entrance exams

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Draw one observation N from the set {1,2,…,100}.What is the probability that the last digit of N^2 is 1?

a)1/20  b)1/50   c)1/10   d)1/5

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Drawing one observation from the set {1,2,3,…100} and labeling it as N. Total number of ways in which this can be done is 100.

Now for N^2 to end with 1, the chosen N must end with 1 or 9 that is N must be in the set {1,9,11,19,21,29,31,39,41,49,51,59,61,69,71,79,81,89,91,99}, i.e., required probability=20/100=1/5…..d) is the correct option.

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