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This problem trains for: SAT-I, AMC-8, GMAT.

How many numbers between 19 and 39 end in the same digit as their square?

Consider the following table of last digits of positive integers and their squares:

Integer ends inSquare ends in
11
24
39
46
55
66
79
84
91
00

Between 19 and 39 the following integers end in the same digit as their squares:

equation

There are 8 such integers.