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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 in | Square ends in |

1 | 1 |

2 | 4 |

3 | 9 |

4 | 6 |

5 | 5 |

6 | 6 |

7 | 9 |

8 | 4 |

9 | 1 |

0 | 0 |

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

There are 8 such integers.