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select 1st column element based on criteria in 2nd AND 3rd column


Hello all, suppose I have a table:

pairs = {{1, 3, 4}, {2, 4, 6}, {3, 6, 7}, {4, 1, 8}, {5, 3, 9}, {6, 2,
    10}, {7, 5, 11}, {8, 2, 13}, {2, 3, 4}, {5, 6, 7}}

how to select rows for which the 2nd column is between 3 and 5, AND
the 3rd column is between 7 and 10? So I want to do something similar
to this:

Select[pairs, 5 >= #[[2]] >= 3 &  AND  10 >= #[[3]] >= 7]

but I just couldn't get it to work. what should I do? Thank you



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