+0

# Full Solution or Hint

+1
106
4

How many 3-digit numbers have the property that the units digit is at least twice the tens digit?

Oct 1, 2020

#1
+2

I'm not very good at this but heres what I know: think about the options you have for each digit. The hundreds digit doesn't matter so you have 1-9 which is 10 options, then for the tens digit you can do casework for each number. For instance if it's 1, then the units digit is anything from 2-9. e.t.c

Oct 1, 2020
#2
+2

This is just one way of doing it:

Beginning with 1 as the hunderds digit, you have the following list:

102  103  104  105  106  107  108  109  112  113  114  115  116  117  118  119  124  125  126  127  128  129  136  137  138  139  148  149 =28 integers.

This same pattern repeats with:2, 3, 4, 5, 6, 7, 8, 9

So: 9 x 28 = 252 integers.

Oct 1, 2020
#3
+2

These are the possibilities.

*0*          9*1*10 = 90

*1*          9*1*8 = 72

*2*           9*1*6  =54

*3*                36

*4*                18

90+72+54+36+18 = 270

Oct 1, 2020
#4
+1

Thanks a lot for the good answer Oct 2, 2020