Mechmeera wrote:A construction company wants to number new houses using digit plates only. If the company puts an order for 1212 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).

A. 260
B. 440
C. 556
D. 792
E. 1200

Is this question correctly formed. I got confused as he asked not how many integers do we need but no of houses. Should'nt that be equal to no of plates. I mean 1plate for 1 house isnt it?

This probably could have been worded a little more clearly. Because the plates are only for digits, any house numbered between 10 and 99 would require 2 plates, as 10-99 are all 2-digit numbers. Similarly, houses between 100 and 999 would require 3-plates each.

Because the houses begin with '1,' we can use 9 plates total for houses numbered 1-9.

For houses numbered 10-99, we'll use 2 plates each, as these are all 2-digit numbers. Because there are 90 values between 10 and 99 inclusive, and we're using 2 plates each for these values, we'll use another 90*2 = 180 plates for these homes.

Thus far, we've used 9 + 180 = 189 plates. This leaves us with 1212 - 189 = 1023 plates remaining. Because any home numbered between 100 and 999 will require 3 plates, we can use those remaining 1023 plates to provide numbers to 1023/3 = 341 homes.

In sum, we have 9 homes with 1 plate.

We have 90 homes with 2 plates each.

And we have 341 homes with 3 plates each.

This gives us a total of 9 + 90 + 341 = 440 homes.