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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).

You can number the first 9 houses with a single digits plate each (i.e. 1st house with 1, 2nd house with 2...9nth house with 9). => You have numbered 9 houses and you have 1212 - 9 = 1203 digits plates left.

Then you start numbering houses 10 to 99 with two digits plates each (i.e. 11th house with 11....99th house with 99). => You have numbered 99 houses and you have 1212 - 9 - 2*90 = 1023 digits plates left.

Now you know that from now on you need 3 digits plates to number each house. Since you have 1023 digits plates left you can number 1023 / 3 = 341 additional houses

So in total you can number 9 + 90 + 341 = 440 houses.

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). 1) 260 2) 440 3) 556 4) 792 5) 1200

Could someone provide alternative solution, the provided solution is not clear ...? thanks.

Plates req for 1 digit plates = 1-9 = 9 Plates req for 2 digit plates = 10-99 = 90 Plates req for 3 digit plates = 100- up = needs to find.

1,212 = plates req for single digit + plates req for two digits + plates req for three digit 1,212 = 9 (n) + 90 (2n) + x (3n) x = (1,212 - 9 - 180)/3 (since n = 1) x = 341

no of houses = 9 + 90 + 341 = 440.
_________________

the trick is in the sentence "construction company wants to number new houses using digit plates only".. so it means in each board only one digit will be written.

so for the first 9 houses, which wil be numbered as, 1,2,3..9, we need 9 plates for the 10th house, the house number should be 10 ( because "numbers of houses are consecutive") so for the 10th house, two plates are required ( a plate with the number 1 and a plate with the number 0) hence for the next 90 houses ( obtained as 99-10), we need 90 * 2 plates = 180 plates

and nw the equation comes 1*9 + 2*90 + 3*a = 1212 ==> a = 341 and number of houses = 9 +90+341 = 440

*** 4 digits are not considered because it is mentioned that "numbers of houses are consecutive" _________________

[caption=]Remember: Anything that can go wrong, will go wrong.[/caption]

I'm trying to understand your alternative solution, but I believe the calculation is incorrect:

1,212 = plates req for single digit + plates req for two digits + plates req for three digit 1,212 = 9 (n) + 90 (2n) + x (3n) x = (1,212 - 9 - 90)/3 (since n = 1) x = 341 <----- this should be 371 according the the statement preceding it

341 is correct but the highlighted 90 should be 180.

I'm trying to understand your alternative solution, but I believe the calculation is incorrect:

1,212 = plates req for single digit + plates req for two digits + plates req for three digit 1,212 = 9 (n) + 90 (2n) + x (3n) x = (1,212 - 9 - 90)/3 (since n = 1) x = 341 <----- this should be 371 according the the statement preceding it

I'm trying to understand your alternative solution, but I believe the calculation is incorrect:

1,212 = plates req for single digit + plates req for two digits + plates req for three digit 1,212 = 9 (n) + 90 (2n) + x (3n) x = (1,212 - 9 - 90)/3 (since n = 1) x = 341 <----- this should be 371 according the the statement preceding it

341 is correct but the highlighted 90 should be 180.

Thanks.

We need the total number of houses not plates per house---90 is correct.

The numbers of houses are consecutive and the number of the first house is 1

How does the underlined text (or any other one) suggest that there is only a digit per plate? I thought consecutive numbers of houses means 1,2,3, ..., 10, 11, ..100, 101,... Also, there could be double digit plates, three-digit plates, etc...

Someone please correct my erroneous statement.
_________________

KUDOS me if you feel my contribution has helped you.

I used the elimination technique to find out the correct answer here. Now lets see how this works :

Number of plates for numbers from 1-9 ->9 Number of plates for number 10-99 ->90x2 = 180 Number of plates for numbers 100-199 ->100x3 =300 similarly for 200-299 -> 300 300-399 -> 300 400-499 -> 300

from the options which are given if we add number of plates required only for number from 100-499 it should be 1200 the number of plates required are a little more than this hence our answer should be very close to 400 and hence the answer
_________________

You don't have to go to 4 digits because 3*900 is greater than the number of plates (1212)

I made the same mistake; I did not take in to account the number of plates, i.e, when we use 2 digit plates, you have to multiply the various arrangements by the number of plates