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A construction company wants to number new houses using digit plates

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A construction company wants to number new houses using digit plates [#permalink]

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New post 08 Apr 2010, 18:15
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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).

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

M07-37
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 08 Apr 2010, 21:17
The question is confusingly worded but I get:

9 houses with 1-digit plates (uses 9 plates)
90 houses with 2-digit plates (uses 180 plates)
341 houses with 3-digit plates (uses 1023 plates)

This uses 1212 plates for 440 houses.
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 09 Apr 2010, 12:17
You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?

99+(1212-9-90*2)/3=440 B
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 09 Apr 2010, 13:02
My first attempt at this forum and I proved myself inadequate. These are the questions that bug me GMAT prep tests.
Quite clever question and cleverer responders. kudos ...
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 09 Apr 2010, 13:10
Just now I got the question :x . I misunderstood the plates part. It one digit one plate. I thought each plate must have a few digits.
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 05 Oct 2010, 04:01
I was confused on reading the question but seems simple to solve.
Thanks for posting
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 05 Oct 2010, 05:59
good question.... :)
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 16 Sep 2016, 23:36
Bunuel Can you help here?
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 17 Sep 2016, 00:12
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sushma0805 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

M07-37


The first 9 houses will require 9 plates. The next 90 houses will require \(2*90 = 180\) plates. The rest \(x - 99\) houses will require \((x - 99)*3\) plates. The total number of plates will be \(9 + 180 + 3x - 297 = 1212\). From this equation \(x = 440\).


Answer: B
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 17 Sep 2016, 00:24
Thanks Bunuel :)
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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 17 Sep 2016, 02:06
Keeping in mind digits plates only what number from the choice leads to three times 1212?
Why three times, as order is for thousands we need one less since repetition is allowed
440 is close

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Re: A construction company wants to number new houses using digit plates [#permalink]

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New post 22 Jan 2018, 16:15
Hi All,

This question ultimately comes down to doing some basic arithmetic and staying organized.

Each of the 1-digit house numbers (numbers 1 - 9, inclusive) requires one plate, so that's 9 houses and 9 plates
Each of the 2-digit house numbers (numbers 10 - 99, inclusive) requires two plates, so that's 90 houses and 180 plates

So far, we've used 9 + 180 = 189 of the 1212 total plates available, which leaves us with 1212 - 189 = 1023 plates

Each of the 3-digit house numbers (numbers 100 - 999, inclusive) requires three plates...

With 1023 plates remaining, we can put numbers on 1023/3 = 341 additional houses

Total houses = 9 + 90 + 341 = 440

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A construction company wants to number new houses using digit plates [#permalink]

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New post 22 Jan 2018, 18:49
sushma0805 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

M07-37


Its saying each house will be numbered using digit plates only... So, for a house with number 10 requires 2 Plates (One for 1 and the other for 0) . So, first 9 house will need 9 plates, next 90 houses will need \(2*90 = 18\)0 plates.. now, the equation will be \(9+180+(x-99)*3 = 1212\)...\(x = 341\) So, totatl will be \(9+180+x.. 440\)
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A construction company wants to number new houses using digit plates   [#permalink] 22 Jan 2018, 18:49
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