A company will use 1212 plates to number all of the houses in a new de

Question

A company will use 1212 plates to number all of the houses in a new development. The numbers on the houses will be consecutive integers, beginning from 1. If each plate displays a single digit (so the number '97' requires two plates, and the number '104' requires three plates) how many houses are in the development?

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

M07-37

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

M07-37

TheGmatTutor · Answer

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.
 B

mmphf · Answer

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

Indien · Answer

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 ...

Indien · Answer

Just now I got the question

. I misunderstood the plates part. It one digit one plate. I thought each plate must have a few digits.

prashantbacchewar · Answer

I was confused on reading the question but seems simple to solve.
Thanks for posting

piyushagarwal · Answer

good question....

rahulgupta99 · Answer

Bunuel  Can you help here?

Bunuel · Answer

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

rahulgupta99 · Answer

Thanks Bunuel

paidlukkha · Answer

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

Sent from my iPhone

EMPOWERgmatRichC · Answer

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

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

rahul16singh28 · Answer

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

danbrown9445 · Answer

House no. 1 to 9 will use 1 plate each (9 houses)
House no. 10 to 99 will use 2 plates each (90 houses)
House no. x to y will use 3 plates each where x and y are 3 digit numbers (z houses)

Total plates are 1212.
Hence 1212 = 1*9 + 2*90 + 3*z
z = 341

There are 341 houses which have 3 digit numbers,
So total number of houses = 9 + 90 + 341 = 440

Bunuel · Answer

Official Solution:

A company will use 1212 plates to number all of the houses in a new development. The numbers on the houses will be consecutive integers, beginning from 1. If each plate displays a single digit (so the number '97' requires two plates, and the number '104' requires three plates) how many houses are in the development?

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

M07-37

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

There will be 9 single-digit numbered houses (ranging from 1 to 9). As a result, only 9 plates are required for these houses.

There will be 90 double-digit numbered houses (ranging from 10 to 99). As a result, only 90*2 = 180 plates are required for these houses.

Therefore, out of the total 1212 plates, 189 have been used for the 99 houses mentioned above, leaving 1023 plates. These plates will be used for triple-digit numbered houses (since they are not enough for both triple and four-digit numbered houses).

Since 1023 plates are sufficient for 1023/3 = 341 houses, the total number of houses must be 341 + 99 = 440.

Answer: B

A company will use 1212 plates to number all of the houses in a new de

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A company will use 1212 plates to number all of the houses in a new de

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards