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In Country X, three digit area codes are to be given to each town. The

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In Country X, three digit area codes are to be given to each town. The  [#permalink]

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New post 29 Jan 2018, 05:47
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In Country X, three digit area codes are to be given to each town. The first digit will be any number from 2-9, inclusive, the second digit can only be either 0 or 1, and the third digit can be any number from 0-9, inclusive. How many different area codes can be issued in Country X?

A. 18
B. 140
C. 144
D. 160
E. 180

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In Country X, three digit area codes are to be given to each town. The  [#permalink]

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New post 29 Jan 2018, 06:26
Bunuel wrote:
In Country X, three digit area codes are to be given to each town. The first digit will be any number from 2-9, inclusive, the second digit can only be either 0 or 1, and the third digit can be any number from 0-9, inclusive. How many different area codes can be issued in Country X?

A. 18
B. 140
C. 144
D. 160
E. 180


The three digit area code in Country X can have the following possibilities

The First digit can contain any number from 2 to 9(8 possibilities)
The Second digit can be either 0 or 1(2 possibilities)
The Third digit can be any number from 0 to 9(10 possibilities)

Therefore, the total number of area codes possible is 8*2*10 = 160(Option D)

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Re: In Country X, three digit area codes are to be given to each town. The  [#permalink]

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New post 30 Jan 2018, 11:16
Bunuel wrote:
In Country X, three digit area codes are to be given to each town. The first digit will be any number from 2-9, inclusive, the second digit can only be either 0 or 1, and the third digit can be any number from 0-9, inclusive. How many different area codes can be issued in Country X?

A. 18
B. 140
C. 144
D. 160
E. 180


There are 8 options for the first digit, 2 options for the second digit, and 10 options for the 3rd digit, so we have a total of 8 x 2 x 10 = 160 possible area codes.

Answer: D
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Re: In Country X, three digit area codes are to be given to each town. The  [#permalink]

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New post 31 Jan 2018, 01:15
Bunuel wrote:
In Country X, three digit area codes are to be given to each town. The first digit will be any number from 2-9, inclusive, the second digit can only be either 0 or 1, and the third digit can be any number from 0-9, inclusive. How many different area codes can be issued in Country X?

A. 18
B. 140
C. 144
D. 160
E. 180


Solution



    • This question can be easily solved using the filling space method.
    • We have three spaces, one space for each digit of the code: ___ ___ ___
      o We need to fill each space, as per the condition given in the question.
      o For the first place, we know that it can any number from 2 to 9
         Thus, the following cases are possible: 2,3,4,5,6,7,8,9
         Total 8 cases.
      o The second place needs to be filled with either 0 or 1.
         Total 2 cases.
      o The third place needs to be filled with any number from 0 to 9
         Thus, the following cases are possible: 0,1,2,3,4,5,6,7,8,9
         Total 10 cases.
    • Therefore, total possible codes that can be issued are = __8__ * __2__ * __10__ = 160 cases.
    • The correct answer is Option D.


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Re: In Country X, three digit area codes are to be given to each town. The  [#permalink]

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New post 04 Feb 2018, 03:33
As there are three positions to fill in,

Lets us go piece by piece,
1) For the first position the place can be filled in 8C1 ways.
2) The second position can be filled in 2C1 ways.
3) The third position can be filled in 10C1 ways.

When adding individually it gives us the answer as 160.

Correct answer D
Re: In Country X, three digit area codes are to be given to each town. The &nbs [#permalink] 04 Feb 2018, 03:33
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