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A 3-character alpha-numeric code does have the following properties

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A 3-character alpha-numeric code does have the following properties  [#permalink]

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New post 29 May 2018, 01:54
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A 3-character alpha-numeric code does have the following properties – the first character can be any number except 0 and 9, the second character can be any small letter between a to z, excluded, and the third character can have any of those characters possible for the first two places. How many such codes can be formed?

A. 26
B. 64
C. 520
D. 6144
E. 9360



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A 3-character alpha-numeric code does have the following properties  [#permalink]

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New post 29 May 2018, 03:04
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EgmatQuantExpert wrote:
A 3-character alpha-numeric code does have the following properties – the first character can be any number except 0 and 9, the second character can be any small letter between a to z, excluded, and the third character can have any of those characters possible for the first two places. How many such codes can be formed?

A. 26
B. 64
C. 520
D. 6144
E. 9360


The 3 character alpha-numeric code has the following characters

First character - Any number except 0 and 9 - Total of 10 - 2 = 8 possibilities
Second character - Any small letter except a and z - Total of 26 - 2 = 24 possibilities
Third character - Any number except 0 and 9 or Any small letter except a and z - Total of 8 + 24 = 32 possibilities

In this case, to find the total number of possibilities, we can use the unit's digit to find the
answer as number ending 8 * number ending 4 * number ending 2 is a number ending 4.
Also, the answer must be close to 10*20*30 is a little more than 6000.
P.S when the answer options are far apart, we can use approximations to arrive at the answer

Therefore, Option D(6144) is the the total number of 3-character alpha-numberic codes.
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Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

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New post 29 May 2018, 03:32
pushpitkc wrote:
EgmatQuantExpert wrote:
A 3-character alpha-numeric code does have the following properties – the first character can be any number except 0 and 9, the second character can be any small letter between a to z, excluded, and the third character can have any of those characters possible for the first two places. How many such codes can be formed?

A. 26
B. 64
C. 520
D. 6144
E. 9360


The 3 character alpha-numeric code has the following characters

First character - Any number except 0 and 9 - Total of 10 - 2 = 8 possibilities
Second character - Any small letter except a and z - Total of 26 - 2 = 24 possibilities
Third character - Any number except 0 and 9 or Any small letter except a and z - Total of 8 + 24 = 32 possibilities

In this case, to find the total number of possibilities, we can use the unit's digit to find the
answer as number ending 8 * number ending 4 * number ending 2 is a number ending 4.
Also, the answer must be close to 10*20*30 is a little more than 6000.
P.S when the answer options are far apart, we can use approximations to arrive at the answer

Therefore, Option C(6144) is the the total number of 3-character alpha-numberic codes.


I think your calculations and answer is correct but by mistake you have mentioned option C in your answer (in brackets though the actual answer is right). I hope this helps.
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Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

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New post 29 May 2018, 03:56
Once again, thanks Manish!
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Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

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New post 29 May 2018, 04:00
pushpitkc wrote:
Once again, thanks Manish!


You are welcome!! The short cuts of approximation and using the units digits are nice. Time saving.
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Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

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New post 31 May 2018, 01:55

Solution



Given:
    • The code is of 3-character alpha-numeric
    • 1st character can be any number except 0 and 9
    • 2nd character can be any small letter between a to z, excluded
    • 3rd character can be any of those characters possible for the first two places

To find:
    • Keeping all the constraints satisfied, how many such codes can be formed

Approach and Working:
    • As the 1st character can be any number except 0 and 9, number of possibilities exist for the first character = 8
    • As the 2nd character can be any small letter between a to z, excluded, number of possibilities exist for the second character = 24
    • As the 3rd character can be any of those characters possible for the first two places, number of possibilities exist for the third character = 8 + 24 = 32
    • Therefore, the total number of possible codes = 8 * 24 * 32 = 6144

Hence, the correct answer is option D.

Answer: D
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Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

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New post 23 Dec 2018, 16:19
Three different characters: C1 C2 C3
Theory: When calculating the number of items it is (xn-xa)+1

C1
8-1+1=8

C2
25th letter is y; 2nd letter is b
25-2+1=24

C3
8+24=32

Theory: Fundamental counting rule C1·C2·C3
8·24·32

I don't like multiplying 3 numbers together. I split the 8 up
(4·24)·(2·32)=96·64

Theory: the units digits of the answer results only from the units digits of the inputs
6·4=x4, so we know the answer ends in 4

B is too small. D must be the answer
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Re: A 3-character alpha-numeric code does have the following properties   [#permalink] 23 Dec 2018, 16:19
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