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A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,

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A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,  [#permalink]

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New post Updated on: 20 Jul 2018, 23:12
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  85% (hard)

Question Stats:

33% (01:50) correct 67% (02:51) wrong based on 45 sessions

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Permutation and Combination - Practice Question #3

3-A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,9 according to the following pattern. The first digit must be 2 or 4, 3rd digit must be a multiple of 3 and no two consecutive digits should be same. How many different codes are possible.

Options

    a) 2,016
    b) 3,888
    c) 4,608
    d) 5,184
    e) 6,236

To solve Question 1: Question 1

To solve Question 2: Question 2


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Originally posted by EgmatQuantExpert on 20 Jul 2018, 05:27.
Last edited by EgmatQuantExpert on 20 Jul 2018, 23:12, edited 1 time in total.
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A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,  [#permalink]

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New post Updated on: 23 Jul 2018, 05:53

Solution



Given:

    • A five-digit code uses the digits 0,1,2,3,4,5,6,7,8,9.
    • The first digit must be 2 or 4
    • 3rd digit must be a multiple of 3
    • No two consecutive digits should be same

To find:
    • The number of different codes possible.

Approach and Working:

Let the 5-digit number is abcde.

    • Ways to fill ‘a’ = 2(2 or 4)

    • Ways to fill ‘c’ = 4 (0,3,6,9)

    • Hence, we filled two different digits in ‘a’ and ‘c’.
      o So, out of 10 digits, b cannot take 2 digits.
      o Thus, ‘b’ can be filled in 8 ways.

    • Now, ‘d’ can be filled in 9 ways as similar digit cannot be in ‘c’ and ‘d’.

    • Similarly, ‘e’ can be filled in 9 ways.

Thus, total ways to fill= 2*8*4*9*9= 5184

Hence, the correct answer is option d.

Answer: d
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Originally posted by EgmatQuantExpert on 20 Jul 2018, 05:28.
Last edited by EgmatQuantExpert on 23 Jul 2018, 05:53, edited 1 time in total.
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Re: A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,  [#permalink]

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New post 20 Jul 2018, 09:12
2
A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,9 according to the following pattern. The first digit must be 2 or 4, 3rd digit must be a multiple of 3 and no two consecutive digits should be same. How many different codes are possible.

1st cell - 2 options (2,4) - the first digit must be 2 or 4
3rd cell - 4 options (0,3,6,9) - multiples of 3
2nd cell - 8 options - can not be surrounded by the same digits that are located in cells 1 and 3, so we have to pick from 10-2=8
4th cell - 9 options
5th cell - 9 options

2*8*4*9*9 = 5,184

Answer D
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Re: A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,  [#permalink]

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New post 21 Jul 2018, 04:14
EgmatQuantExpert wrote:
Permutation and Combination - Practice Question #3

3-A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,9 according to the following pattern. The first digit must be 2 or 4, 3rd digit must be a multiple of 3 and no two consecutive digits should be same. How many different codes are possible.

Options

    a) 2,016
    b) 3,888
    c) 4,608
    d) 5,184
    e) 6,236

To solve Question 1: Question 1

To solve Question 2: Question 2


To read our article: Must Read Articles and Practice Questions to score Q51 !!!!


code is of the form abcde
let's fill the constraints first:
a can be filled in 2 ways (2 or 4)
c can be filled in 4 ways (0,3,6, or 9)
b can be filled in 8 ways (can't be same as a or c)
d can be filled in 9 ways (can't be same as c)
e can be filled in 9 ways (can't be same as d)
total = 2*4*8*9*9 = 5184.
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Re: A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,  [#permalink]

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New post 21 Jul 2018, 22:12
IMO it should be 2*8*3*9*9= 3888 (B)
I do not understand how 0 can be considered a multiple of 3. In that way 0 is multiple of each and every number.
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Re: A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,  [#permalink]

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New post 22 Jul 2018, 04:00
Hey raks85,

Yes, 0 can be written as a multiple of any integer.
Regards,
Ashutosh
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Re: A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,  [#permalink]

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New post 23 Jul 2018, 05:57
Hello everyone,

Thanks for participation.

We have posted the official answer to the question.

Regards,
Ashutosh
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Articles and Question to reach Q51 | Question of the week

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Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

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Re: A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8, &nbs [#permalink] 23 Jul 2018, 05:57
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