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# A 9-character numeric passcode is constructed at random. If the last n

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A 9-character numeric passcode is constructed at random. If the last n  [#permalink]

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13 Apr 2018, 02:29
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Difficulty:

25% (medium)

Question Stats:

85% (01:26) correct 15% (02:44) wrong based on 78 sessions

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A 9-character numeric passcode is constructed at random. If the last number cannot be prime and the first digit cannot be 0, 1, or 7, how many different codes can be constructed?

A. 210,000,000
B. 300,000,000
C. 360,000,000
D. 420,000,000
E. 560,000,000

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A 9-character numeric passcode is constructed at random. If the last n  [#permalink]

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13 Apr 2018, 04:21
1
Bunuel wrote:
A 9-character numeric passcode is constructed at random. If the last number cannot be prime and the first digit cannot be 0, 1, or 7, how many different codes can be constructed?

A. 210,000,000
B. 300,000,000
C. 360,000,000
D. 420,000,000
E. 560,000,000

The first digit excludes [0, 1 and 7] , therefore 7 possible values.
The last digit excludes [2, 3, 5 and 7] therefore 6 possible values
The second to eight digits (7 digits) can have all 10 values

Therefore different codes that can be constructed is 7*10*10*10*10*10*10*10*6 = 7*6*(10^7) = 420,000,000

Hence option D = 420,000,000 is the answer.

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Re: A 9-character numeric passcode is constructed at random. If the last n  [#permalink]

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16 Apr 2018, 16:05
Bunuel wrote:
A 9-character numeric passcode is constructed at random. If the last number cannot be prime and the first digit cannot be 0, 1, or 7, how many different codes can be constructed?

A. 210,000,000
B. 300,000,000
C. 360,000,000
D. 420,000,000
E. 560,000,000

We have 7 options for the first digit. We have 10 options for each of the second to eighth digits (any digit 0 through 9, inclusive), and 6 options for the last digit (because the final digit cannot be 2, 3, 5, or 7).

So we have a total of 7 x 10^7 x 6 = 42 x 10^7 = 420,000,000 codes.

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Re: A 9-character numeric passcode is constructed at random. If the last n  [#permalink]

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28 Apr 2018, 18:15
Only difference in options is first two digits

1st digit can be taken in 7 ways
Last digit can be taken in 6 ways ( excluding 2,3,5,7)

Rest all other can take 10 values

7*6=42

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Re: A 9-character numeric passcode is constructed at random. If the last n &nbs [#permalink] 28 Apr 2018, 18:15
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# A 9-character numeric passcode is constructed at random. If the last n

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