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Chris gave Brian a four-digit code to disarm Chris’s security system.

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Chris gave Brian a four-digit code to disarm Chris’s security system.  [#permalink]

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New post 04 Dec 2019, 00:50
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Difficulty:

  75% (hard)

Question Stats:

43% (01:36) correct 57% (01:41) wrong based on 47 sessions

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Chris gave Brian a four-digit code to disarm Chris’s security system. However, when Brian typed in the code, it didn’t work. If Brian realizes that Chris must have written exactly one digit incorrectly, but Brian does not know which digit is incorrect or what its correct value is, how many more attempts will Brian need to guarantee that he identifies the correct four-digit code?

A. 36
B. 39
C. 3,024
D. 6,561
E. 9,999


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Chris gave Brian a four-digit code to disarm Chris’s security system.  [#permalink]

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New post Updated on: 08 Dec 2019, 21:05
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Bunuel wrote:
Chris gave Brian a four-digit code to disarm Chris’s security system. However, when Brian typed in the code, it didn’t work. If Brian realizes that Chris must have written exactly one digit incorrectly, but Brian does not know which digit is incorrect or what its correct value is, how many more attempts will Brian need to guarantee that he identifies the correct four-digit code?

A. 36
B. 39
C. 3,024
D. 6,561
E. 9,999


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Explanation:
_ _ _ _
As 0 to 9 can be fitted for above 4 numbers.
Also, we don't know which number is incorrect. He had check every number from 0000 to 9999, minus 1 ( as one combination will be correct)
Total Tries needed = 10 X 10 X 10 X 10 - 1 = 9999


CCCW can be arranged in 4 ways
W can be corrected in 9 ways
Total number of ways = 4 * 9 = 36

IMO-A

Originally posted by rajatchopra1994 on 04 Dec 2019, 01:52.
Last edited by rajatchopra1994 on 08 Dec 2019, 21:05, edited 1 time in total.
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Re: Chris gave Brian a four-digit code to disarm Chris’s security system.  [#permalink]

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New post 08 Dec 2019, 09:15
for a 4 digit code 1 is wrong so total ways to match code ; CCCW ; 4!/3! ; 4 ways of combination is possible
now since 0-9 are 10 digits and the one W is not correct so we have 9 digits left
total possible ways ; 4*9 ; 36
IMO A


Bunuel wrote:
Chris gave Brian a four-digit code to disarm Chris’s security system. However, when Brian typed in the code, it didn’t work. If Brian realizes that Chris must have written exactly one digit incorrectly, but Brian does not know which digit is incorrect or what its correct value is, how many more attempts will Brian need to guarantee that he identifies the correct four-digit code?

A. 36
B. 39
C. 3,024
D. 6,561
E. 9,999


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Re: Chris gave Brian a four-digit code to disarm Chris’s security system.  [#permalink]

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New post 08 Dec 2019, 09:32
Bunuel wrote:
Chris gave Brian a four-digit code to disarm Chris’s security system. However, when Brian typed in the code, it didn’t work. If Brian realizes that Chris must have written exactly one digit incorrectly, but Brian does not know which digit is incorrect or what its correct value is, how many more attempts will Brian need to guarantee that he identifies the correct four-digit code?

A. 36
B. 39
C. 3,024
D. 6,561
E. 9,999


Are You Up For the Challenge: 700 Level Questions


Total number of ways = 4 * 9 = 36 since CCCW can be arranged in 4 ways and W can be corrected in 9 ways.


IMO A
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Re: Chris gave Brian a four-digit code to disarm Chris’s security system.  [#permalink]

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New post 11 Dec 2019, 07:02
Hi,

How can 0 be in the thousands place because if it would be , then it will make 3-digit code.
I guess it should be 9*3 (because there are 9 numbers and since 0 cannot taken thousands place it will not be counted.)
Hence, for thousands place, there should be 8 numbers (excluding 0)

So, Total ways = 27 + 8 = 35.

Please tell me if I am wrong.
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Re: Chris gave Brian a four-digit code to disarm Chris’s security system.  [#permalink]

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New post 11 Dec 2019, 10:41
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aarushisingla wrote:
Hi,

How can 0 be in the thousands place because if it would be , then it will make 3-digit code.
I guess it should be 9*3 (because there are 9 numbers and since 0 cannot taken thousands place it will not be counted.)
Hence, for thousands place, there should be 8 numbers (excluding 0)

So, Total ways = 27 + 8 = 35.

Please tell me if I am wrong.


Hi aarushisingla ,

0-9 are 10 digits and the one W is not correct so we have 9 digits left
Since In Lock , 0 can be also put. Lock Password can be 0000 or 0900 or 0090 or 0000.

Hope U got my Point. Please Do PM , if You didn't get it.

Regards,
Rajat Chopra
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Re: Chris gave Brian a four-digit code to disarm Chris’s security system.   [#permalink] 11 Dec 2019, 10:41
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