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Bunuel
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset 06 Oct 2020, 04:00
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95% (hard)

Question Stats:

40% (02:53) correct 60% (02:34) wrong based on 72 sessions

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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset the passcode such that the new passcode cannot have the digit 1 immediately followed by the digit 3. How many different passcodes can be formed?

A. 9700
B. 9701
C. 9702
D. 9703
E. 9704

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B
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Bunuel
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset 06 Oct 2020, 04:01
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Bunuel
A smartphone uses a four-digit passcode, like 0131. Sam wants to reset the passcode such that the new passcode cannot have the digit 1 immediately followed by the digit 3. How many different passcodes can be formed?

A. 9700
B. 9701
C. 9702
D. 9703
E. 9704

Are You Up For the Challenge: 700 Level Questions
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Try similar but harder problem here: https://gmatclub.com/forum/a-locker-cod ... 34451.html
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset Updated on: 06 Oct 2020, 04:37
Originally posted by Vivor on 06 Oct 2020, 04:17.
Last edited by Vivor on 06 Oct 2020, 04:37, edited 1 time in total.
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Total combinations = 10^4 - 10^2*3 = 9700

Edit: Just noticed that I double-counted the combination '3131'

Total combinations = 10^4 - (3*10^2 - 1) = 9701
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset 06 Oct 2020, 04:20
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Number of passcodes that have 31 as first 2 digits= 1*1*10*10=100
Number of passcodes that have 31 as middle 2 digits= 10*1*1*10=100
Number of passcodes that have 31 as last 2 digits= 1*1*10*10=100

Number of passcodes that have 31 as first 2 digits and last 2 digits= 1*1*1*1=1

different passcodes can be formed such that the digit 1 immediately can't be followed by the digit 3 = 10000-100-100-100+1 = 9701

Bunuel
A smartphone uses a four-digit passcode, like 0131. Sam wants to reset the passcode such that the new passcode cannot have the digit 1 immediately followed by the digit 3. How many different passcodes can be formed?

A. 9700
B. 9701
C. 9702
D. 9703
E. 9704

Are You Up For the Challenge: 700 Level Questions
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Akp880
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset 06 Oct 2020, 04:30
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset the passcode such that the new passcode cannot have the digit 1 immediately followed by the digit 3. How many different passcodes can be formed?

A. 9700
B. 9701
C. 9702
D. 9703
E. 9704


Explanation:
Total number of arrangements = 10^4=10000

Invalid arrangements =
3 1 _ _ : 100
_ 31 _ : 100
_ _ 31 : 100

but here are 1 cases has been considered twice
31_ _ and _ _ 31 for locking combination 3131 will have same digit pattern

Thus total no of possible combination=10000-(100+100+100)-1
=9701

Hence B is the correct answer.
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset 06 Oct 2020, 04:48
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Bunuel
Bunuel
A smartphone uses a four-digit passcode, like 0131. Sam wants to reset the passcode such that the new passcode cannot have the digit 1 immediately followed by the digit 3. How many different passcodes can be formed?

A. 9700
B. 9701
C. 9702
D. 9703
E. 9704

Are You Up For the Challenge: 700 Level Questions

Try similar but harder problem here: https://gmatclub.com/forum/a-locker-cod ... 34451.html
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Hi Bunuel,

if I apply the reasoning in that post:

Total number of arrangements = 10^4

Invalid arrangements =
1 3 _ _ : 100
_ 1 3 _ : 100
_ _ 1 3 : 100

So, valid cases = 10^4 - 300 = 9700, but there is 1 case which was considered twice:
1 3 1 3 was considered once in 1 3 _ _ and once in _ _ 1 3, so we need to consider such cases only once = 1

So the total number of cases = 10^4 - 300 + 1 = 9701

Answer B

Is it right?
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Bunuel
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A smartphone uses a four-digit passcode, like 0131. Sam wants to reset 06 Oct 2020, 05:04
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daniformic
Bunuel
Bunuel
A smartphone uses a four-digit passcode, like 0131. Sam wants to reset the passcode such that the new passcode cannot have the digit 1 immediately followed by the digit 3. How many different passcodes can be formed?

A. 9700
B. 9701
C. 9702
D. 9703
E. 9704

Are You Up For the Challenge: 700 Level Questions

Try similar but harder problem here: https://gmatclub.com/forum/a-locker-cod ... 34451.html

Hi Bunuel,

if I apply the reasoning in that post:

Total number of arrangements = 10^4

Invalid arrangements =
1 3 _ _ : 100
_ 1 3 _ : 100
_ _ 1 3 : 100

So, valid cases = 10^4 - 300 = 9700, but there is 1 case which was considered twice:
1 3 1 3 was considered once in 1 3 _ _ and once in _ _ 1 3, so we need to consider such cases only once = 1

So the total number of cases = 10^4 - 300 + 1 = 9701

Answer B

Is it right?
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The OA will be automatically revealed on Tuesday 13th of October 2020 04:00:07 AM Pacific Time Zone.

I don't want to spoil the OA for others who might attempt the question but
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good job!
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