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A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5,

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

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A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

(A) 144
(B) 152
(C) 160
(D) 168
(E) 176

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[Reveal] Spoiler: OA

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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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The first digit can be filled in 8 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 8 * 1 * 10 = 80

Case 2 -
If second digit is 0,Third digit can take 9 values ( Third digit can't be zero)
number of codes = 8 * 1 * 9= 72

Total number of codes = 152

Answer B
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A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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Bunuel wrote:
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

(A) 144
(B) 152
(C) 160
(D) 168
(E) 176

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Total digits = 10

Code digits = X Y Z

Now Slot X can take 8 values except 0 & 1

Slot Y can take 1 value, either 0 or 1

Then, if Slot Y takes digit "0" then slot Z can only take 9 digits (It can't take digit zero)

If slot Y takes digit "1" then slot Z can take all digits i.e, all 10 digits.

Therefore possible different codes are = 8*1*9+8*1*10 = 72+80=152 Option B

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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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Bunuel wrote:
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

(A) 144
(B) 152
(C) 160
(D) 168
(E) 176

Kudos for a correct solution.


Split it up in 2 scenarios:

First scenario, second digit = 1: 8*1*10 = 80 (The first digit has 8 possible numbers, the second is one and the last can be any number since the second is one)
Second scenario, second digit = 0: 8*1*9 = 72 (The first digit has again 8 possible numbers, the second is 0 in this case and therefore the last can only have 9 other digits)

Since this is an "OR" relationship, add the two 80+72 = 152

Answer B
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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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Bunuel wrote:
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

(A) 144
(B) 152
(C) 160
(D) 168
(E) 176

Kudos for a correct solution.


we have two cases here

case 1 when 2nd digit is 0, then we can have 9 different digits in third place and 8 different digits on 1st place

no of possibilities = 9 * 8 = 72

case 2 when 2nd digit is 1, then we can have 10 different digits in third place and 8 different digits on 1st place

no of possibilities = 10 * 8 = 80

total = 72 + 80 = 152

Answer choice B

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

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New post 08 Nov 2015, 08:17
Result is difference of all possible choices, minus the choices where second digit is 0 and third digit is 0.

1)All choices

On the first place you can have 8 different digits. on second you can have 2 digits and on the third you can have 10 digits.
So, 8*2*10=160

2)Second and third places are 0

On the first place you can still have 8 different digits, on the second you can have only one possible coice (0) and on the third you again have only one possible choice (0).
So, 8*1*1=8

Difference is 160-8=152
Answer B.

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

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Taking two cases :

1st where the center digit is 0 ; no of possibilities = 8*1*9

2nd where the center digit is 1; no of possibilites = 8*1*10

Total = 8*1*19 = 152
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Last edited by rishi02 on 24 Sep 2016, 14:26, edited 1 time in total.

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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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Total possibilities : 8 x 2 x 10= 160
Possibilities with zero in second and third places are 8x1x1=8
Ans 160-8 = 152

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

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Hi everyone,

This is my video explanation of the question. Hope you enjoy!



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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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Bunuel wrote:
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

(A) 144
(B) 152
(C) 160
(D) 168
(E) 176

Kudos for a correct solution.

1. Number of possibilities for the first digit is 8
2. Case 1 is when the second digit is 0, number of possibilities for the third digit is 9, for a total of 8*9
3. Case 2 is when second digit is 1, number of possibilities for the third digit is 10, for a total of 8*10
4. Total number of possibilities is (2) + (3) =152
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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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New post 22 May 2017, 12:07
First Digit can be: 2,3,4,5,6,7,8,9
Second Digit can be: 0,1
Third Digit can be: 0,1,2,3,4,5,6,7,8,9


Case 1: If Second Digit is 0

8 * 1 * 9 = 72

Case 2: If Second Digit is 1

8 * 1 * 10 = 80

Total = 72+80 = 152

Answer is B

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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

(A) 144
(B) 152
(C) 160
(D) 168
(E) 176

answer b
8*1*9+8*1*10 = 72+80=152

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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, [#permalink]

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New post 12 Sep 2017, 03:24
First place can take 8 digits, second digit can take 2 digits(0,1) and third place can take any of the digits.
2 cases possible :
Case 1 : When zero is present in second place - 8*1*9 = 72
Case 2 : When 1 is present in second place - 8*1*10 = 80

Total = 152

Option B

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Re: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5,   [#permalink] 12 Sep 2017, 03:24
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