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three-digit code

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gmat740 MBA Student
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three-digit code

Post Sat Aug 08, 2009 9:26 pm
A three-digit code for certain logs 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

OA-B
IMO-A

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prindaroy Master | Next Rank: 500 Posts Default Avatar
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Top Reply
Post Sat Aug 08, 2009 9:56 pm
Case 1:

8 possibilities for 1st number, number 2 is 1, 10 possibilities for 3rd number

so 8 * 10 = 80

Case 2:

8 possibilities for 1st number, number 2 is 0, 9 possibilities for 3rd number

so 8 * 9 = 72

so total = 80 + 72 = 152 or B

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Thanked by: sellaia, rawatar

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