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Counting Numbers -3

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by GmatKiss » Sat May 19, 2012 1:05 pm
3)Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90
(B) 82
(C) 80
(D) 45
(E) 36
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by neelgandham » Sat May 19, 2012 1:32 pm
Total number of three-digit numbers greater than 700 = 299.

Total number of three-digit numbers greater than 700 and with all distinct digits = 3*9*8 = 216. (First digit can take 3 values: 7, 8 or 9 and the second digit can take 9 values and third digit can take 8 values.

Total number of Numbers greater than 700 and with all digits the same = 3 (777, 888, 999).

Total number of Numbers with two digits equal to each other and the remaining digit different from the other two = Total number of three-digit numbers greater than 700 - Total number of three-digit numbers greater than 700 and with all distinct digits - Total number of Numbers greater than 700 and with all digits the same

Total number of Numbers with two digits equal to each other and the remaining digit different from the other two = 299-216-3=80.

Answer Choice C.
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