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Of the three digit numbers greater than 500, how many have exactly one

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Of the three digit numbers greater than 500, how many have exactly one [#permalink]

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New post 13 Dec 2017, 06:11
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C
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E

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Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

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Re: Of the three digit numbers greater than 500, how many have exactly one [#permalink]

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New post 13 Dec 2017, 06:22
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JackMasterNone wrote:
Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

Source: Expert's global practice tests


Three-digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.

We need to calculate B. B = Total - A - C

The number of three-digit numbers which are greater than 500 is 499 (from 501 to 999, inclusive).
A. all digits are distinct = 5*9*8 = 360 (first digit can have only five values 5, 6, 7, 8, or 9);
C. all three are alike = 5 (555, 666, 777, 888, 999).

So, 499 - 360 - 5 = 134.

Answer: A.

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Hope it helps.
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Re: Of the three digit numbers greater than 500, how many have exactly one   [#permalink] 13 Dec 2017, 06:22
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