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# What did I do wrong? (GRE Math)

Go to solution Solved by Thalia,

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How many 3-digit positive integers are odd and do not contain the digit 5?

I got 320, but the answer that is given in 288. I just realized that I missed some numbers, but I ended up with 280.

I would greatly appreciate if someone could explain why the answer is 288.

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• Solution

There are 900 3-digit numbers (100-999)

Half of them are odd: 900/2=450

There are 9 groups of hundreds (100s, 200s, etc)

Ignoring the 500s for the moment, each group of 100 has 14 odd numbers with a 5 (5, 15, 25, 35, 45, 51, 53, 55, 57, 59, 65, 75, 85, 95)

8 (groups of 100 ignoring the 500s) * 14=112

450-112=338

All of the numbers in the 500s have a 5. Half of them are odd: 100/2=50

338-50=288

Edited by Thalia
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Thank you much. I must have done some miscounting along the way.

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• 2 years later...

Its a three digit no., so let's say it is ABC (C - units place, B - tens place, A - hundreds place)

possible values for each:

C: 1, 3, 5, 7, 9 [4 possible values]

B: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 [9 possible values]

A: 1, 2, 3, 4, 5, 6, 7, 8, 9 [8 possible values]

So, possible number combinations to give required 3 digit nos. :4 x 9 x 8 = 288

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