How many four-digit counting numbers are greater than 7000 or are even

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try...principle of counting: the total possibility is the product of the possibilities for each digit(use multiplication for 'and' and addition for 'or' in any statement)first N1: numbers greater than 7000 for the thousands: the possible digits are 7,8,9... so there are three. for hundreds, tens and units digit: 0-9 so ten.N1 = 3*10*10*10 = 3,000N2: even four-digit numbers less than 7000 for the thousands: 1-6 and thus five for hundreds and tens: ten again for units digit: 0,2,4,6,8 (since it must be even) so five.N2 = 5*10*10*5 = 2,500the numbers you want are either numbers greater than 7000 or the even numbers less than 7000.N1 and N2 have no common numbersthus the total possibility is N1 + N2 = 5,500Edit: thanks Leltos, consider N1 as the numbers greater than or equal to 7000, so N1 is still correct.Then my mistake is in N2, change the first "5" to "6" then we have the correct answer. Not sleeping is bad for mathematics related questions. Sorry.

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Dave's 2nd answer is close, but he forgets that both 1000 and 7000 are counted. There are 3001 even numbers from 1000-7000 inclusive.2999 + 3001 = 6000.d_c makes a similar mistake, counting the numbers 1-6 as 5 instead of 6. Further, he includes 7000 with numbers greater than 7000, but later excludes it from even numbers cancelling out his error. N1 is 1 too big, N2 is 501 too small.=> N1 = 2999, N2 = 3001, total = 6000.

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First of allthere are 3000 counting numbers between 7000 and 10,000 one half of these are even and one half are odd therefore 1,500 are even and 1,500 are odd

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