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Earn +20 ptsQ: How many positive integers are there less than 10000?
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How many integers are between 1000 and 10000?
9000 integers.
How many positive integers less than 100 have an odd number of positive divisors?
The squares -- nine of them.
How many positive integers less than or equal to 100 have a prime factor that is greater than 4?
There are 80 such integers.
How many positive integers less then 50 are multiples of 4 but not multiples of 6?
10
How many pairs of consecutive integers have a product less than 10000?
n(n+1) <10000 so n is close to square-root of 10000 which is 100. Obviously 100x101 is too much, but 99x100 is OK
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