Set X consists of the first 100 positive even integers. Set

Hi All,

We're told that Set X consists of the first 100 positive EVEN integers and Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with NO repeat elements, we're asked for the sum of all unique terms in the new set. This question involves 'bunching' and requires some Arithmetic.

To start, we can find the sums of Set X and Set Y without too much trouble:

Set X includes the EVEN integers from 2 to 200, inclusive (2, 4, 6, ...... 198, 200). We can 'pair' terms into pairs of 202 (re: 2 + 200, 4 + 198, etc.). This will gives us 50 pairs of 202, which totals (50)(202) = 10,100

Set Y includes the multiples of 5 from 5 to 500, inclusive (5, 10, 15, ..... 495, 500). We can 'pair' terms into pairs of 505 (re: 5 + 500, 10 + 495, etc.). This will gives us 50 pairs of 505, which totals (50)(505) = 25,250

When combining these two sets, there WILL be duplicates though - all of the multiples of 10 from 10 to 200, inclusive will be in BOTH sets. We're told NOT to count the duplicate entries though, so we would have to subtract one of each of those terms from the total. Again, we can 'bunch' the numbers into 'pairs' of 210 (10 + 200, 20 + 190, etc.). This will gives us 10 pairs of 210, which totals (10)(210) = 2100.

Total = 10,100 + 25, 250 - 2100 = 33, 250

Final Answer: A

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Rich