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Can you all please help me on this math question before Saturday? This question seems to come up a lot and so I really want to know how to do it.

21. S is the sum of the first 100 consecutive positive even integers, and T is the sum of the first 100 consecutive positive integers. S is what percent greater than T?

Answer: 100%

Thanks for the help in advance.

By Legendofmax (Legendofmax) on Friday, October 08, 2004 - 04:54 pm: Edit

Hm if you want to do it mathematically:

(n(b + e))/2

Where n is the number of terms, b is the first number, and e is the last number. As long as the numbers are evenly spaced, this will work. For set S you have (100(2 + 200))/2, which is 10100.

For the second set: (100(1+100))/2 = 5050.

So set S = 10100, set T = 5050. If you notice, S is twice as great as T, so it is 100% greater (when you say 100% greater, that means taking the initial number plus the percent of that number).


If you want to know where I got that 200 from in the set S equation, it's because it wants the first 100 consecutive even integers. Term 1 = 2, term 2 = 4, term 3 = 6, term 4 = 8, etc. Notice how the value of the term is simply 2 * term number. That means the 100th term = 200.

By Bakk (Bakk) on Friday, October 08, 2004 - 06:04 pm: Edit

If you want to know where I got that 200 from in the set S equation, it's because it wants the first 100 consecutive even integers. Term 1 = 2, term 2 = 4, term 3 = 6, term 4 = 8, etc. Notice how the value of the term is simply 2 * term number. That means the 100th term = 200.

Remember that this is the SAT, that long problems always have a short answer, and that using your head will always beat the calculator, and all those mumbo-jumbo formulas. Look at the last part of the proposed answer and you'll see that the key to find 200 is none other than the key to a VERY simple answer and that it does not require all the extra work. If you realize that "Term 1 = 2, term 2 = 4, term 3 = 6, term 4 = 8, etc. Notice how the value of the term is simply 2 * term number.", you'll know that the pattern will work for 100 or 10,000 numbers, or 1,2 or 3 for that matter. It will always be 100%.

Doing well on the SAT does not require finishing problems but just picking the correct answer.