<p>1) 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?</p>
<p>A) 100%
B) 50%
C) 10%
D) 2%
E) 1%</p>
<p>The answer is A</p>
<hr>
<p>Circle C has radius r^.5
Squares with sides of length 1 are to be drawn so that, for each square, one vertex is on circle C and the rest of the square is inside circle C. What is the greatest number of such squares that can be drawn if the squares do not have overlapping areas?</p>
<p>A) 0
B) 1
C) 2
D) 3
E) 4</p>
<p>Answer is E.</p>
<hr>
<p>Both of these problems are from the Sunday May 2000 SAT and they're both level 5 problems.</p>
<p>For question number one, start writing out some terms and you’ll see a pattern:</p>
<p>Group S: 2, 4, 6, 8, 10
Group T: 1, 2, 3, 4, 5</p>
<p>Every term in S is double its corresponding term in T, so the sum of S will be double, or 100% greater, than the sum of T. </p>
<p>Sequence problems will always have shortcuts. The College Board says you can do the test without a calculator, so any time it looks like you’ll have to add up a whole slew of numbers, there must be a shortcut. Any time you have to compare sequences, write out the first 5 or so terms from each and you should see a pattern. </p>
<p>As for question 2, I don’t get what you mean by radius^.5. Let me know and maybe I can help.</p>
<p>@PrestigePrep</p>
<p>Why is it 100 % greater than Sum of T shouldn’t be less ?
Example:
2 + 4 + 6 + 8 + 10 = 30
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55</p>
<p>@Prestigeprep
Thank you so much!
It should be 2^.5, not r^5. I’m sorry if the typo confused you!</p>
<p>@GenericMath</p>
<p>The sum of S is greater than the sum of T because the former is all even integers from 0-200 whereas the latter is all integers from 0-100.</p>
<p>For the first one just list it out for the fast way. You will instantly notice that each term is doubled in the 0-200 even integer list so you know it will be double or 100% greater. Another way which I like is using a simple formula. By using this you always know your right just in case. Here is the formula:</p>
<p>number of terms ( (first term+last term)/2)</p>
<p>0-200 even integers</p>
<p>100( (2+198)/2)</p>
<p>100(200/2)</p>
<p>100(100)</p>
<p>10,000</p>
<p>0-100 consecutive integers</p>
<p>100( (1+99)/2)</p>
<p>100(100/2)</p>
<p>100(50)</p>
<p>5000</p>
<p>you can easily see that 10,000 is 100% greater than 5000.</p>
<p>For the second problem, its really simple. You know that the radius is 2^1/2, which is basicual squareroot 2. Well double that and you get the diameter which is 2 squarerooot 2. Since the squares cant overlap eacher other you know that only 2 will fit on the top half of the circle because each of their sides are 1. 1+1 =2 which is less than 2 square root 2. The same thing goes for the bottom half. Which means 2+2 = 4. There you have it. Really simple.</p>