<p>Question 1: (Bluebook, page 400, #20)</p>
<p>The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set?</p>
<p>a) 25
b) 26
c) 50
d) 51
e) 52</p>
<p>I got the right answer, but I did it out the reallllly long way, and I'm sure there is a quick way to do this... which is why I'm asking. What I did was:</p>
<p>An=A1+(n-1)d
An= -25 + (n-1)
An= -26 +n</p>
<p>Then Sum formula</p>
<p>Sn=26=(n/2)(A1+An)
26=(n/2)(-25-26+n)
52=n(-51+n)
0=n^2 - 51n - 52</p>
<p>Then I used quadratic formula to solve for n... that is not the way to do these SAT problems, I think they should take 30 seconds max.</p>
<p>Question 2: (Bluebook, page 424, #6) )If x^2 + y^2 = 73 and xy=24, what is the value of (x+y)^2</p>
<p>a) 73
b) 97
c) 100
d) 121
e) 144</p>
<p>I did a really long and complicated way using the quadratic formula and got that y = 8 or 3, so whichever one it equals, the answer has to be d) 121. However, that way took me way to long as well, so any suggestions on how to do this quickly would be great.</p>
<p>Question 3: (Bluebook, page 426, #14)
If (a+b)^.5 = (a-b)^-.5, which of the following must be true</p>
<p>a) b = 0
b) a+b = 1
c) a-b = 1
d) a^2 + b^2 = 1
e) a^2 - b^2 = 1</p>
<p>Using guess and check/random logic I decided that the answer was A, which is wrong. How the heck do I do this?</p>