  # SAT Math Question Help!!!

<p>Hello~ I've got a few math questions, and it would be really wonderful if I could get an answer + explanations from one of the math geniuses out there. Thanks!</p>

<p>Blue book; test 1; section 6; question 5 (p.408)</p>

<p>On the disk (of 6 equal sections) shown above, a player spins the arrow twice. The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of the sector where the arrow stops after the second spin. On every spin, each of the numbered sectors has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a/b is greater than 1?</p>

<p>a) 15/36
b) 16/36
c) 18/36
d) 20/36
e) 21/36</p>

<p>The answer is a. Why is that?</p>

<p>Blue book; test 1; section 9; question 14 (p. 426)</p>

<p>If (a + b)^1/2 = (a - b)^-1/2, 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>and... Blue book; test 1; section 9; question 16 (p. 427)</p>

<p>Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z?</p>

<p>a) x + y + k
b) x + y - k
c) x + y + 2k
d) x + y - 2k
e) 2x + 2y - 2k</p>

<p>Thanks for helping out!</p>

<p>On the disk (of 6 equal sections) shown above, a player spins the arrow twice. The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of the sector where the arrow stops after the second spin. On every spin, each of the numbered sectors has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a/b is greater than 1?</p>

<p>a) 15/36
b) 16/36
c) 18/36
d) 20/36
e) 21/36</p>

<p>There are 36 possible outcomes, so the denominator will be 36.
We are interested in the outcomes where a > b (so a/b > 1)</p>

<p>6-5, 6-4, 6-3, 6-2, 6-1 makes 5
5-4, 5-3, 5-2, 5-1 makes 4
4-3, ... makes 3
3-2, 3-1 makes 2
2-1 makes 1</p>

<p>Add 'em up for 15 desirable outcomes; divide by 36; get 15/36 (which is properly 5/12)</p>

<p>if (a + b)^1/2 = (a - b)^-1/2, 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>Multiply both sides by (a - b)^1/2 to get
(a^2 - b^2 )^1/2= 1</p>

<p>Then square to get
a^2 - b^2 = 1</p>

<p>Rationalizing the denominator is always a good starting strategy.
Note also the restriction that a must be greater than b.</p>

<p>Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z?</p>

<p>a) x + y + k
b) x + y - k
c) x + y + 2k
d) x + y - 2k
e) 2x + 2y - 2k</p>

<p>Let X' be the set X less the k common members
Let Y' be the set Y less the k common members</p>

<p>The size of X' is x - k
The size of Y' is y - k</p>

<p>Z, by inspection, is the union of X' and Y' and its size is x + y - 2k</p>

<p>You've already gotten good answers, but just FYI for the future - check the Consolidated</a> Blue Book Solutions thread for links to previously discussed problems</p>

<p>Wow, thanks a lot my\$0.02 and tanman!</p>

<p>It really helped out with the solutions!!!</p>