question from official sat guide! help!

Test Preparation
1

<p>ok, i was doing section 9 of the first test and everything was fine except for this question that tripped me up. it wasnt hard but i ran out of time on it. the only way i could solve it was to plug in numbers, but that took more than a while, especially since i started with c, b, a, then d, and finally e which was the right answer. </p>

<p>is there a faster way to do this, or something recognizable that allows you to eliminate some of the choices instead of plugging in numbers??</p>

<p>page 426, #14</p>

<p>If (a+b)^1/2 = (a-b)^-1/2, which of the following must be true?
a) b=0
b) a+b=1
c) a-b=1
d) a^2 + b^2 = 1
e) a^2 - b^2 = 1</p>

2

<p>Solution:</p>

<p>Square both sides to get:</p>

<p>a+b = 1/(a-b)</p>

<p>Multiply by (a-b) on both sides:</p>

<p>a^2 - b^2 = 1</p>

<p>and the answer is choice E.</p>

3

<p>wow thanks!</p>

4

<p>here are some more questions that were a little hazy</p>

<p>1) M can complete a certain job working on her own in 9 hours, but while working with N the two can complete the same job in 6 hours. How many hours would it take for N to complete the job on his own?</p>

<p>a) 3
b) 4.5
c) 6
d) 9
e) 18 (this is the answer)</p>

<p>what is a general way to answer question like this? i've never learned how, especially if the answers are closer together.</p>

<p>2) How many different committees of 3 people can be selected from a group of 5 people?</p>

<p>a) 10 (this is the answer)
b) 15
c) 25
d) 60
e) 120 </p>

<p>any way to solve this other than write out all the possibilities? (which i tried and messed up)</p>

<p>3)Four lines can divide a rectangle into a maximum of how many nonoverlapping regions?
a) 8
b) 9
c) 10
d) 11 (this is the answer)
e) 16</p>

<p>i know it's something really really obvious, but i cant see it somehow.</p>

5

<p>if anyone has any questions post them in this thread. the questions here will probably be the hard obscure tricky ones which would be great help in review the final days before the SAT, because i think most people here dont have much trouble with the archetypal questions that appear on every single test, or at least not easy ones.</p>

6

<p>Please don't post those questions in CC. They are copyrighted. Look at the sticky.</p>

7

<h1>12, page 682...So simple, yet so confusing. The answer is (A) 0.</h1>

8

<p>1)</p>

<p>One thing you can do is approach this logically. Let's assume that N works at the same rate, and therefore takes 9 hours as well to perform the job alone. If the two work together, the time should be exactly half, or 4.5 hours, to complete the job. But the actual time is 6 hours, so we know that N works SLOWER than M, so the time alone for N must be greater than 9 hours. Choice E, 18 hours, is the only one that fits.</p>

<p>Alternatively, you can do some algebra:</p>

<p>M's rate can be solved using the equation:</p>

<p>rate x time = work
Let's call M's rate m:
m * 9 = 1 (1 complete job) m = 1/9
With the two working together, the equation is:
(m+n)*6 = 1 (where N's rate is n)
Put in m = 1/9, and solve for n:
n = 1/18
So working alone, N should take 18 hours to complete 1 job.</p>

<p>2)</p>

<p>There are three slots, or spaces, to assign. Additionally, order does not matter in this case, since once we have a given committee of 3 people, it doesn't matter what order they are in.</p>

<p>Therefore, you fill in the slots:</p>

<p>__ __ __ with
5 4 3
since we have 5 choices for the first slot, 4 choices for the second slot, and 3 choices for the third slot.
But you cannot forget that order does <em>not</em> matter, so you have to adjust this number. Namely, you divide the number by the number of ways three people can be arranged in three positions:
3x2x1</p>

<p>Therefore, the total number of combinations is:</p>

<p>(5<em>4</em>3)/(3<em>2</em>1) = 10, choice A.</p>

<p>3)</p>

<p>Divide the rectangle in such a way that each subsequent line intersects every other line inside the rectangle (and no three lines intersect all at the same point). Then, simply count the number of regions. You should have 11, choice D.</p>

<p>Using logic, you can probably eliminate choice E at a glance, since the largest answer is often a trap in a question that asks for a <em>maximum</em>.</p>

9

<p>This is simply a number theory question. Work backwards, with n = p first, since both equations must be true at the same time. So n = p; for any nonzero value of p, 3p will be different from n, contradicting the first equation. The only way BOTH can be true is if p = 0, because 3p is STILL zero, making it equal to n. The trap answer is E.</p>

<p>Alternatively, you can just plug in the answers, and see which one works.</p>

10

<p>thanks godot</p>

11

<p>Yes-Thanks Godot.</p>