<p>Here are two problems for the PSAT I am finding difficulty with:</p>
<li><p>There’s a 2x2x2 cube, and a line running diagonally through it.
How do you find the length of this diagonal? </p></li>
<li><p>Point P is in the center of one face of a cube and point Q is the center of the opposite face. If the length of the shortest possible path from P to Q is
2 times the square root of 2 centimeters, what is the volume of the cube in cubic centemeters?</p></li>
</ol>
<p>1.the length of the line is 4+2Xsquare root 2</p>
<p>2.i think the answer is (square root 2)^3 cm^3</p>
<p>Isn't #1 2(sqrt3)?
[quote]
running diagonally through it
[/quote]
this alludes to the long diagonal, the one that cuts through the cube.
use the formula</p>
<p>a^2+b^2+c^2=d^2
or if you don't want to use that formula, its simply x(sqrt3), with x being the side.</p>
<h1>2 is 16(sqrt2)</h1>
<p>You know that the shortest distance from P to Q is 2(sqrt2) aka the side.
so just plug it into the volume formula.</p>
<p>(2(sqrt2))^3= 16(sqrt2)</p>
<p>Thanks!
Here's a geometry one I don't get:
In the xy coordinate plane system, a circle has center C with coordinates (6, 2.5). This circle has exactly one point in common with the x axis. If the point (3.5, t) is also a point of the circle, what is the value of t?</p>
<p>Answer should be 5/2</p>
<p>The above problem probably won't be on the SAT. I've never seen the circle equation required for the SAT and as far as I can see, your problem requires it (unless there are multiple choice then maybe).</p>
<p>First, since it touches the x-axis, the y will be the radius: radius = 2.5</p>
<p>Plug into the circle equation:</p>
<p>(x-6)^2+(y-2.5)^2 = 6.25</p>
<p>Plug in your x = 3.5 and you get</p>
<p>(y-2.5)^2 =0</p>
<p>y = 2.5 to solve.</p>
<p>an easier way would be to plug both coordinates into the distance formula.
The distance from (6, 2.5) and (0, 2.5) should be the same from (6, 2.5) and (3, X)</p>
<p>a calculator program would have solved this problem in 10 seconds :]</p>
<p>@lolilaughed:
This question was actually on the the 2007 PSAT (or official practice one...I forgot which).</p>
<p>^ Wow! I'm surprised; I guess the SAT intended you to use the distance formula then.</p>
<p>How about this one?
In triangle ABC, if a>b>c, which of the following must be true?
I. 60<a<180
II. 45<b<90
III. 0<c<60
(A)I only
(B)II only
(C)I and III only
(D)II and III only
(E)I, II, III</p>
<p>C . </p>
<p>10 char.</p>
<p>It's E, but I don't know how it works.</p>
<p>Oh right, wow. Heres what i did(if i had done it more carefully) . We know that theres 180 degrees in a triangle, so the biggest angle(A) cant be 180 because then we wouldnt have any other angles. It cant be smaller than 60 because then the other angles would be bigger. </p>
<p>number 2. B cant be 180, but it can be 90. Or can it? No of course not because if B was 90, then A wouldnt be bigger than B b/c if C was 1, then A wuld be 59. </p>
<p>Number 3.</p>
<p>C can't be 180 or 90, it has to be smaller. Can it be 60? No because if it was 60 then the smallest B can be is 61, and that wuld make A the smallest . Does 59 work? 59+60+61 ... Yes it does. And it cant be 0 because...that wouldnt be an angle.</p>
<p>This process takes about a min or less, just remmber to check by plugging in a few numbers. Theres probably a faster way</p>
<p>
Since the circle is tangent to the x-axis its r=2.5.
The vertical line passing through (3.5,t) is 6-3.5=2.5 from the center.
That means the line is tangent to the circle.
t=[y-coordinate of C]
t=2.5</p>
<p>
a+b+c=180</p>
<p>I. If 60≥a>b>c then
60+60+60>a+b+c ------- false, so 60<a. I must be true.</p>
<p>II. a>b≥90 can't be true because then a+b>180, so b<90 indeed.
But - a counterexample to 45<b:
{a,b,c}={177,2,1}, so II is false.</p>
<p>III. If a>b>c≥60 then
a+b+c>60+60+60 ------- false, so c<60. III must be true.</p>
<p>The answer is C.
Quix's intuition was right. ;)</p>