# Psat math questions

<p>THE VARIOUS AVERAGES (ARITHMETIC MEANS) OF THREE OF THE FOUR NUMBERS, C, D, E, AND F ARE CALCULATED, AND ARE ARRANGED FROM THE GREATEST TO LEAST AS FOLLOWS.</p>

<p>THE AVERAGE OF C, D, AND E</p>

<p>THE AVERAGE OF D, E, AND F</p>

<p>THE AVERAGE OF E, F, AND C</p>

<p>THE AVERAGE OF F, C, AND D</p>

<p>A) c>D>F>E
b) d>F>E>C
c) d>e>c>F
d) E>C>F>D
e) E>D>C>F</p>

<p>Which of the following could be lengths of a triangle?
a)2,3,1
b)3,6,9
c)3,10, 6
d)4, 7, 2
e)7, 8, 9</p>

<p>The area of the bottom, side, and front of a rectangular box are r, s ,and t square inches, respectively. What is the volume in cubic inches</p>

<p>A train 200 meters long was traveling at a constant ate of 20m.s through a tunnel, it took 7 seconds from the time tht. the front of the train entered the tunnel until the time that the back of the tain left the tunnel. What is the length of the tunnel in meters
A, 1000
B, 1200
C, 1200
D, 1600
E 2000</p>

<p>THANKS</p>

<ol>
<li>E</li>
<li>E</li>
<li>in terms of what?</li>
<li>Assuming those are right numbers, the train only traveled 140 meters, which is impossible for it to have traveled the tunnel's distance and one length of the train in only 140 meters. I'm going to assume you mean at 200m/s which makes it 1400m traveled - 200m train = tunnel 1200m long. This makes the answer B or C (another typo).</li>
</ol>

<p>1) The relationship among the averages can be translated to...</p>

<p>(C+D+E)/3 > (D+E+F)/3 > (E+F+C)/3 > (F+C+D)/3
or
C+D+E > D+E+F > E+F+C > F+C+D</p>

<p>We can look at two inequalities at a time to determine the relationship between individual numbers.</p>

<p>C+D+E > D+E+F
is the same as
C > F</p>

<p>D+E+F > E+F+C
is the same as
D > C</p>

<p>E+F+C > F+C+D
is the same as
E > D</p>

<p>so E > D > C > F</p>

<p>I gtg but I'll do the other two if no one else has</p>

<p>2) The triangle inequality theorem states that the sum of the lengths of two sides of any triangle must exceed the length of the third side. A, B, C, and D each have instances in which the sum of two sides is equal to or less than a third side, which is not possible. E is correct.</p>

<p>3) Let's let the base length be L, base width be W, and height be H.</p>

<p>bottom area = r = LW
side area = s = HW
front area = t = LH</p>

<p>the volume of the box is LWH. How can we put r, s, and t in terms of L, W, and H? Multiply</p>

<p>rst = LW * HW * LH
rst = L^2 * H^2 * W^2
so
LHW = sqrt(rst)</p>

<p>Hence the volume (LWH) is sqrt(rst)</p>

<p>4) I think you meant 70 seconds (1 min 10 seconds is what the original problem says), not 7 seconds.</p>

<p>Let's look at everything from the perspective of the front of the train. It takes 70 seconds for the front of the train to travel through the tunnel and 200 m back out. The train is traveling 20 m/s, so the total distance it travels in that time interval is 70*20 = 1400 m.</p>

<p>Tunnel + 200 m = 1400 m
Tunnel = 1200 m</p>

<p>thank you so much Jamesford. You give great explanations which are super helpful</p>

<p>Thanks!!</p>

<p>Sent from my iPod touch using Tapatalk</p>

<p>Here is another really clever way to figure out the one with the averages. One of my students came up with this:</p>

<p>Look at the first group on the list: C, D, E. If it has the highest average, it must be because they have left off the SMALLEST number. So now we know F is smallest.</p>

<p>The next highest grouping is D,E,F which leaves out C, so C is the next smallest after F.</p>

<p>Then, E F C leaves out D so D is third smallest.</p>

<p>Finally F C D leaves out E and has the smallest average, so E is largest of the numbers.</p>

<p>^ That's what I did.</p>