<p>These questions are from the Dr. John Chungs SAT Math Book, but I don’t really understand his explanation to these question.
All of these questions are from Test 1 section 3.</p>
<h1>7 - ( You will need the book for this one, so ccer’s who have the book can u help me out)</h1>
<p>The question si which of the following graphs shows a relationship in which y is directly proportional to x?
A. its a parabola
B. the line goes from left to right so i guess its a positive correlation
C. A negative correlation
D. Is a horizontal line at like (0,2)
E. Is a vertical line at like (2,0)</p>
<p>These questions are from the Dr. John Chungs SAT Math Book, but I don’t really understand his explanation to these question.
All of these questions are from Test 1 section 3.</p>
<h1>9 - To arrive on time, a ship needs 5 hours to complete a voyage. If the ship must arrive in 4 hours, by what percent must the speed of the ship be increased?</h1>
<p>A. 15%
B. 20%
C. 25%
D. 27%
E. 30%</p>
<p>His explanation is that you do d/5 -d/4 OVER d/5 (this is the percent change formula btw) and he says lets plug in d as 20 because its a multiple of 4 and 5. So he does 20/5 - 20/4 which is 1/4 which as a percent equal (C) 25%.</p>
<p>But my question is why cant I convert the hours into minutes so, 5<em>60=300, 5</em>4=240, and then I subtract the difference, which would be 60 and then divide 60 over 300, and then this would give me 20%?? So why cant I do that, why is it wrong, and when DO i Know when I should convert hours into minutes, and when I should be putting it basically into a fraction, and then using the percent formula?</p>
<p>These questions are from the Dr. John Chungs SAT Math Book, but I don’t really understand his explanation to these question.
All of these questions are from Test 1 section 3.</p>
<h1>11 - A certain job can be done in 20 hours by 4 people. How many people are needed to do the same job in 10 hours?</h1>
<p>A. 2
B. 4
C. 6
D. 8
E 10</p>
<p>He uses the inverse proportion: xy=k. 20<em>4= 10</em>x, so then x=8</p>
<p>I know almost nothing about inverse proportion, direct variation and indirect variations and what their formulas are. Can someone please explain to me what these are and ther formulas, and when do i use them. Is it lke when in the question they give you the hint of where hey day direct variation or indirect variation in side the question?</p>
<p>x and y are directly proportional if x/y is constant. For example suppose x and y are directly proportional and x = 2 when y = 3. Then If x = 6, what is y?</p>
<p>Well from the given, x/y = 2/3. Since this is constant, when x = 6, y must be 9. This is because 6/9 = 2/3.</p>
<p>You can solve this more formally by cross multiplying:</p>
<p>x and y are inversely proportional if xy is constant. For example suppose x and y are inversely proportional and x = 2 when y = 3. Then If x = 6, what is y?</p>
<p>Well from the given, xy = 2<em>3 = 6. Since xy is constant, when x = 6, y must be 1. This is because 2</em>3 = 6*1.</p>
<p>You can solve this more formally as follows:</p>
<p>20<em>4=10</em>y
80 = 10y
Dividing both sides by 10 yields y = 8.</p>
<p>Here’s one additional hint to decide if you have a direct or inverse relationship: just ask yourself “as I increase one variable does the other increase or decrease?” If it increases the relationship is direct. If it decreases the relationship is inverse.</p>
<p>In this problem, clearly as you increase the number of people, the amount of time to finish the work DECREASES. That is why this relationship is inverse.</p>
<p>Whether you work in hours or minutes is irrelevant - you should get the same answer. Your mistake is that you’re computing a percent change of time. But the question is asking for percent change of SPEED. Speed is equal to distance/time.</p>
<p>This is a particularly difficult question that is asking you to first convert time to speed, and then to compute a percent change. </p>
<p>I haven’t seen anything this difficult on an SAT. If it does (or did) appear it would certainly be one of the last couple of questions in the section. You should ONLY be studying questions of this difficulty level if you are going for an 800.</p>
<p>The graph of a direct relationship is a line that passes through the origin. Conversely, if a line passes through the origin, then this is the graph of a direct relationship.</p>
<p>Just for your information, an inverse relationship has a graph which is a hyperbola.</p>
<p>Your description doesn’t seem to match up with the picture here. But I can tell you that if you draw the altitude from a vertex of an equilateral triangle to the base it gets split into two 30, 60, 90 triangles. </p>
<p>This is because in an equilateral triangle (or even any isosceles triangle), the altitude, median, and angle bisector are all equal. Thus, the altitude splits one 60 degree angle into two 30 degree angles.</p>
<p>In general, when dealing with equilateral triangles you are very likely going to be using the special 30, 60, 90 triangle - NEVER a 45, 45, 90 triangle.</p>
<p>Yes sir… I am shooting for an 800 on the math section…so I’m working on all types of math questions (btw…your explanations are really helping) thanks and please continue to help me and others.
thanks again</p>
<p>I’m guessing that one of them is a horizontal or vertical line. I believe that these two lines technically fail the definition of directly proportional because 1 of the variables is constantly 0. Thus it does not increase as the other variable increases.</p>
<p>For example, a horizontal line has equation y = 0. This means that as x increases, y does not (it stays 0). Thus TECHNICALLY the definition of directly proportional is violated. </p>
<p>This is an incredibly sneaky technicality which I have never seen come up on an actual SAT.</p>
<p>This is problem is not very hard nor confusing. There are tons of ways to solve it, in about ten seconds. This is a simple percentage in or out question that 5th graders tackle with ease. </p>
<p>No calculation is needed, except to ask yourself this:</p>
<p>By how much do I need to increase 4 to arrive at …5. Is 5 minus 1 hard? Is 1 divided by 4 hard! It has to be 25 percent. </p>
<p>Another way is to do 5/4 - 1 and express it in percentages … meaning 125/100 - 100/100 = 25/100. </p>
<p>Really, the key is not to let a problem confuse you with its terms. Ratios are ratios and they work directly and indirectly.</p>
<p>Xiggi – I think this not the first time that I’v responded to one of your posts with this point: your answer is totally correct – but many people won’t think of it. So once again, I am going to recommend…MAKE UP SOME NUMBERS!</p>
<p>For example, since we are dealing with 5 hours and then 4 hours, I am going to make the trip 100 miles. Then, the 5 hour trip must be at 20 mph. And the 4 hour trip must be at 25 mph, an increase of 5 mph – which is 1/4 of 20 or 25% of the original speed.</p>
<p>I know that your method is quicker, but only after you’ve had the insight. I find that making up numbers is a really useful strategy while you are still waiting for insight to strike. And often, the concrete numbers lead you to the right answer even though the insight never came…</p>
<p>Pckeller, do you want to know something interesting, and perhaps funny? I agree with you! And, I did make up numbers. Here we go:</p>
<p>Fwiw, when a problem is posted, I always try to answer it “on the fly” which means with a very small paper and a pencil. Before suggesting an answer, I look how I solved it. In this case, I did it three times. </p>
<p>My first solution was … tada to pick the number 100. Why because I always like 100 when we have percentages. The solution that I had was quick and showed 25 percent.</p>
<p>Then I did it again, but used the number 20 because it is easy with 4 and 5. Of course, since only the numbers change, the final results was still 20 to 25 (again 25 percent increase, duh)</p>
<p>Then I did it with simply looking at the reverse ratios of 5 and 4, with again the same result. Among the solutions, I liked the last one for its simplicity. Again I DID the 100 first, probably out of instinct. </p>
<p>Fwiw, here would your solution had you used 5 as D.</p>
<p>For example, since we are dealing with 5 hours and then 4 hours, I am going to make the trip 5 miles. Then, the 5 hour trip must be at 1 mph. And the 4 hour trip must be at 1.25 mph, an increase of .25 mph – which is 1/4 of 1 or 25% of the original speed.
:)</p>
<h1>1) Pick a random rate for the 5hrs part. I chose 10mi/hr.</h1>
<h1>2) Set up a proportion: (10miles/1hr)=(x miles/5hrs) Cross multiply. Answer: 50 miles. This is the distance traveled.</h1>
<h1>3) Overall, you’re going to have to travel 50 miles, so now set up another proportion with what you have to find the new rate: (4hrs/50miles)=(1hr/xmiles). Answer: 12.5</h1>
<h1>4) Now, think “12.5 is what percent of 10” –>12.5=(x/100)10 x=125 So, 25% INCREASE.</h1>