<p>7) In triangle ABC, AB=3, and D is the midpoint of line AC. What is the length of line BC.
- Basically, imagine an almost right triangle sitting on its hypotenuse. There's a line drawn from the uppermost corner going to point D (the midpoint). This creates an equilateral triangle (angles shown to all be 60), and an obtuse angle.
Note: The answers are also presented in radical form, but I just put the given decimals.
A. ~5.20
B. ~5.66
C. ~6.93
D. ~8.49
E. ~8.66</p>
<p>8) If q and r are positive numbers, what percent of (q+1) is r?
A. 1/100r(q+1)
B. q+1/100r
C. 100(q+1)/r
D. [(100r/q) + 1]
E. 100r/q+1</p>
<p>16) In an art class, there were just enough staples, rulers and glue bottles so that every 2 students had to share a staple, every 3 students had to share a ruler, and every 4 students had to share a glue bottle. If the sum of the number of staplers, rulers, and glue bottles used by the class was 65, how many students were in the class?
(Free-Response Question)</p>
<p>18) How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer?
(Free-Response Question)</p>
<p>Appreciate it guys, really trying to hone down on my failed attempts at the SAT.</p>
<p>18) How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer?</p>
<p>3 times an even integer, and a multiple of 5</p>
<p>So numbers satisfying these criteria are multiples of 5 and 6 (since 6=3*2). Note that all numbers that are 3 times an even integer are multiples of 6, and that the product of any positive integer times an even integer is even.</p>
<p>So you’re looking for numbers which are multiples of 5 and 6, or multiples of 30. There are 33 such numbers less than 1000.</p>
<p>I was actually able to recognize .625=5/8 part, but honestly had no idea of how to actually use that information. I guess I understand now.</p>
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<p>Right, that makes sense. I was basically making fractions from like the factors of five and multiplying it or, basically, something completely idiotic.</p>
<p>Honorlions, sometimes it is useful to write down equations that represent what you know, and then see if an idea for solving them occurs to you.</p>
<p>For example, with the question about staplers, rulers, and glue, we know how many students share each item, and we know that there are exactly enough of each to be shared.</p>
<p>So, if we let n be the number of students, s be the number of staplers, r be the number of rulers, and g be the number of glue bottles, we have
n = 2s
n = 3r
n = 4g
Also, we know that the total number of staplers, rulers, and glue bottles is 65.
s + r + g = 65.
Substitute for s, r, and g in terms of n.
This gives
n/2 + n/3 + n/4 = 65.
Solving for n gives n = 60.</p>
<p>I think the key to this one is to write down equations for what you know. Once you see them together, it becomes easier to figure out how to solve them.</p>
<p>For question 8), think about the procedure you would follow if you got r questions right on an exam with t total questions, and you wanted to find the per cent. What percent of t is r? Write down an equation for it.
Then, just adjust your label t to (q + 1).</p>
<p>I actually did come up with two similar equations, but like the other problem, didn’t know how to take the equations and get the answer I needed. But writing out’s certainly not a bad idea at all…</p>
<p>7) The description is somewhat confusing. Can you link to a picture? Also, why not give the answers as stated in the problem? The answers are sometimes a clue to the solution of the problem.</p>
<p>Answer would be A if I reconstructed the figure correctly after some confusion over its description. Was A) 3*sqrt(3) ? I hesitate to explain the solution when I can’t be sure what the figure looked like.</p>
<p>If your description is correct, there is more information you could find out about triangle ABC. </p>
<p>Since ABD is equilateral, AB = 3 and AC = 6. Also, BD and CD are equal to 3. Now look at the angle BDC (120) and determine Angle C = 30. All of those simple steps point to B being a 90 degrees angle. From there, you can find BC easily through the Pyth Theorem.</p>
<p>Uggh, seems like there’s no way for me to like upload the diagram. But at xiggi- if it were a pythag. thereom type question, I would’ve gotten it. It’s very obviously not a right triangle in the picture and the angles don’t even add up.</p>
<p>However, is the answer not 3sqrt3 or sqrt27? Is ABD not equilateral? Is AC not 6? And are you sure that angle A is not 60 degrees and angle C not … 30 degrees?</p>