<p>Hey everyone,</p>
<p>I'm back with some more difficult questions haha</p>
<p>Can anyone explain how to do these questions?</p>
<p>Thanks!</p>
<p>Question #20 - top of right column. Answer is A. You have a group of kids. Now, two variables need to be the same, so when they add up together, they need to be less than 30. That eliminates all but A and B. Now, you need to consider that the other amount is triple that; so multiply each by 3. 27 and 18. You can’t fit that number and then 27 together. So, B goes. You have 18 kids taking one language, 6 taking the other, and then 6 in the middle. That totals 30 kids. :)</p>
<p>Question #15 – If each is equal to 1 (the little segments) we can assume that the diameter of the whole circle is 6. The shaded circle will then have a diameter of 5. Area is pir^2. So, 6.25p. Now, we need to get the area of the C circle – which is 4. Or 4pi. Subtract 6.25pi from 4pi and you get 1.25pi. Which is equal to choice C. 5pi/4. :)</p>
<p>Question #20, left column: If each circle is 1, then the length from the center of one circle to the center of the one next to it is 1, as well. The radius would be .5. And since you can ballpark it, as for it is drawn to school, you can assume that half of the small circle is .25. but, you need to double that (it’s only half) to .5 – so Choice B.</p>
<p>Question #12 is not so bad. Simply play with the answers. Start with A. </p>
<p>If y = 5, then x = 4. They are equally spaced apart. So, that would mean 2x would have to be 8. But, no. It’s not. It’s 7. Eliminate A.</p>
<p>If y = 6, that means there is an increase of 1.5 each time. So, x = 4.5. 2x would then be 9. If you go from 6 to 7.5 and then to 9. That fits. </p>
<p>Choice B is your answer.</p>
<p>for #19 just pick numbers.</p>
<p>let y=3</p>
<p>x(3)=x+(3)
3x=x+3
2x=3
x=3/2 or 1.5
only the range in choice D contains 1.5</p>
<p>That’s what I did, initially. But if you plug in another number - say, 1.25. It won’t work.</p>
<p>1.25 * 3 = 3.75
1.25 + 3 = 4.25</p>
<p>But, then again, none of the answers ever get that close to working…</p>
<p>yeah but in the problem it says y>2</p>
<p>Yeah, let y = 3 and then x = 1.25.</p>
<p>I am not understanding the left column #20 logic at all…Can somebody else explain that please?</p>
<p>I did the pythagoran theorem for the diagonal of the square, got root 32, figured that the space between the large corner circles and the actual square corner was about half of the radius, or .5, and subtracted 1 from root 32. Then I subtracted the two diameters equaling 4. Finally, I divided that by 2 and got .328, which should be around the radius of the small circle…but apparently not…</p>
<p>^^ sasquatch i think estimating the space between the corner circles and the square corner is less than .5 (its more like .4ish)</p>
<p>For # 15 6.25pi- 4pi is 2.25 so answer is 9/2.<br>
For the 4 circles, I drew a square using each center point as a corner. That box has sides of 2. Then I drew the diagonal. The diagonal is 2 /2. Subtract the radius of the 2 larger circles which are each 1. So 2/2 - 2 for diameter of small circle. Factor 2( /2 -1) Divide by 2 to find radius of the small circle. I got /2 -1 for the answer. Answer D</p>
<p>Thanks Yankee, now I get it perfectly.</p>
<h1>15 should be 9/4 not 9/2.</h1>
<p>For number 19 on the right, I think I might be able to shed some light…</p>
<p>I’d like to think of it as a limit, sort of. First, plug in 2 for y and SOLVE for x. Solving for x instead of randomly plugging in numbers for x is key here. You’ll get 1.5. Now, plug in some large number for y… let’s say 100. When you do that and then solve for x, x will = 100/99. If you plug in numbers this way and solve for x instead of randomly picking a number for x after picking a number for y, you’ll find a pattern. As y gets reaaaally, really big (as y approaches infinity), x will almost reach 1 but not quite… (x will approach 1). So x approaches one AND includes 1.5. The only answer choice that satisfies this is D. </p>
<p>hey, I rhymed in the beginning…!</p>
<p>what a terrible question (19)</p>
<p>
</p>
<p>Actually, that’s wrong. See, this is a mother****** of a trick question. Here’s the wording so I can explain:</p>
<p>“Each student in a group of 30 students studies German, Italian, or both. The total number of students studying German is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only Italian?”</p>
<p>Now with key words in bold:</p>
<p>“Each student in a group of 30 students studies German, Italian, or both. The total number of students studying German is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only Italian?”</p>
<p>Now the initial assumption is that all the number of students in each German, Italian, and Both has to add up to 30. This is wrong because the “Both” students count three times their value due to the fact that they add into the total number of students in German/Italian. The “total” part means that you have to include the Both students in your initial calculations, and then exclude them when you come up with the final answer of the students taking only Italian. All that has to add up in the end is the number of students taking Both, ONLY Italian, and ONLY German.</p>
<p>Then we have the phrase “three more than”, this immediately implies addition, not multiplication.</p>
<p>This then means that our math should look like this:</p>
<p>Let x = number of students taking Both
Let x also = number of students ONLY taking Italian
Let x (+ 3) = number of students ONLY taking German</p>
<p>Because the question does not distinguish between which language has the same number of students is equal to the number of students taking both a logical assumption is that they both are. And in essence they both are equal, you simply then have to take into account the “+ 3” that distinguishes the German group from the Italian group. This also lets you know that it is the group of Italians that equals the group of Both.</p>
<p>The equation then is:</p>
<p>3x + 3 = 30
3x = 27
x = 9</p>
<p>This then means that:</p>
<p>Number of students taking ONLY Italian: 9
-Total number of students taking Italian (9 Italian Only + 9 Both) = 18</p>
<p>Number of students taking ONLY German (x + 3) : 12
-Total number of students taking German (12 German Only + 9 Both) = 21</p>
<p>Number of students taking Both: 9</p>
<p>This then means that the difference between the TOTAL number students taking German and the TOTAL number of students taking Italian is 3 (21 - 18 = 3). And the total number of students is 30. Oh, and the number of students ONLY taking Italian is 9, which means that our answer is B.</p>
<p>Oh, and by the way. This was a pain to figure out algebraically, I spent the last few minutes trying to reverse engineer my solution into a clear equation for you. I simply solved it just by eliminating C - E because of simple math (only Italian + Both (which is the same as Italian) + German (Italian + 3) which were over thirty for all of them). Then I tried 9 and it worked. Just thought you should know how I solved it the first time through.</p>
<p>Oh and OP, great job on choosing two ridiculous SAT questions. If I hadn’t looked closely at this one I probably would have gotten it wrong.</p>
<p>EDIT: Er, Monoclide, I just wanted to apologize if I sounded like a prick in quoting your answer. I was kind of excited about figuring this out.</p>
<p>
</p>
<p>It’s not a problem! Thank you for pointing that out! Now, it’s really crucial that I reread the question after solving it to make sure that what I got … is not only what they are looking for, but works nicely. </p>
<p>Thank you!</p>
<p>Right #15 (Again)-</p>
<p>You know that the radius of the second smallest circle is 2, so the area is 4pi. Then the shaded circle’s radius is 2.5, so the area is 6.25pi. 6.25pi-4pi=2.25pi. 2.25pi=~7 Then just find out which answer choice equals ~7, which is D.</p>
<p>
</p>
<p>I honestly do not believe that’s right… In fact, the ETS probably put that answer there specifically to trick test-takers. Anyway, here’s what I did. We know that the radius of each of the large circles is 1. Now, something cool we can do is make a square: if we draw lines from the center of each large circle to the center of each adjacent circle, we’ll have made a square. Now, the length of each side of the square is 2. Using pythagorean theorem, we find that the diagonal of the square (which goes through the center circle) is sqr(8).</p>
<p>Now, notice how part of the diagonal are two radii of the large circles. To find just the diameter of the small circle, we subtract 2. So now the diameter of the small circle is sqr(8)-2</p>
<p>sqr(8) can be changed to 2sqr(2), so now we have 2sqr(2)-2. Because it asks for the radius, we need to divide this by 2, so we now have sqr(2)-1, choice D. That should be right.</p>
<p>
</p>
<p>Actually lantzk, I believe you’re wrong. I have the QAS that this problem comes from, and it says the answer is A (which is the answer I got when I took the test). I thought of it like this: We know that there are a total of 15 people total that either only take German or only take Italian. We also know that there are 15 people that take both languages. Now, what’s really cool is that we can set up a VERY simple system of equations to solve the problem.</p>
<p>let x=the number of people that only take German</p>
<p>let y=the number of people that only take Italian</p>
<p>we know that x+y=15</p>
<p>We also know, and this is key, that there are 15 people in BOTH German and Italian.</p>
<p>So, because we know that the total number of people taking German is 3 more than then total number people taking Italian, we know that:</p>
<p>x+15=y+15+3</p>
<p>This simplifies to x=y+3</p>
<p>We said early that x+y=15, so x=15-y</p>
<p>So now we have:</p>
<p>15-y=y+3
This simplifies to y=6. We’re looking for the number of people that only study Italian, and we deemed y as the variable for such a thing, so the answer is choice A.</p>