What's the fastest way to do these math problems?

<p>In an art class, there were just enough staplers, rulers, and glue bottles so that every 2 students had to share a stapler, every 3 had to share a ruler, and every 4 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?</p>

<p>The LCM of 3, 4, and 2 is 12, so the number of students is a multiple of 12. Seeing as 12 is too small, starting off with 36 students yields 18 staplers + 12 rulers + 9 glue bottles = 39. 48 students yields 24 + 16 + 12 = 52. 60 yields 30 + 20 + 15 = 65, so the answer is 60 students.</p>

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<p>If a and b are integers such that a + b < 1000 and a/b = .625, what is the greatest possible value of b? </p>

<p>a = .625b, so .625b + b < 1000 —> b < 615</p>

<p>.625 = 5/8, a = 5/8 b, so b must be divisible by 8. We test down from 615: 614, 612, 610, 608 and find that 608 is the answer.</p>

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<p>How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer? </p>

<p>Let’s look at this problem with numbers less than 100. We find 30, 60, 90 are the only solutions. All three are multiples of 30, which would indicate that every answer is a multiple of 30. 1000/30 = 33.33333, so we round down and get 33.</p>

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<p>I think you were there, but decided to plug numbers when you can simply calculate it to the end with a simple equation:</p>

<p>x/2 + x/3 + x/4 = 65
6x/12 + 4x/12 + 3x/12 = 65
13x/12 = 65
13x = 12<em>65
x= 12</em>65/13
x=12*5</p>

<p>This simply looks long … you answer sheet would be a LOT simpler</p>

<p>6x + 4x +3x
----------- = 65 and 13x = 5.13.12
12</p>

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<p>The largest integer <1000 is 999. Once you establish that .625 is also 5/8, all you need to do is 999/13 (which is 76.xx) and multiply the largest integer (76) by 8 to find 76*8 or 608.</p>

<p>I did it in my head. For part B it involved dividing by 3. </p>

<p>I just looked how each y value incremented in equal intervals.</p>

<p>for the a\b one, I converted that to a fraction, 5\8. So I know that a and b are always integers, so that means that they’re mutiples of 5 and 8. </p>

<p>So I did 5x+8x = 999, got x = 76.84, rounded that to a whole number 76. 76*8 = 608</p>

<p>[edit]not 1000, 999, still worked in this case, but this is almost always why I get questions wrong. Misread the less then sign.</p>

<p>On a square gameboard that is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value for k?</p>

<p>A 10
B 25
C 34
D 42
E 52</p>

<p>The number of squares along the border is n + (n-2) + (n-2) + n = k. Then
4n - 4 = k
n -1 = k/4
n = k/4 + 1</p>

<p>Since we can’t have fractions of a square, k must be divisible by 4. The only choice divisible by 4 is E, 52.</p>

<p>Of the 240 campers at a summer camp, 5/6 could swim. If 1/3 of the campers took climbing lessons, what was the least possible number of campers taking climbing lessons who could swim?</p>

<p>20
40
80
120
200</p>

<p>From the info in the problem, we know 200 can swim and 80 took climbing lessons. At this point, I just tried the choices. 20 who did both would mean 60 who climbed only and 180 who swam only, giving 20 + 60 + 180 > 240, so that’s wrong. 40 climbing and swimming would mean 40 climb only and 160 swim only, which works and must be the answer.</p>

<p>What’s a direct way of obtaining the answer as 40, say if you didn’t have it as an answer choice?</p>

<p>before i go to page 4 and try to offer advice with today’s question i just have to say this thread is amazing and helps me think of all the creative ways of solving the higher-tier math problems (which some i have troubles knowing where to start/understanding wth the question/info is giving) thanks james and spidey and everyone whose contributed to this thread. (can’t believe i just found this)</p>

<ol>
<li>In the figure here <a href=“ImageShack - Best place for all of your image hosting and image sharing needs”>ImageShack - Best place for all of your image hosting and image sharing needs; line l is parallel to line m. If v = 2w, which of the following must be equal to q?</li>
</ol>

<p>A. v + t
B. v - t
C. t
D. 2v
E. s + t</p>

<p>This you probably could’ve done it faster just eliminating (and i rarely say this for any problem… unless it said not drawn to scale). Rather than giving numbers to the variables…V+T=180 (a is out), v=q so subtracting would only make it less(b is out), t is less than q (c is out), 2v=s which is less than q(d is out), S+t is only one left and is the only one numerically possible to equal q… this would’ve taken 10-15 seconds rather than having to crunch down the numbers and then apply numbers to the problem when you just apply variables just looking at it.</p>

<p>You could try option1+option2+neither-both=total:
200+80+0(since it didn’t say no one did nothing)-x=240
280-x=240
x=40 </p>

<p>I’m not really sure why it said least… what answer choices would this requirement have eliminated? All in all i’m not sure what this question actually asks for and just thoguht maybe that formula would help.</p>

<p>x = 3v
v = 4t
x = pt</p>

<p>For the system above, if x =! 0, what is the value of p?</p>

<p>3v=pt
12t=pt
p=12
not sure if that’s faster or diff at all</p>

<p>My god…all of you are soo slow.</p>

<p>For climber,swimmer problem – you were just about done once you knew there were 80 climbers and only 40 non swimmers…Since there are only 40 non-swimmers available, best case is that all of them happen to be climbers, so of the 80 climbers, at least 40 have to be swimmers (again, because there were only 40 non-swimmers available).</p>

<p>I’m not going to lie: I thought that a=7 for #1 F LOL</p>

<p>Edit* I was right lol woops, didn’t read the ‘a-b’ part… See this proves that it’s important to underline such things</p>