PSAT math questions

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1

<p>A gas tank with a capacity of 18 gallons is empty. A pump can deliver g gallons of gas every t seconds. In terms of g and t, how many seconds will it take this pump to fill the tank?</p>

<p>Answer: 18t/g</p>

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<p>Answer: C</p>

<p>Can someone explain these questions? I usually do well on math (~750) but when I do get questions wrong, they're usually something like the one above (deriving equations from the text/ I, II, III questions). I know they're simple, but they trip me up. How do you go about doing these?</p>

<p>Thanks for the help</p>

2

<p>Just treat it like a distance, rate, time problem. Such that distance = rate x time</p>

<p>Where 18 gallons is the “distance”, g is the “rate”, and t is the “time”</p>

<p>Then we have:</p>

<p>18 = rt</p>

<p>t = d/r = 18/g</p>

<p>Plugging back in we get </p>

<p>18 = (18/g)t = 18t/g</p>

3

<p>"t = d/r = 18/g</p>

<p>Plugging back in we get</p>

<p>18 = (18/g)t = 18t/g "</p>

<p>wait, you said t= 18/g
then you plugged it in so that it was
d= (t)t
…?</p>

<p>wouldnt it be 18= g(18/g) ?
[that makes no sense though lol]
am i misunderstanding you?</p>

4

<p>For the first one, plugging in some numbers makes it pretty easy. </p>

<p>Let’s say the thing pumps 9 gallons every 2 seconds. Clearly it would take 4 seconds to fill 18 gallons. Now just plug in the numbers you made up (9=g , t=2) into the answer choices and see which one equals 4.</p>

<p>18t/g
=(18 * 2) / 9
= 36/9
=4</p>

<p>so 18t/g is the answer. not sure if this is the fastest way but it works.</p>

5

<p>Any idea about the second question?</p>

6

<p>1) These types of problems are very very easy if you’ve taken an AP science where you do a lot of dimensional analysis</p>

<p>We have an expression
g gallons/t seconds</p>

<p>and we have the quantity 18 gallons. We want to manipulate our expression such that the unit of measurement left is seconds. How can we get seconds as our unit and have gallons “cancel out”?</p>

<p>18 gallons * (t seconds/g gallons), so gallons cancel
18t/g seconds</p>

<p>It takes a lot longer to explain than it does to actually do. </p>

<p>2) For the I II III problems, you MUST check I, II, AND III to see if any of them work.</p>

<p>I. 60 < a < 180</p>

<p>This is true. a cannot equal 60 or less than 60. If a = 60, then b and/or c would have to equal or be greater than 60, but that’s not possible because a > b > c. If a is less than 60, then b and c would have to be less than 60 (b/c a is the largest) and we wouldn’t have the full 180 degrees for a triangle.</p>

<p>II. 45 < b < 90</p>

<p>This doesn’t have to be true. Why does b have to fall in that range? We could have c = 1, b = 2, and a = 177 which is acceptable because a > b > c.</p>

<p>III. 0 < c < 60</p>

<p>Obviously c has to be larger than 0. c also cannot be equal to or exceed 60. If c is equal to or greater than 60, then b and/or a would have to be smaller than or equal to c, which is not possible as a > b > c.</p>

7

<p>2nd question:</p>

<p>All it is getting at is that if there are three unequal angles in a triangle, the biggest one has to be more than 60 and the smallest one has to be less than 60. If either of those were not true, then the angle measures would not add up to 180.</p>

8

<p>jamesford, i never thought of using dimensional analysis for these questions (its been a few months since chem lol) so thank you!</p>

9

<p>oh wow! I forgot I had solved for t not r just forgot what I said before =D</p>

<p>However, the concept I was trying to use is correct:</p>

<p>Basically we’re trying to solve for t in terms of g and t</p>

<p>d = rt</p>

<p>d = 18, r = g/t</p>

<p>18 = (g/t)t</p>

<p>So 18t/g = t</p>

<p>Do you understand me now? :)</p>

<p>Oh and you could always just pick numbers and plug them in if you forgot how to actual solve the problem…</p>

10

<p>I solved the first one wrong the first try too. :(</p>

<p>When it says g gallons for every t seconds, this is the rate, g . So like 6 gallons every 2 seconds, is 3 gallons per sec, etc.</p>

<p>The equation is rate * time = amount, so we get x = time, then x(g ) = 18</p>

<p>x=18t\g.</p>

<p>First try I thought the time in what they gave referred to the total time, but the SAT is known for wording questions like this.</p>

11

<p>the trick here is to know that g gallon is not the rate, the rate here is g/t.</p>