Help with some Math PSAT Problems

Test Preparation
1

<p>Today I took the Practice PSAT counselor’s give you when you sign up. I scored a 201, 32 points better than the Sophmore PSAT I took last year when I got a 169. I’m somewhat happy, but I know that if I keep studying I’ll be able to get my 220+ goal.</p>

<p>So, can someone explain to me how to find the answers to these questions and the rules/properties you need to understand in order to answer the questions?</p>

<li>If (x+y)^2 - (x-y)^2 = 84 and x and y are positive integers, which of the following could be a value of x + y ?</li>
</ol>

<p>a. 10
b. 12
c. 14
d. 16
e. 18</p>

<p>The answer is a. 10</p>

<li>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?</li>
</ol>

<p>a. 18t/g
b. 18g/t
c. 18gt
d. g/18t
e. gt/18</p>

<p>The answer is a. 18t/g</p>

<li>How many different 3-digit positive integers can be formed using the digits 2,3,4,5,6,7,8 if the units digit is 2 and no digit is repeated within an integer?</li>
</ol>

<p>a. 12
b. 15
c. 24
d. 30
e. 36</p>

<p>The answer is d. 30. I go this question correct but only because I actually wrote out all the possible integers and counted them out. I’m sure there is a much faster and logical way to do this, so can someone explain it to me?</p>

<li>In a Triangle ABC, if a>b>c, which of the following must be true?</li>
</ol>

<p>I. 60 < a < 180
II. 45 < b < 90
III. 0 < c < 60</p>

<p>a. I only
b. II only
c. I and III only
d. II and III only
e. I, II, and III</p>

<p>The answer is I and III only.</p>

<li>If x^10 = 5555 and x^9/y = 5, what is the value of xy?</li>
</ol>

<p>It was a grid in, and the answer was 1111.</p>

<p>Thanks a million for any help guys!</p>

2

<p>LOL were twins. i am also a jr and got a 200 on the practice</p>

<p>i got the same wrong- except 28 which i figured out by plugging in values for a ,b, and c (90, 60, and 30, respectively)</p>

<p>what else r u doing to study?</p>

3

<p>I'll break this up in case anyone else wants to jump in.
18. Let r be the rate of fill (gallons per unit time)
r = g/t
Let T be the time needed to fill the tank.
rate * time = #gallons
rT = 18 = g/t * T so T = 18t/g</p>

4

<ol>
<li>Use the difference of squares formula, a^2 - b^2 = (a + b)(a - b)</li>
</ol>

<p>(x+y)^2 - (x-y)^2 = (x+y+x-y)(x+y-x+y) = 2x*2y = 84
xy = 21
Since x and y are given to be positive integers, only 1 and 21 or 3 and 7 will work. 22 is not one of the choices, so the answer is x+y = 10.</p>

5

<ol>
<li>You want to make an integer of form 2 _ _ , with no repeated digits. The first digit has been chosen for you already. The next digit can be chosen 6 ways (3,4,5,6,7, or 8). Once you have chosen that one, only five options are left for the last digit. 6 times 5 is 30.</li>
</ol>

6

<ol>
<li> The angles of a triangle sum to 180 degrees. If the angles are all different, the largest one must be greater than 60 degrees, because otherwise, they would all be less than 60 degrees and couldn't sum to 180. (Having them all equal to 60 isn't allowed). Similarly, the smallest angle must be less than 60, because otherwise, they would all be greater than 60 and the sum would exceed 180. The middle angle b does have to be less than 90, but it doesn't have to be more than 45, so 45 < b < 90 is incorrect.</li>
</ol>

7

<p>For 19, it said the ones digit is 2, not the hundreds.</p>

<p>So its _ _ 2. Same answer though.</p>

8

<p>If you can think this way, a sort of shortcut to 16 would be to figure out what square subtracted from another square equals 84. (It's 100 - 16... they really aren't usually out to trip you up that badly with huge numbers.) Then see what numbers you can find that, in this case, add to 10 and also subtract to 4, which are 7 and 3. Basically, it's all guess-and-check with intuition, but that's how I figure those out.</p>