This is from a practice PSAT from the Collegeboard. I was exhausted when I was taking this practice test because of school and stuff so I think I could have done a lot better but who knows? Anyway, I have multiple math questions. If you can explain and solve only one, please do</p>
<p>I wouldnt’ be asking so many quesitons if there was a solutions part to this practice test but there isn’t .</p>
<ol>
<li>The members of a school club are ordering T-shirts. There is a one-time charge of $150 for artwork on the T-shirts and a $10 charge for each T-shirt ordered. If x represents the number of T-shirts ordered, which of the following represents the total cost, in dollars, per T-shirts?
A. 10+150x
B. x+15
C. 10x+150x
D. (10+150x)/x
E. (10x+150)/x
Answer: E (I tried to use real easy numbers to plug in and this usually works but for this case it didn’t )</li>
</ol>
<p>Essentially, you need to find a formula that represents the total cost of the x number of T-shirts you purchase. Of the choices given, only 10x + 150 satisfies this condition. The ‘150’ portion of the equation represents the constant, one-time charge of $150 dollars that you pay while the ‘10x’ portion of the equation represents the cost of each T-shirt you buy. For example, if you purchased two T-shirts, the total cost would be equal to 150 + 10(2) or $170. Since the equation asks for the total cost of each T-shirt, it makes sense to divide by x, the number of T-shirts you purchased.</p>
<ol>
<li>How many positive integers less than 1000 do not have 7 as a digit? (I hate this type of problem)
A. 700
B. 728
C. 736
D. 770
E. 819
Answer: B</li>
</ol>
<p>**As you stated, the answer is indeed B. 728.</p>
<p>This type of question deals with the concepts of permutations and combination. Essentially, you are asked to find a positive integer less than 1000 that does not have 7 as a digit, which for convenience can be represented as XXX, wherein X cannot be 7. Essentially, each X can be either of the following digits: 0, 1, 2, 3, 4, 5, 6, 8, 9, a total of 9 digits to choose from. Therefore, the number of positive integers less than 1000 that do not have a 7 as a digit is equal to 9^3 - 1, since you have nine choices for a digit for each place value. Since 000 is not a positive integer, you can subtract that value from the total number of positive integers that do not contain 7 as a digit.**</p>
<ol>
<li>Points A, B, and X do not all lie on the same line. Point X is 5 units from A and 3 units from B. How many other points in the same plane as A,B, and X are also 5 units from A and 3 units from B?
A. None
B. One
C. Two
D. Four
E. More than four
Answer:B</li>
</ol>
<p>This question is pretty tricky such that you’ll want to draw a diagram that you can refer to while working through this problem. Pretend that A, B, and X form a right triangle - for convenience anyway - with segment AX being the vertical leg, AB being the horizontal leg, and BX being the hypotenuse using the info given: AX = 5 and BX = 3. You should be able to see that by reflecting the triangle across the horizontal axis, you will have another point X that is also five units away from A and three units away from B. No other reflections will yield the same distances. Thus, the answer is B.</p>
<ol>
<li>What is the smallest integer whose square root is greater than 2?
A. 3
B. 4
C. 5
D. 6
E. 9
Answer: C</li>
</ol>
<p>This question is fairly simple once you think about it. For this question, you will want to find the integer whose square root is less than or equal to 2. The square root of 4 is 2. By definition, any integer greater than 4 will have a square root greater than 2. The smallest integer that satisfies this condition is 5 because it is the next integer after 4, whose square root is 2.</p>
<ol>
<li>If there are m minutes in h hours, what is m in terms of h?
A. 60/h
B. h/60
C. 60+h
D. 60h
E. 3600h
Answer: D</li>
</ol>
<p>This question simply asks you to substitute in numbers you know for the variables listed. There are 60 minutes in an hour. Therefore, given a number of hours h, there are 60h minutes in that amount of hours. For example, if h = 1, m = 60 because in one hour are there 60 minutes. Likewise, if h = 2, m = 120 because there are 60 * 2 minutes in 2 hours.</p>
<ol>
<li>For all integers x and y that are greater than 1, xy> x+y
… Of the following values for x and y, which shows that the statement above is not true?
A. X=0, Y=2
B. X=1, Y=1
C. X=2, Y=2
D. X=3, Y=1
E. X=4, Y=3
Answer: C</li>
</ol>
<p>For this type of question, I always like to plug in the given answer choices since that method takes the least amount of time. Using the values listed for C, you will find that xy > x + y does not hold true because (2)(2) is not greater than (2 + 2).</p>
<ol>
<li>In the xy plane, the line with equation ax+by=1 where a and b are constants intersects the y=axis where y=2. What is the value of b?</li>
</ol>
<p>This is another tricky problem that may be difficult to solve unless you have a firm grasp of algebra. Since the equation intersects the y-axis where y=2, (0,2) must be a solution to the equation, such that (a)(0) + (b)(2) = 1. Since anything times 0 is 0, you can simplify the equation to 2b = 1. Thus, using algebra, you can conclude that b must equal 1/2.