Compete these sat math questions

Test Preparation SAT Preparation
1

<p>These questions are from the collegeboard Sat book, I know their answers but I don’t know their explanations so I would appreciate if somebody helps me out…

  1. If x and y are positive integers and 3^2x . 3^2y = 81, what is the value of x+y?
    A. 3/2
    B. 2
    C. 4
    D. 81/2
    E. 81
  2. A class has twice as many boys as girls. The students in the class stand in one line, with a girl at the front of the line. Which of the following must be true?
    A. The last person in line is a girl.
    B. the last person in line is a boy
    C. There are more boys than girls in the class
    D. There are at least two girls standing to each other.
    E. There are at least two boys standing next to each other.
  3. Which of the following is an equation of the line that has a y-intercept of 2 and ab x-intercept of 3?
    A. -2x+3y=4
    B. -2x+3y=6
    C. 2x+3y=4
    D. 2x+3y=6
    E. 3x+2y=6
  4. In a certain game, each of 5 players received a score between 0 and 100, inclusive. If their average score was 80, what is the greatest possible number of the 5 players who could have received a sore of 50?
    A. None
    B. one
    C. Two
    D. Three
    E. Four
  5. One adult and 10 children are in an elevator. If the adult’s weight is 4 times the average weight of the children, then the adult’s weight is what fraction of the total weight of the 11 people in the elevator?
  6. If 3a + 4b=b, which of the following must equal 6a+6b?
    A. 0
    B. 12
    C. 2b
    D. 12b
    E. 6b-8
  7. A salesperson’s commission is k percent of the selling price of a car. Which of the following represents the commission, in dollars, on 2 cars that sold for $14,000 each?
    A. 280k
    B. 7,000k
    C. 28,000 k
    D. 14,000/100+2k
    E. 28,000+k/100
  8. A restaurant has 19 tables that can seat a total of 84 people. Some of the tables seat 4 people and the others seat 5people. How many tables seat 5 people?
    A. 4
    B. 5
    C. 6
    D. 7
    E. 8
  9. In an election 2.8 million votes were cast and each vote was for either candidate I or candidate II. Candidate I received 28,000 more votes than candidate II. What percent of the 2.8 million votes were cast for candidate I?
    A. 50.05%
    B. 50.1%
    C. 50.5%
    D. 51%
    E. 55%
  10. Each term of a certain sequence is greater than the term before it. The difference between any two consecutive terms in the sequence is always the same number. If the third and sixth terms of the sequence are 17 and 77, respectively, what is the eighth term?
    Appreciate any help explaining… </p>
2

<p>@silverturtle please help me out!!</p>

3

<h1>1:</h1>

<p>If x is an integer and k is an integer, that means when you square root x, you get an integer. Therefore, square root all of your answer choices and find the one that when square rooted, is an integer. © is the correct answer, because the square root of 9 is 3.</p>

<h1>2:</h1>

<p>I’m not sure if I am reading the question wrong, but it seems like they are trying to trick you? © should be the correct answer because they told you, “A class has twice as many boys as girls.” Therefore, there are more boys than girls. </p>

<h1>3:</h1>

<p>An equation with a y-intercept of (0,2) and a x-intercept of (3,0) will have the slope (0-2 / 3-0), or -2/3. Therefore, you have the equation y = mx + b, which translates to y = -2x/3 + b. Then, plug in one of your points for x and y. If you solve for b, you get 2 = 0 + b, so b = 2. Therefore, the equation is y = -2x/3 + 2. Convert this to standard form, and you get (D) as the correct answer.</p>

<h1>4:</h1>

<p>If you know the average of their scores is 80, then the sum of all of the players’ scores divided by 5 is 80 (per the formula for finding the mean). So, all of the players’ scores added up equals 400. You cannot have 5 players scoring 50 points each, because then the total would only be 250. You cannot have 4 players scoring 50 points each, because then 4 players scoring 50 each is 200, which leaves 200 points out, and you cannot have a score higher than 100. You cannot have 3 players scoring 50 points each, which is 150 points total, leaving 250 out for two people, which is impossible because two people can only score a maximum of 200 points. Therefore, the answer is 2 players scoring 50 points each, which is 100 points total, leaving 300 out for three people, 100 points each. © is the correct answer.</p>

<h1>5:</h1>

<p>The easiest way to solve this problem is to plug in random numbers. Pretend that the adult weighs 8 pounds, and the child weighs 2 pounds. If there are 10 children, their total weight is 20 pounds. So, the fraction of the adult’s weight from the entire group would be 8 / 28, or 2 / 7.</p>

<h1>6:</h1>

<p>If 3a + 4b = b, you can simplify that by subtracting 4b on both sides to get 3a = -3b, and divide 3 on both sides to get a = -b. Substitute that into 6a+6b, and you get -6b + 6b, which equals 0. (A) is the correct answer.</p>

<h1>7:</h1>

<p>If he sold 2 cars, $14,000 each, he sold a total value of $28000. Since he gets a commission of k percent, the fraction of $28000 he gets is k / 100. Multiply k / 100 by $28000 and you get 280k. (A) is the correct answer.</p>

<h1>8:</h1>

<p>Let x be the number of 4-seat tables and y be the number of 5-seat tables. x + y = 19, because there are 19 tables. 4x + 5y = 84, which is the total number of people seated. If you simplify x + y = 19 to x = 19 - y, substitute that into 4x + 5y = 84, and you get y = 8. Therefore, the correct answer is (E). </p>

<h1>9:</h1>

<p>Let x be Candidate I and y be Candidate II. x = 28000 + y, because Candidate I received 28,000 more votes. You also know that x + y = 2800000, because the total number of votes is 2.8 million. Substitute x = 28000 + y into x + y = 2800000, and you get y = 1386000. Substitute this back into the first equation, and you get x = 1414000. Divide this by 2.8 million, and you get 0.505, or 50.5%. © is the correct answer.</p>

<h1>10:</h1>

<p>If the third term is 17 and the sixth term is 77, you have the spaces __ __ 17 __ __ 77. 77-17 equals 60, so the interval must be 20 since there are two spaces in between 17 and 77, and you add one. So, if you filled all the spaces in you would get -37 -17 17 37 57 77 97 117. So, the correct answer is 117.</p>

<p>I hope this helped a bunch, because it took me a while! Good luck on the SAT!</p>

4

<p>The answer for #1 is B</p>

5

<p>(3^2x) + (3^2y) = 81
We know that 3^4 = 81</p>

<p>so, 3^2x + 3^2y = 3^4</p>

<p>in that regard, set 2x+2y = 4
2 (x+y) = 4</p>

<p>so x+y = 2, therefore the answer is B.</p>

6

<p>Thank you very much this really helped and for the 1st question it’s was a mistake putting it because I already know how to solve it… </p>