SAT practice Test 3 — Questions and Answers
Question 1: If three times a number is equal to that number minus 7, what is the number?</span>
- -1.5</span></label></li>
- 1.5</span></label></li>
- -3.5</span></label></li> (Correct answer)
- 3.5</span></label></li>
Correct answer: -3.5</span></label></li>
Let 'x' represent the unknown number. The problem states 'three times a number is equal to that number minus 7,' which translates into the algebraic equation 3x = x - 7. To solve for x, subtract 'x' from both sides: 2x = -7. Finally, divide both sides by 2: x = -7/2, which is -3.5.
Question 2: >The amount of skin samples that David needs for an experiment must be greater than 11 but less than or equal to 27. Which of the following represents an acceptable range for David's experiment?</span>
- 11<s<27</span></label></li>
- 11<span style="text-decoration: underline;"><</span>s<27</span></label></li>
- 11<s<span style="text-decoration: underline;"><</span>27</span></label></li> (Correct answer)
- 11<span style="text-decoration: underline;"><</span>s<span style="text-decoration: underline;"><</span>27</span></label></li>
Correct answer: 11<s<span style="text-decoration: underline;"><</span>27</span></label></li>
The problem states that the number of skin samples, 's', must be 'greater than 11', which is represented by the inequality 11 < s. It also states that 's' must be 'less than or equal to 27', which is represented by s <= 27. Combining these two conditions into a single compound inequality gives the acceptable range as 11 < s <= 27.
Question 3: If 2x+2y=0, which of the following must be equivalent to 2x-2y?</span>
- -4y</span></label></li> (Correct answer)
- <sup>2x</sup>/<sub>2y</sub></span></label></li>
- y</span></label></li>
- y<sup>2</sup></span></label></li>
Correct answer: -4y</span></label></li>
Given the equation 2x + 2y = 0, we can isolate 2x by subtracting 2y from both sides, resulting in 2x = -2y. The question asks for an equivalent expression for 2x - 2y. By substituting -2y for 2x in the expression, we get (-2y) - 2y. This simplifies to -4y.
Question 4: Which of the following is equivalent to 4x<sup>2</sup>-4x-48? </span>
- 3(x-3)(x+4)</span></label></li>
- 4(x-3)(x+4)</span></label></li> (Correct answer)
- 3(x-3)(x-4)</span></label></li>
- 4(x+3)(x+4)</span></label></li>
Correct answer: 4(x-3)(x+4)</span></label></li>
To check which option is equivalent to 4x^2 - 4x - 48, we can expand the given correct answer, 4(x-3)(x+4). First, multiply the binomials: (x-3)(x+4) = x^2 + 4x - 3x - 12 = x^2 + x - 12. Then, distribute the 4: 4(x^2 + x - 12) = 4x^2 + 4x - 48. This shows that 4(x-3)(x+4) is equivalent to 4x^2 + 4x - 48. (Note: There is a discrepancy in the sign of the middle term between the question's expression and the provided correct answer's expansion.)
Question 5: If 2a+3b=26 and 5a+4b=51, what is the value of a+b? </span>
- 8</span></label></li>
- 9</span></label></li>
- 10</span></label></li>
- 11</span></label></li> (Correct answer)
Correct answer: 11</span></label></li>
We are given a system of two linear equations: 2a + 3b = 26 and 5a + 4b = 51. To find the value of a + b, a straightforward method is to add the two equations together. Adding the left sides gives (2a + 3b) + (5a + 4b) = 7a + 7b. Adding the right sides gives 26 + 51 = 77. So, 7a + 7b = 77. Dividing the entire equation by 7 yields a + b = 11.
Question 6: If x<sup>2</sup>+4xy+y<sup>2</sup>=-44 and y-x=14, which of the following could be the value of x? </span>
- 10</span></label></li>
- 2</span></label></li>
- -8</span></label></li>
- -10</span></label></li> (Correct answer)
Correct answer: -10</span></label></li>
From the second equation, y - x = 14, we can express y as y = x + 14. Substitute this expression for y into the first equation: x^2 + 4x(x+14) + (x+14)^2 = -44. Expanding and simplifying leads to a quadratic equation: x^2 + 4x^2 + 56x + x^2 + 28x + 196 = -44, which becomes 6x^2 + 84x + 240 = 0. Dividing by 6 gives x^2 + 14x + 40 = 0. Factoring this quadratic equation yields (x+4)(x+10) = 0, so the possible values for x are -4 and -10. Since -10 is one of the options, it is a possible value for x.
Question 7: If three times a number (x) is equal to that number plus six, what is five times that number plus 20 minus that number? </span>
- 24</span></label></li>
- 28</span></label></li>
- 32</span></label></li> (Correct answer)
- 36</span></label></li>
Correct answer: 32</span></label></li>
First, translate the initial statement into an equation: 'three times a number (x) is equal to that number plus six' becomes 3x = x + 6. Solving for x, subtract x from both sides to get 2x = 6, which means x = 3. Next, evaluate the second expression: 'five times that number plus 20 minus that number' translates to 5x + 20 - x. Substitute x=3 into this expression: 5(3) + 20 - 3 = 15 + 20 - 3 = 35 - 3 = 32.
Question 8: If 4y=y+4, what is the value of 3y?</span>
- 1</span></label></li>
- 2</span></label></li>
- 3</span></label></li>
- 4</span></label></li> (Correct answer)
Correct answer: 4</span></label></li>
The problem provides the equation 4y = y + 4 and asks for the value of 3y. To solve for 3y, first subtract 'y' from both sides of the given equation. This operation directly results in 3y = 4. Therefore, the value of 3y is 4.
Question 9: John joins a new specialty video streaming service for horror movie lovers. The cost is $5 per month (m) plus a one-time membership fee of $12. If John pays for his first two years in advance, which equation properly states his purchase? </span>
- 5m+12</span></label></li> (Correct answer)
- 24+5m</span></label></li>
- 5m-24</span></label></li>
- 24m+5</span></label></li>
Correct answer: 5m+12</span></label></li>
The problem asks for the equation that properly states John's purchase based on the given cost structure. The cost is described as '$5 per month (m)' and 'a one-time membership fee of $12'. This translates directly into the algebraic expression 5m + 12, where 'm' represents the number of months. The information about paying for two years in advance is additional detail for a specific calculation, not for the general equation of the cost structure.
SAT practice Test 3
If three times a number is equal to that number minus 7, what is the number?