Digital SAT · Math · Exam Prep · NYC Test Prep
Digital SAT Practice Test 6 — Module 1 Math: Full Walkthrough of All 27 Questions with Answers & Explanations
Every question on Digital SAT Practice Test #6, Math Module 1, transcribed verbatim, with the official College Board answer key, a step-by-step worked solution, a plain-English explanation for every item, theory refreshers on every tested skill, and a free PDF download. Built by SOMATH, the math school on the Upper West Side of Manhattan.
Looking for the answers, explanations, and full walkthrough of Digital SAT Practice Test 6 — Math Module 1? You are in the right place. This is a complete, question-by-question walkthrough of SAT Test #6, Math Module 1 — every one of the 27 questions transcribed verbatim, with the official College Board answer for each item and a worked solution showing exactly which SAT Math tool the question wants and how to apply it.
Use this post with the official PDF: first attempt each question on your own, then open the answer reveal only after you have committed to an answer. The module mixes equations, functions, data, percentages, and geometry, so it is also a useful checklist of the skills that need attention before the next test date.
Whether you are a student prepping for the next SAT, a parent looking for answer explanations, or a teacher building a review packet, this walkthrough is designed to be a clear, student-friendly study resource. It is written by the team that teaches Digital SAT prep at SOMATH, a math-focused school on the Upper West Side of New York City.
Official answer key — SAT Practice Test 6, Math Module 1
| Question # | Correct Answer |
|---|---|
| 1 | A |
| 2 | D |
| 3 | D |
| 4 | D |
| 5 | A |
| 6 | 31 |
| 7 | 11 |
| 8 | D |
| 9 | B |
| 10 | B |
| 11 | A |
| 12 | B |
| 13 | 0.5 or 1/2 |
| 14 | 7.5 or 15/2 |
| 15 | B |
| 16 | C |
| 17 | D |
| 18 | D |
| 19 | D |
| 20 | 189/5 or 37.8 |
| 21 | −24 |
| 22 | D |
| 23 | A |
| 24 | C |
| 25 | D |
| 26 | A |
| 27 | 54 |
Theory refresher: every skill tested in this module
Linear Equations in 1 Var
Translate the situation into one equation with one unknown, isolate the variable, and check the value in the original context. Questions 1, 7, and 10 all reduce to this pattern.
Linear Inequalities
An inequality describes an allowed range rather than one exact value. Substitute test values or compare each row to the boundary expression; Question 4 and Question 11 use this idea.
Linear Functions
For y = mx + b, the slope is the change in y per one unit of x, and b is the value at x = 0. Use a known point to find a missing intercept.
Linear Equations in 2 Vars
At a y-intercept, x = 0. Substitute that coordinate into the equation and solve for y; Question 20 is a direct intercept calculation.
Ratios/Rates/Proportions
Unit conversions are ratios written as fractions equal to 1. Choose a conversion factor so the unwanted unit cancels, as inches cancel in Question 6.
Equivalent Expressions
Expand carefully, use special products such as (a-b)(a+b)=a²-b², and combine like terms. To isolate a variable inside an equation, undo operations in reverse order.
Nonlinear Equations in 1 Var
For a squared variable, isolate the square and take both roots before applying any restriction such as “positive solution.” For a quadratic equation, use factoring or the quadratic formula.
Nonlinear Functions
For exponential functions, the initial value is the value when the exponent is zero. For graphs of nonlinear functions, identify the requested x-value or interval before interpreting the y-values.
One-Variable Data
The median of an odd-sized data set is the middle position. With grouped data, count cumulative frequencies to locate that position, then determine which interval could contain it.
Percentages
An increase of r% changes a quantity by the multiplier 1 + r/100. Consecutive changes multiply; do not add the percentages.
Area & Volume
The area of a right triangle is ½(base)(height). The legs meeting at the right angle provide the base and height.
Circles
A circle in the form (x-h)² + (y-k)² = r² has center (h,k) and radius r. Shifts change the center, while a radius scale changes r².
Right Triangles & Trig
For an acute angle in a right triangle, tan θ = opposite/adjacent. A 30–60–90 triangle has side ratio 1 : √3 : 2.
Lines/Angles/Triangles
Parallel lines inside a triangle create similar triangles. Set ratios of corresponding sides equal, then use the known whole-side relationship to find the requested smaller side.
Questions 1–14: Foundations, functions, and algebra
Start with the core moves: isolate a variable, read a function, compare values to an inequality, and use the information in a formula.
Question 1 · Linear Equations in 1 Var
(p + 3) + 8 = 10
What value of p is the solution to the given equation?
- A) −1
- B) 5
- C) 15
- D) 21
Answer: A) −1
Key idea. Combine the constants first, then undo the addition of 11.
(p + 3) + 8 = 10 p + 11 = 10 p = 10 − 11 p = −1
Why A works. Substitution gives (−1 + 3) + 8 = 2 + 8 = 10. The other values do not make the equation true.
Question 2 · Nonlinear Functions
The scatterplot shows the relationship between x and y. Which of the following graphs shows the most appropriate model for the data?
See figure in the original College Board PDF above.
- A) (graph)
- B) (graph)
- C) (graph)
- D) (graph)
Answer: D)
Key idea. The points rise slowly at first and then more quickly, so the curved increasing model is the best match.
Compare the overall shape, not one isolated point: • A linear model would have a constant rate of change. • The plotted values curve upward as x increases. • Choice D is the increasing curved model that follows that pattern.
Why D works. Its curve captures the increasing rate of change shown by the scatterplot; the other displayed models have the wrong overall shape.
Question 3 · Nonlinear Equations in 1 Var
k² − 53 = 91
What is the positive solution to the given equation?
- A) 144
- B) 72
- C) 38
- D) 12
Answer: D) 12
Key idea. Isolate the square, then take the positive square root because the question asks for the positive solution.
k² − 53 = 91 k² = 144 k = ±12 positive solution: k = 12
Why D works. Both 12 and −12 square to 144, but only 12 is positive.
Question 4 · Linear Inequalities
During a portion of a flight, a small airplane’s cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour, during this portion of the flight?
- A) s ≤ 20
- B) s ≤ 150
- C) s ≤ 170
- D) 150 ≤ s ≤ 170
Answer: D) 150 ≤ s ≤ 170
Key idea. “Between 150 and 170” gives a lower bound and an upper bound, both inclusive.
lower bound: s ≥ 150 upper bound: s ≤ 170 combine: 150 ≤ s ≤ 170
Why D works. It includes every speed from 150 through 170 and excludes anything outside that interval.
Question 5 · Nonlinear Functions
An object was launched upward from a platform. The graph shown models the height above ground, y, in meters, of the object x seconds after it was launched. For which of the following intervals of time was the height of the object increasing for the entire interval?
See figure in the original College Board PDF above.
- A) From x = 0 to x = 2
- B) From x = 0 to x = 4
- C) From x = 2 to x = 3
- D) From x = 3 to x = 4
Answer: A) From x = 0 to x = 2
Key idea. Use the graph’s upward portion only; the object rises before it reaches its highest point.
The graph rises from x = 0 through a time after x = 2. It does not rise for all of 0 to 4, 2 to 3, or 3 to 4 because those intervals include or occur after the peak. Therefore, 0 to 2 is the only listed interval that is entirely increasing.
Why A works. The height is increasing throughout that entire two-second interval.
Question 6 · Ratios/Rates/Proportions
How many yards are equivalent to 1,116 inches? (1 yard = 36 inches)
Student-produced response — enter as a fraction or decimal.
Answer: 31
Key idea. Divide by the number of inches in one yard.
1,116 inches × (1 yard / 36 inches) = 1,116 / 36 yards = 31 yards
Why this works. The inches unit cancels, leaving yards.
Question 7 · Linear Equations in 1 Var
The function f is defined by f(x) = 14 + 4x. The function f represents the total cost, in dollars, of attending an arcade when x games are played. How many games can be played for a total cost of $58?
Student-produced response — enter as a fraction or decimal.
Answer: 11
Key idea. Set the cost function equal to 58 and solve for the number of games.
14 + 4x = 58 4x = 44 x = 11
Why this works. The $14 is the fixed charge, so the remaining $44 pays for 11 games at $4 each.
Question 8 · Linear Functions
The function f is defined by f(x) = x + b, where b is a constant. When x = 0, f(x) = 30. What is the value of b?
- A) −30
- B) −1/30
- C) 1/30
- D) 30
Answer: D) 30
Key idea. At x = 0, the x-term disappears, leaving the constant b.
f(0) = 0 + b 30 = b b = 30
Why D works. In the form x + b, b is the output when x is zero.
Question 9 · Nonlinear Functions
The function P is defined by P(t) = 1,800(1.02)t. The function P gives the estimated number of marine mammals in a certain area, where t is the number of years since a study began. What is the best interpretation of P(0) = 1,800 in this context?
- A) The estimated number of marine mammals in the area when the study began was 102.
- B) The estimated number of marine mammals in the area when the study began was 1,800.
- C) The estimated number of marine mammals in the area increased by 102 each year after the study began.
- D) The estimated number of marine mammals in the area increased by 1,800 each year after the study began.
Answer: B) The estimated number of marine mammals in the area when the study began was 1,800.
Key idea. Evaluate at t = 0: an exponential factor to the zero power is 1.
P(0) = 1,800(1.02)⁰ P(0) = 1,800(1) P(0) = 1,800 t = 0 means the study began.
Why B works. The coefficient 1,800 is the initial population, not an annual additive increase.
Question 10 · Linear Equations in 1 Var
A manager is responsible for ordering supplies for a shaved ice shop. The shop’s inventory starts with 4,500 paper cups, and the manager estimates that 70 of these paper cups are used each day. Based on this estimate, in how many days will the supply of paper cups reach 1,700?
- A) 20
- B) 40
- C) 60
- D) 80
Answer: B) 40
Key idea. Subtract the daily use from the starting inventory and set the result equal to 1,700.
4,500 − 70d = 1,700 −70d = −2,800 d = 40
Why B works. In 40 days, 70 × 40 = 2,800 cups are used, and 4,500 − 2,800 = 1,700.
Question 11 · Linear Inequalities
y > 4x + 8
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
| x | y |
|---|---|
| 2 | 19 |
| 4 | 30 |
| 6 | 41 |
| x | y |
|---|---|
| 2 | 8 |
| 4 | 16 |
| 6 | 24 |
| x | y |
|---|---|
| 2 | 13 |
| 4 | 18 |
| 6 | 23 |
| x | y |
|---|---|
| 2 | 13 |
| 4 | 21 |
| 6 | 29 |
Answer: A)
Key idea. Compute the required minimum y-value for each x and check that every y in one table is strictly larger.
For x = 2: 4x + 8 = 16 For x = 4: 4x + 8 = 24 For x = 6: 4x + 8 = 32 Table A has y-values 19, 30, 41. 19 > 16, 30 > 24, and 41 > 32. Every row in A satisfies y > 4x + 8.
Why A works. The other tables contain at least one y-value that is not greater than its required boundary value.
Question 12 · Equivalent Expressions
Which expression is equivalent to (x² + 11)² + (x − 5)(x + 5)?
- A) x⁴ + 23x² − 14
- B) x⁴ + 23x² + 96
- C) x⁴ + 12x² + 121
- D) x⁴ + x² + 146
Answer: B) x⁴ + 23x² + 96
Key idea. Expand the square, use the difference-of-squares product, and combine like terms.
(x² + 11)² = x⁴ + 22x² + 121
(x − 5)(x + 5) = x² − 25
Sum = x⁴ + 22x² + 121 + x² − 25
= x⁴ + 23x² + 96
Why B works. The two constant terms combine to 121 − 25 = 96, and the x² terms combine to 23x².
Question 13 · Nonlinear Functions
The function h is defined by h(x) = 8/(5x + 6). What is the value of h(2)?
Student-produced response — enter as a fraction or decimal.
Answer: 0.5 or 1/2
Key idea. Substitute 2 for x and simplify the fraction.
h(2) = 8/(5(2) + 6)
= 8/(10 + 6)
= 8/16
= 1/2 = 0.5
Why this works. Function notation asks for direct substitution of the input.
Question 14 · Area & Volume
Note: Figure not drawn to scale.
The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?
See figure in the original College Board PDF above.
Student-produced response — enter as a fraction or decimal.
Answer: 7.5 or 15/2
Key idea. Use the two perpendicular side lengths as the base and height of the right triangle.
area = ½(base)(height)
= ½(3)(5)
= 15/2
= 7.5
Why this works. The legs of a right triangle are perpendicular, so they can serve as the base and height.
Questions 15–22: Graphs, data, and percent change
These questions reward careful translation: know what x = 0 means, count positions in a data table, and turn language about change into a multiplier.
Question 15 · Nonlinear Functions
The graph models the number of active projects a company was working on x months after the end of November 2012, where 0 ≤ x ≤ 6. According to the model, what is the predicted number of active projects the company was working on at the end of November 2012?
See figure in the original College Board PDF above.
- A) 0
- B) 5
- C) 8
- D) 9
Answer: B) 5
Key idea. “At the end of November 2012” corresponds to x = 0, so read the graph’s y-value there.
At the end of November 2012: x = 0. The graph’s value at x = 0 is 5. Therefore, the predicted number of active projects is 5.
Why B works. The required value is the graph’s y-intercept.
Question 16 · Linear Functions
The relationship between two variables, x and y, is linear. For every increase in the value of x by 1, the value of y increases by 8. When the value of x is 2, the value of y is 18. Which equation represents this relationship?
- A) y = 2x + 18
- B) y = 2x + 8
- C) y = 8x + 2
- D) y = 3x + 26
Answer: C) y = 8x + 2
Key idea. The stated change gives slope 8; use the point (2, 18) to find the intercept.
y = 8x + b 18 = 8(2) + b 18 = 16 + b b = 2 y = 8x + 2
Why C works. It has the required slope of 8 and gives y = 18 when x = 2.
Question 17 · Equivalent Expressions
P = N(19 − C)
The given equation relates the positive numbers P, N, and C. Which equation correctly expresses C in terms of P and N?
- A) C = (19 + P)/N
- B) C = (19 − P)/N
- C) C = 19 + P/N
- D) C = 19 − P/N
Answer: D) C = 19 − P/N
Key idea. Divide by N, then isolate C by subtracting from 19.
P = N(19 − C) P/N = 19 − C C = 19 − P/N
Why D works. Moving C from the right side requires subtracting P/N from 19, not changing the denominator of 19.
Question 18 · Nonlinear Equations in 1 Var
w² + 12w − 40 = 0
Which of the following is a solution to the given equation?
- A) 6 − 2√19
- B) 2√19
- C) √19
- D) −6 + 2√19
Answer: D) −6 + 2√19
Key idea. Apply the quadratic formula and compare the two exact roots to the choices.
w = [−12 ± √(12² − 4(1)(−40))]/2 = [−12 ± √304]/2 = [−12 ± 4√19]/2 = −6 ± 2√19 One listed solution is −6 + 2√19.
Why D works. It is exactly one of the two roots obtained from the quadratic formula.
Question 19 · One-Variable Data
The table shown summarizes the number of employees at each of the 17 restaurants in a town. Which of the following could be the median number of employees for the restaurants in this town?
| Number of employees | Number of restaurants |
|---|---|
| 2 to 7 | 2 |
| 8 to 13 | 4 |
| 14 to 19 | 2 |
| 20 to 25 | 7 |
| 26 to 31 | 2 |
- A) 2
- B) 9
- C) 15
- D) 21
Answer: D) 21
Key idea. With 17 values, the median is the ninth value after the data are ordered.
Median position = (17 + 1)/2 = 9th Cumulative counts: 2 to 7: positions 1–2 8 to 13: positions 3–6 14 to 19: positions 7–8 20 to 25: positions 9–15 The ninth value is in the interval 20 to 25. Only 21 could be the median.
Why D works. 21 lies in the only interval that contains the ninth observation.
Question 20 · Linear Equations in 2 Vars
What is the y-coordinate of the y-intercept of the graph of 3x/7 = −5y/9 + 21 in the xy-plane?
Student-produced response — enter as a fraction or decimal.
Answer: 189/5 or 37.8
Key idea. At a y-intercept x is zero, so substitute x = 0 and solve for y.
3(0)/7 = −5y/9 + 21 0 = −5y/9 + 21 5y/9 = 21 y = 21(9/5) y = 189/5 = 37.8
Why this works. Every point on the y-axis has x-coordinate 0.
Question 21 · Nonlinear Functions
The graph of y = 2x² + bx + c is shown, where b and c are constants. What is the value of bc?
See figure in the original College Board PDF above.
Student-produced response — enter as a fraction or decimal.
Answer: −24
Key idea. Read c from the y-intercept, then use the other labeled point on the graph to solve for b.
The graph passes through (0, −6), so c = −6. The graph also passes through (−2, −6). −6 = 2(−2)² + b(−2) − 6 −6 = 8 − 2b − 6 0 = 8 − 2b b = 4 bc = 4(−6) = −24
Why this works. A graph of a quadratic supplies coordinate pairs that can be substituted into its equation.
Question 22 · Percentages
In 2008, Zinah earned 14% more than in 2007, and in 2009 Zinah earned 4% more than in 2008. If Zinah earned y times as much in 2009 as in 2007, what is the value of y?
- A) 0.5600
- B) 1.0056
- C) 1.1800
- D) 1.1856
Answer: D) 1.1856
Key idea. Convert each percent increase to a multiplier and multiply the two successive multipliers.
2008 factor = 1 + 0.14 = 1.14 2009 factor = 1 + 0.04 = 1.04 y = 1.14(1.04) = 1.1856
Why D works. The second 4% increase is applied to the already increased 2008 amount.
Questions 23–27: Geometry and modeling
Finish by extracting center-radius information, trig ratios, exponential multipliers, a linear rule from a table, and a similarity ratio.
Question 23 · Circles
Circle A (shown) is defined by the equation (x + 2)² + y² = 9. Circle B (not shown) is the result of shifting circle A down 6 units and increasing the radius so that the radius of circle B is 2 times the radius of circle A. Which equation defines circle B?
See figure in the original College Board PDF above.
- A) (x + 2)² + (y + 6)² = (4)(9)
- B) 2(x + 2)² + 2(y + 6)² = 9
- C) (x + 2)² + (y − 6)² = (4)(9)
- D) 2(x + 2)² + 2(y − 6)² = 9
Answer: A) (x + 2)² + (y + 6)² = (4)(9)
Key idea. Shift the center down, then square the doubled radius.
Circle A: center (−2, 0), radius 3. Shift down 6: new center (−2, −6). Double radius: new radius = 6, so r² = 36 = 4(9). (x + 2)² + (y + 6)² = 36 = (4)(9)
Why A works. A downward shift gives y + 6, and doubling a radius of 3 gives a squared radius of 36.
Question 24 · Right Triangles & Trig
Note: Figure not drawn to scale.
Right triangle ABC is shown. What is the value of tan A?
See figure in the original College Board PDF above.
- A) 3/54
- B) 1/√3
- C) √3
- D) 27√3
Answer: C) √3
Key idea. The 30° angle makes angle A equal to 60°, and tan 60° equals √3.
Angle C is 90° and angle B is 30°. So angle A = 180° − 90° − 30° = 60°. tan A = tan 60° = √3. Equivalently, in a 30–60–90 triangle: opposite to A = 27√3, adjacent to A = 27 tan A = 27√3 / 27 = √3.
Why C works. The tangent ratio for a 60° angle is √3.
Question 25 · Nonlinear Functions
At the time that an article was first featured on the home page of a news website, there were 40 comments on the article. An exponential model estimates that at the end of each hour after the article was first featured on the home page, the number of comments on the article had increased by 190% of the number of comments on the article at the end of the previous hour. Which of the following equations best represents this model, where C is the estimated number of comments on the article t hours after the article was first featured on the home page and t ≤ 4?
- A) C = 40(1.19)t
- B) C = 40(1.9)t
- C) C = 40(19)t
- D) C = 40(2.9)t
Answer: D) C = 40(2.9)t
Key idea. An increase by 190% means the new amount is 100% + 190% = 290% of the old amount.
initial comments = 40 hourly multiplier = 1 + 1.90 = 2.90 C = 40(2.9)^t
Why D works. 1.9 is the increase alone; the full multiplier must include the original 1 as well.
Question 26 · Linear Functions
| x | g(x) |
|---|---|
| −27 | 3 |
| −9 | 0 |
| 21 | 5 |
The table shows three values of x and their corresponding values of g(x), where g(x) = f(x)/(x + 3) and f is a linear function. What is the y-intercept of the graph of y = f(x) in the xy-plane?
- A) (0, 36)
- B) (0, 12)
- C) (0, 4)
- D) (0, −9)
Answer: A) (0, 36)
Key idea. Use g(x) to recover two points on the linear function f, then find the line’s y-intercept.
g(−27) = 3 = f(−27)/(−27 + 3) f(−27) = 3(−24) = −72 g(−9) = 0 = f(−9)/(−9 + 3) f(−9) = 0 f passes through (−27, −72) and (−9, 0). slope = (0 − (−72))/(−9 − (−27)) = 72/18 = 4 f(x) = 4x + b 0 = 4(−9) + b b = 36 The y-intercept is (0, 36).
Why A works. The line defined by the recovered points is f(x) = 4x + 36.
Question 27 · Lines/Angles/Triangles
In right triangle ABC, angle C is the right angle and BC = 162. Point D on side AB is connected by a line segment with point E on side AC such that line segment DE is parallel to side BC and CE = 2AE. What is the length of line segment DE?
Student-produced response — enter as a fraction or decimal.
Answer: 54
Key idea. Parallel segment DE creates a similar smaller triangle, and CE = 2AE makes AE one-third of AC.
CE = 2AE AC = AE + CE = AE + 2AE = 3AE AE/AC = 1/3 Because DE ∥ BC, triangles ADE and ABC are similar. DE/BC = AE/AC = 1/3 DE = (1/3)(162) = 54
Why this works. Corresponding sides of similar triangles have one common scale factor.
How SOMATH prepares NYC students for the Digital SAT
SOMATH (School of Math) is a math-focused school on the Upper West Side of Manhattan, cofounded by Marcelo Ambrozio (Northwestern-trained lead math teacher) and Vivianne Wright (Harvard-trained, also runs MBA House, one of the largest international GMAT/EA prep firms). Vivianne’s track record with standardized tests — hundreds of admits to Harvard Business School, Stanford GSB, Wharton, MIT Sloan, and INSEAD — is the same rigor we bring to SAT prep for high schoolers.
Our Digital SAT track:
- Small-group in-person classes (6–8 students max) at 226 W 79th Street on the Upper West Side. Same room, same teacher, same students, week after week.
- Structured curriculum aligned to the current Digital SAT framework across all four Math domains and all four Reading & Writing domains.
- Bluebook + Desmos drilling. We do not just teach math — we teach how to use the built-in Desmos calculator to solve problems 2–3× faster than by hand.
- Full-length timed Modules 1 and 2 for both Math and R&W with graded free-response feedback. Every student sees their scores tracked week by week.
- Free 30-minute in-person diagnostic evaluation before enrollment ($99 one-time enrollment fee applies for new students who continue into our program). The evaluation identifies exactly which domain needs the most work and produces a written diagnostic within 48 hours.
Ready to raise your SAT Math score?
Start with a free 30-minute in-person diagnostic at our Upper West Side classroom. Includes a written diagnostic report within 48 hours — yours to keep whether you enroll or not. A one-time $99 enrollment fee applies if you join a course.
Book Free Evaluation → or call (646) 668-6151
Want your child in an SAT Math class at SOMATH?
Small-group Digital SAT Math prep on the Upper West Side. Full Bluebook + Desmos drilling, timed Modules 1 & 2, weekly score tracking, and a free 30-minute in-person diagnostic before enrollment.
Digital SAT Practice Test 6 Math Module 1 FAQ
What does this Practice Test 6 Math Module 1 walkthrough cover?
It covers all 27 questions in the module, including the multiple-choice choices and student-produced responses. Every item has the official answer, a worked solution, and a short explanation of the underlying SAT Math skill.
Which questions in Practice Test 6 Math Module 1 are student-produced responses?
Questions 6, 7, 13, 14, 20, 21, and 27 are student-produced responses in this module. For these items, the walkthrough shows a numeric or fractional answer that can be entered in the Bluebook response grid.
How should I handle the graph and figure questions in this module?
Read the graph or figure directly in the College Board PDF, then translate the visual information into a mathematical statement. In this module, that approach is especially useful for the model questions, the quadratic graph, the circle transformation, the trigonometry question, and the similar-triangle question.
Why does Question 22 multiply 1.14 by 1.04?
A 14% increase changes an original amount to 1.14 times the original, and a further 4% increase changes that new amount to 1.04 times it. Sequential percent changes multiply, so the overall factor is 1.14 × 1.04 = 1.1856.
What is the key idea in Question 27?
Because DE is parallel to BC, triangles ADE and ABC are similar. The condition CE = 2AE makes AE one-third of AC, so the corresponding side DE is one-third of BC: 162 ÷ 3 = 54.