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|---|---|---|---|---|---|---|---|
ba21cec2-d5a7-4a27-bc0d-5b8d3fc7c795 | 69 | Puzzle | Among the four given pairs of gears, which one is likely to last longer over time? | [
"A. 16 and 9",
"B. 20 and 15",
"C. 18 and 12",
"D. 12 and 8",
"E. 14 and 7"
] | A | {"1": "To determine which pair of gears will last longer, we need to consider the common factors of the number of teeth in each gear pair. Gears with fewer common factors will have less repetitive contact between the same teeth, reducing wear and tear over time.", "2": "For the pair of gears with 16 and 9 teeth, the on... | medium |
02403eb2-d175-491b-868b-2040883091f8 | 94 | Statistics | Find the ratio of the blue shaded area to the pink shaded area? | [
"A. π",
"B. 2/π",
"C. 1",
"D. π/2",
"E. 1/2"
] | C | {"1": "Let the circle have diameter D and the inscribed square therefore have side length s = D/√2, giving square area A_square = s² = D²/2.", "2": "On each side of the square draw a semicircle of diameter s, creating four “loom” regions inside the original circle. We compare A_square to A_looms (the combined area of t... | medium |
ff8573d4-05d0-41de-ab2a-eb00acda90f8 | 294 | Geometry Area | Find the area of the square shaded in red? | [
"A. 64",
"B. 36",
"C. 49",
"D. 4",
"E. 25"
] | D | {"1": "Given the red squares side length is x. Both circles have radius 5, and the squares top corners are tangent to the circles.", "2": "From the left circles center drop a vertical to the squares top, splitting that distance into x (down to the square) and 5 - x above it. Likewise, the horizontal distance splits int... | medium |
30f44167-024b-4af5-b7c1-f94cb9cdc389 | 300 | Puzzle | In how many ways can Tom reach Jerry by following only the direction of the arrows and covering the minimum possible distance? | [
"A. 462",
"B. 1716",
"C. 924",
"D. 252",
"E. 3432"
] | C | {"1": "Tom needs to reach Jerry by traveling in a 6x6 grid, which means he must travel 6 steps in the horizontal direction and 6 steps in the vertical direction.", "2": "The total number of steps Tom needs to take is 12, consisting of 6 horizontal (H) and 6 vertical (V) steps.", "3": "The problem of finding the number ... | medium |
c34305f8-1243-42cd-a6aa-bef9911b91ab | 286 | Puzzle | Identify the top-down 2D view of the last shown structure on the left? | [
"A. A",
"B. B",
"C. C",
"D. D",
"E. None of the above."
] | B | {"1": "To determine the top-down 2D view of the 3D structure, start by counting the number of blocks visible from above. This involves only counting the topmost block in each vertical stack since that's all that can be seen from a top-down perspective.", "2": "In the given structure, identify the number of blocks visib... | long |
d9da1af2-414c-444e-8149-2395453d83a6 | 307 | Puzzle | In the final example shown for off folds in the video, a sheet of paper is folded and a hole is punched as shown. Choose from the given options how the paper will appear when fully unfolded? | [
"A. A",
"B. B",
"C. C",
"D. D",
"E. E"
] | A | {"1": "The problem involves a sheet of paper that is folded using 'off folds', which are folds that do not align with the standard quarter or half folds but instead involve unusual fractions of the paper.", "2": "In this example, two off folds are applied to the paper. The first off fold involves folding three quarters... | long |
9c4d940a-7fd4-4446-817e-42043a2aa456 | 253 | Chart | What percentage of Walmart’s total revenue is lost to taxes and interest combined? | [
"A. 1.22%",
"B. 3%",
"C. 9%",
"D. 1.4%",
"E. 1.39%"
] | E | {"1": "The video explains Walmarts business operations for FY24, focusing on its massive revenue, tight profit margins, and financial structure, highlighting how Walmart, despite being the largest company by revenue, retains only a small percentage of earnings after expenses.", "2": "To answer the question about the pe... | long |
b20750dd-ffef-450c-9f00-6de49574a63c | 111 | Chart | What percentage of the US working population has an annual income exceeding $100,000? | [
"A. 25%",
"B. 14%",
"C. 12%",
"D. 18%",
"E. 36%"
] | A | {"1": "The video 'If the United States Were 100 People' discusses U.S. population statistics by imagining the population as 100 people.", "2": "Around the 2-minute mark, the video focuses on the annual income distribution among working adults.", "3": "The income chart divides the 100 working adults into groups based on... | long |
d64f5d49-6a2b-4628-b284-12d2b8e21c26 | 219 | Arithmetic | What is the average speed for the truck? | [
"A. 3.55 m/s",
"B. 4 m/s",
"C. 3.6 m/s",
"D. 5 m/s",
"E. 4.5 m/s"
] | A | {"1": "The average speed is calculated by dividing the total distance traveled by the total time taken.", "2": "From the video graph, the final distance at the end of the trip is 160 meters at 45 seconds.", "3": "Thus, the total distance traveled is 160 meters, and the total time is 45 seconds.", "4": "Average speed = ... | medium |
a0c10b5b-a578-41f6-994a-f8c08aca3c77 | 161 | Statistics | What is the 60th percentile of the class marks? | [
"A. 35",
"B. 35.5",
"C. 35.2",
"D. 36",
"E. 36.5"
] | D | {"1": "The original list of ordered samples is: 15, 20, 25, 31, 34, 34, 35, 35, 36, 36, 36, 38, 38, 39, 43.", "2": "To find the 60th percentile of the class marks, we first need to determine the position of this percentile in the ordered data set. The formula to find the position of the pth percentile is given by: p/10... | medium |
f2bb48cf-f41a-48a9-abae-175f913606a6 | 273 | Counting | Can you calculate the number of all possible triangles in the final one? | [
"A. 14",
"B. 9",
"C. 11",
"D. 13",
"E. 12"
] | D | {"1": "Identify the pattern as Model 2: a single outer triangle with n embedded triangles, and recall the shortcut formula total = 4n + 1.", "2": "Examine the diagram and count the number of triangles embedded inside the outermost triangle: there are 3 embedded triangles.", "3": "Assign n = 3 and substitute into the fo... | long |
fbeebdbd-39c4-4e81-9a2e-c06438315772 | 197 | Counting | Find how many boxes are on the trailer? | [
"A. 28",
"B. 30",
"C. 55",
"D. 52",
"E. 50"
] | E | {"1": "From the side view, we observe three layers of boxes: the bottom layer has 7 boxes, the middle layer has 6 boxes, and the top layer has 4 boxes.", "2": "Each layer is 3 boxes deep, as confirmed by the back and top views. Therefore, the bottom layer contains 7 x 3 = 21 boxes.", "3": "Similarly, the middle layer c... | medium |
6fa78322-cc98-4e07-bee5-c0b5a9e10583 | 58 | Geometry Area | Find the area of the paperplane like shape shaded in blue? | [
"A. 48",
"B. 31.5",
"C. 36",
"D. 26.27",
"E. 27.92"
] | D | {"1": "Start with a piece of paper measuring 8 × 6, for an area of 48 square units.", "2": "Fold the paper so that each crease bisects the top angle, forming two isosceles right triangles whose legs are each 3 (half of the rectangles 6-unit short side).", "3": "The hypotenuse of each isosceles right triangle is 3√2, an... | medium |
342f440e-c10e-42ff-a5b1-81ebf09b59fe | 164 | Geometry Length | In the second example, what is the length of the tangent if the sides of the rectangle are 20 and 5? | [
"A. 15",
"B. 5",
"C. 25",
"D. 10",
"E. 20"
] | D | {"1": "We are given a rectangle with sides 20 and 5, and we need to find the length of the tangent using the tangent-secant theorem.", "2": "According to the tangent-secant theorem, the square of the length of the tangent is equal to the product of the lengths of the secant segments.", "3": "In this problem, the secant... | medium |
a96e6b05-ffce-43f4-9539-ceb9db714cc4 | 398 | Statistics | Find the probability that a random point lies in the yellow shaded region? | [
"A. 33%",
"B. 25%",
"C. 78%",
"D. 38%",
"E. 50%"
] | D | {"1": "The yellow region is the part of the big circle that lies outside the two identical blue circles and the one green circle that are tangent to each other and to the big circle. To find the yellow regions area, we subtract the area of these three smaller circles from the area of the big circle. This is expressed a... | medium |
1c329837-272b-4991-bc57-321a1476ae70 | 171 | Geometry Length | What is the radius of the largest circle? | [
"A. 12",
"B. 9",
"C. 3",
"D. 6",
"E. 15"
] | B | {"1": "A circle tangent to two rays with angle 60° has its center on the angle bisector, forming right triangles at the vertex with one acute angle of 30°.", "2": "For the first circle of radius 1, the perpendicular from its center to a ray is the short leg (length 1) of a 30-60-90 triangle, so the hypotenuse (vertex-t... | short |
cce549d9-f3d6-48f0-a3fe-2d49291249af | 268 | Counting | What is the total number of distinct triangles visible? | [
"A. 30",
"B. 40",
"C. 35",
"D. 20",
"E. 25"
] | C | {"1": "Identify the outer pentagon: 5 triangles.", "2": "Count the triangles formed by each pentagon side with the central point: 5 triangles.", "3": "Count the triangles formed by each inner segment connecting outer vertices to the central point: 5 triangles.", "4": "Identify triangles formed within each section of th... | short |
03bb5639-4b1e-48ae-8542-905647627ffe | 323 | Counting | How many individual cubes are there in total? | [
"A. 7",
"B. 8",
"C. 6",
"D. 9",
"E. 10"
] | E | {"1": "Recall the rule: any cube that has another cube resting on it must be present, even if hidden from view.", "2": "Partition the shape into two parts: the left section (a 2×2 grid) and the right section.", "3": "Count the left 2×2 grid: three cubes are visible and one must be hidden underneath to support the top c... | medium |
40660eef-ea44-4e93-a6e0-b28a33466d22 | 82 | Chart | Analyse the timeline and identify the year in which the number of deaths caused by HIV/AIDS first exceeded those caused by tuberculosis? | [
"A. 2000",
"B. 2002",
"C. 2001",
"D. 2004",
"E. 2003"
] | B | {"1": "The chart is a timeline tracking global causes of death across multiple years. We have to focus is on two categories: Tuberculosis and HIV/AIDS, observing how their rankings and death counts change over time.", "2": "In 1993, Tuberculosis is a major cause of death with 1,771,586 deaths, ranking high on the chart... | medium |
70753650-761e-4855-b45e-0c6966ece078 | 263 | Puzzle | Where is Mike Wazowski hiding among the Toy Story aliens? | [
"A. Just left of Woody’s belt buckle, peeking between two aliens.",
"B. In the top center area, partially hidden between two aliens with raised arms.",
"C. After Woody’s right shoulder, nearby the top-right of the image, blending with the crowd.",
"D. Near the bottom left corner, slightly behind an alien wavi... | C | {"1": "Observe the image filled with identical three-eyed green aliens from Toy Story, and note the presence of a blurred Woody figure in the foreground.", "2": "Recall that Mike Wazowski is a character from Monsters, Inc., known for his single large eye, small horns, and lack of antennas, which makes him visually dist... | short |
998d6ba5-ea65-4250-8561-a3396ba02d36 | 54 | Geometry Length | What is the radius of the circle? | [
"A. 26.4 cm",
"B. 21 cm",
"C. 21.25 cm",
"D. 28 cm",
"E. 24.25 cm"
] | C | {"1": "Let the vertical segment of length 16 be extended by an unknown amount x so that its top reaches the circle. Then one right triangle has horizontal leg 9 + 12 = 21 and vertical leg x, with hypotenuse r. By Pythagoras: r² = 21² + x².", "2": "The other right triangle is formed by the extended vertical of length 16... | short |
84e42677-0f08-4685-a253-10d4b659a19f | 67 | Geometry Area | Find the approximate area of a single square? | [
"A. 7",
"B. 25",
"C. 64",
"D. 17",
"E. 36"
] | B | {"1": "The problem involves a rectangle measuring 17 units by 26 units, with seven squares placed inside it.", "2": "We need to find the area of a single square. The key is to focus on a right triangle whose hypotenuse is equal to the side of the square.", "3": "Let's denote the legs of the right triangle as A and B, a... | short |
43c62167-f6fb-44f6-b96c-3b771aa0b3b4 | 257 | Chart | In 2015, how much more oil did the Rest of the World (excluding the countries explicitly listed) consume compared to Germany? | [
"A. 23",
"B. 25",
"C. 15",
"D. 20",
"E. 18"
] | D | {"1": "The video explains what oil is used for and how its price is influenced by OPECs production decisions, geopolitical developments, and global supply-demand trends. It also shows how oil consumption and production have shifted due to the rise of non-OPEC producers and changing demand from major economies.", "2": "... | long |
00999e39-cfee-4b55-8171-aaa5bf90c8c8 | 188 | Geometry Angle | Find the value of angle EDF marked in green? | [
"A. 90 degree",
"B. 60 degree",
"C. 30 degree",
"D. 42 degree",
"E. 45 degree"
] | E | {"1": "Note that A, B is the diameter of the semicircle and C lies on the arc, so ∠ACB is an inscribed angle subtending a semicircle (180°). Hence ∠ACB = ½·180° = 90°.", "2": "Let I be the incenter of ΔACB, with E the tangency point on BC and F the tangency point on CA. Then IE ⟂ BC and IF ⟂ CA, so ∠IEC = ∠IFC = 90°.",... | short |
bedbd0f6-22f4-4617-8310-6b44b0914c45 | 260 | Chart | Based on the revenue trend of Apple Pay, estimate the company’s total services revenue in 2019? | [
"A. 31 billion",
"B. 25 billion",
"C. 60 billion",
"D. 22 billion",
"E. 48 billion"
] | A | {"1": "The video analyzes Apples growing role in consumer payments through services like Apple Pay and the impact this has on traditional banks. It also presents Apple Pays revenue trend and contextualizes it within the broader Apple services ecosystem.", "2": "Around 2:32, the video shows a bar chart tracking Apple Pa... | long |
4295670b-18ba-425c-8204-33ba2dd12185 | 225 | Geometry Area | What is the area of the given hexagon? | [
"A. 223",
"B. 222",
"C. 120",
"D. 37",
"E. 60"
] | B | {"1": "The regular hexagon is composed of 6 equilateral triangles, each with 60° interior angles, and is inscribed within the square ABCD.", "2": "Connect the top vertex E of the hexagon to the rightmost vertex F of the hexagon. The triangle BEF and the smaller blue triangle AEG (with an area of 20) are similar because... | medium |
c620c910-f5da-43f1-8ea4-1916a4f3a57f | 418 | Puzzle | Based on the video, if 6 points are placed on the circumference of a circle, how many distinct regions can be formed inside the circle? | [
"A. 31",
"B. 33",
"C. 48",
"D. 64",
"E. 32"
] | A | {"1": "To determine how many distinct regions can be formed inside a circle by connecting 6 points on its circumference, we use a formula derived from combinatorics.", "2": "The number of regions formed is given by the sum: 1 plus the number of pairs among the points (6 choose 2), plus the number of quadruples among th... | medium |
619e6082-3bbb-4bd3-93fe-135db3c273f1 | 116 | Geometry Area | Find the area of the blue shaded region? | [
"A. 0.43",
"B. 0.11",
"C. 0.35",
"D. 0.27",
"E. 0.23"
] | E | {"1": "Given an equilateral triangle of side length 1 with three inscribed squares of side lengths A, 2A, and 3A.", "2": "Dividing the triangles base into segments corresponding to those squares yields A/√3 + 6A + √3A = 1, so A = (9 - 2√3) / 46.", "3": "Compute A² = ((9 - 2√3) / 46)² = (93 - 36√3) / 2116.", "4": "The t... | medium |
5228d155-4adc-473f-8ddc-dcbc688fde22 | 271 | Counting | Can you calculate the number of tirangles present in the last example? | [
"A. 19",
"B. 34",
"C. 27",
"D. 20",
"E. 18"
] | B | {"1": "Identify the number of baselines in the given triangle. In this example, there are three distinct baselines.", "2": "For each baseline, assign numbers starting from 1. For the bottom baseline, assign numbers 1 to 6, as it is divided into six parts.", "3": "For the second baseline, start a new series of numbers f... | long |
4d4d9f87-bae9-4dbd-9d99-902cfe012e2e | 6 | Geometry Angle | Find the value of the angle marked in orange? | [
"A. 22.5 degree",
"B. 90 degree",
"C. 30 degree",
"D. 15 degree",
"E. 45 degree"
] | A | {"1": "The two lines from the center to the corners of the square form a central angle of 90° (since it is the corner of the square).", "2": "Construct a circle centered at the external vertex. By the inscribed-angle theorem, the inscribed angle subtending the same arc as the 90° central angle is 90°/2 = 45°.", "3": "W... | medium |
d379804a-245c-47b5-82dd-67adf83fe11f | 15 | Geometry Area | Calculate the are of the shaded region? | [
"A. 25",
"B. 10",
"C. 5",
"D. 20",
"E. 40"
] | D | {"1": "The problem involves a rectangle ABCD made up of five congruent rectangles. Given that the length of AD is 10 units, we need to find the area of triangle ABE.", "2": "Since the five rectangles are congruent, the ratio of their sides is 1:2. Let the vertical side of each rectangle be L and the horizontal side be ... | short |
01667fae-a28e-4076-9925-1d8ae442029d | 389 | Topology | In the given video, which option is correct to remove the red string from the ring without any tools? | [
"A. Cut the string",
"B. Move the string to the middle of the track, pass the string through the ring, keep the direction, use the gap of the red string to circle the ring and move it along the track to remove it.",
"C. Move the string along the track and remove it",
"D. Move the string to the middle of the t... | D | {"1": "Observe that the circular ring has a continuous track with a narrow gap at its midpoint and the red string has two balls at its ends that act as stoppers.", "2": "Slide the string so that one of the balls sits exactly at the midpoint gap of the rings track; do not attempt to go around the rest of the ring yet.",... | medium |
3f02adb7-8fae-4001-995e-b05b3fca30bc | 141 | Geometry Length | Determine the radius of the large circle? | [
"A. 0.69",
"B. 0.6",
"C. 0.5",
"D. 0.7",
"E. 0.89"
] | E | {"1": "Start by considering the square with side length equal to 1. Construct semi-circles on two adjacent sides of the square, each with a radius of 0.5, since the radius is half the side length of the square.", "2": "Circumscribe a circle around the heart shape formed by the semi-circles. Let the radius of this large... | short |
2400bd8c-6fbc-4a77-b7a7-1fc9507dbac4 | 117 | Chart | By approximately what percentage did UMH Properties stock increase from 2016 to 2021? | [
"A. 100%",
"B. 70%",
"C. 80%",
"D. 50%",
"E. 150%"
] | D | {"1": "The overall video discusses suburban development, housing affordability, and economic challenges in America's suburbs and cities, covering real estate investment, changing demographics, and impacts on housing-related companies.", "2": "Following the storyline, after discussing housing challenges and suburban cha... | long |
2eddb323-261f-48a3-ae53-38549f44951e | 248 | Geometry Area | Which rectangle shaded area is greater? Red shaded rectangle or Blue shaded rectangle ? | [
"A. There is insufficient information to solve the problem",
"B. Depends on the scale used in the drawing",
"C. Both are equal",
"D. Red shaded Rectangle",
"E. Blue shaded rectangle"
] | C | {"1": "Start with a rectangle, then copy and rotate it about a point to create two overlapping rectangles shaded red and blue.", "2": "The problem asks which of the two shaded areas, red or blue, is larger.", "3": "After overlapping, the rectangles share a common region.", "4": "In the non-shared parts, two triangles f... | short |
8fc9fbc0-3d16-455e-8804-43e37a57d43d | 176 | Statistics | What are the median and mode of the data shown in the first stemplot? | [
"A. Mean: 124.5, Mode: 127, 128",
"B. Mean: 124.5, Mode: 127",
"C. Mean: 124, Mode: 127",
"D. Mean: 124, Mode: 128",
"E. Mean: 126, Mode: 127, 128"
] | A | {"1": "The stem plot shows numbers where each stem (left column) represents the tens digit, and each leaf (right) represents the units digit. So a stem of 10 and a leaf of 0 gives 100, and so on.", "2": "Extract and list all the numbers in ascending order:\n100, 101, 101, 102, 103, 105, 106, 106 (8 leaves)\n111, 112, 1... | long |
1720a2d8-288f-441a-a6d1-01bfa6f702ea | 407 | Statistics | Can you find the probability asked? | [
"A. 0.43",
"B. 0.50",
"C. 0.89",
"D. 0.64",
"E. 0.15"
] | E | {"1": "We are asked to calculate the probability that a randomly chosen point within the large rectangle falls in the shaded blue region.", "2": "From the diagram, the shaded region lies outside a semicircle and a small rectangle, but still inside the larger rectangle. So we will find the shaded area by subtracting the... | medium |
95bc3bae-47a0-4ab0-ad25-3bf2720e00d2 | 397 | Topology | You have a wooden stand puzzle with a blue ring trapped around a vertical piece. A string passes through the ring, attached to two wooden beads and circles. The objective is to remove the blue ring without cutting the string or disassembling the puzzle. The steps provided are:
(A) Move the right wooden bead to the top... | [
"A. ACBD",
"B. ACDB",
"C. DACB",
"D. DCAB",
"E. ADCB"
] | C | {"1": "First, pass the right wooden circle through the gap. This step allows the circle to move freely and sets up the next steps (Step D).", "2": "Next, move the right wooden bead to the top. This creates enough space for the ring to maneuver (Step A).", "3": "Then, pass the ring through the wooden bead. This step is ... | short |
023297fc-11b2-45ad-afea-9e4fad73b188 | 98 | Puzzle | Calculate the area of the regions shaded in orange? | [
"A. 3/4",
"B. 1/2 + π/4",
"C. 1/2",
"D. 1 - π/4",
"E. 1/4"
] | C | {"1": "Consider the square of side length s (area = s^2). Four semicircles of radius s/2 are drawn on each sides midpoint, and the parts of these semicircles outside the square are colored orange.", "2": "Each orange region is a congruent semicircular segment of radius s/2, so all four have equal area by symmetry.", "3... | short |
39d2a00c-3901-4152-b621-6af7e10170ba | 118 | Chart | Between May 2020 and May 2021, by approximately how much did the transit ridership for Metro-North Railroad bridge and tunnel crossings increase in New York City? | [
"A. 65%",
"B. 45%",
"C. 90%",
"D. 105%",
"E. 85%"
] | A | {"1": "The video discusses shifts in suburbanization, city life, and how people moved out of major cities after the pandemic.", "2": "Following the storyline, after discussing changes in city life and movement patterns, the video transitions to how public transit usage changed; around 34 minutes, a graph appears showin... | long |
c5544974-cf70-47b0-bb1b-d9065f2e7dc8 | 131 | Geometry Length | Find the length of OD? | [
"A. 9",
"B. 36",
"C. 24",
"D. 16",
"E. 49"
] | C | {"1": "Let E, F and G be the points where the semicircle centered at O is tangent to AB, CD and BC. Then OE ⟂ AB and OF ⟂ CD, and OE = OF = R.", "2": "Since AO = OD, triangles AEO and DFO are congruent, so AE = DF = X.", "3": "AB = 9 gives EB = 9 - X, and CD = 16 gives CF = 16 - X.", "4": "By equal tangents, from B we ... | short |
18621953-4da4-4751-8ee1-5a2ba8264dd4 | 227 | Arithmetic | If the given matrix is multiplied by a scalar value of 2, what will be the determinant of the resulting matrix? | [
"A. 36",
"B. 24",
"C. 68",
"D. 72",
"E. 144"
] | E | {"1": "Multiply every element of the matrix A by 2:", "2": "New matrix = [[6×2, 6×2], [-2×2, 4×2]] = [[12, 12], [-4, 8]].", "3": "Now find the determinant: |New A| = (12 × 8) - (12 × -4).", "4": "Final answer for determinant: 96 - (-48) = 96 + 48 = 144."} | short |
909eecb4-99e4-406c-b268-b32b2dc18de5 | 377 | Topology | Two nails are trapped and seems impossible to remove. However, with careful tricks it might be solved. Below are the steps to solve the puzzle. Arrange them correctly to solve the puzzle:
A) Rotate the right nail counterclockwise
B) Rotate the right nail 180 degrees
C) Flip both nails over
D) Slide the right nail behin... | [
"A. CADBEF",
"B. DABEFC",
"C. BCAFED",
"D. ABCDEF",
"E. CADBFE"
] | E | {"1": "Flip both nails over to reorient their loops for separation (Step C).", "2": "Rotate the right nail counterclockwise to align its shank with the left nail’s gap (Step A).", "3": "Slide the right nail behind the crossbar to disengage its head from the loop (Step D).", "4": "Rotate the right nail 180 degrees to mo... | short |
71e52c92-55c9-450b-9539-4bfa5fe631fa | 348 | Chart | By how many percentage points does the gap between China and the Rest of the World (excluding the U.S.) in global battery manufacturing change from 2023 to 2030? | [
"A. Shrinks by 6%",
"B. Increases by 16%",
"C. Increases by 10%",
"D. Shrinks by 14%",
"E. Shrinks by 23%"
] | A | {"1": "The video presents how U.S. industrial policy, driven by the Inflation Reduction Act and the CHIPS Act, aims to reduce global supply chain dependence on China by shifting manufacturing toward domestic production and allied nations.", "2": "In the final quarter of the video, the focus shifts from legislative impa... | long |
71466c42-eb50-452d-bc81-ecdc939c640c | 145 | Geometry Area | Find the difference of the blue shaded area from the orange shaded? | [
"A. 9",
"B. 9π",
"C. 9π/2",
"D. 9(1 - π/4)",
"E. π"
] | E | {"1": "Define the areas: Let each orange area be 'a' units, each blue area be 'c' units, and the overlap between the quarter circle and the semicircle be 'b' units.", "2": "Express the total areas: The total orange area is 4a, and the total blue area is 4c. We need to find the difference 4a - 4c.", "3": "Relate the are... | medium |
55bf5f62-d921-4308-a135-b09a2e010d74 | 158 | Geometry Length | Determine the length of the elastic band? | [
"A. 6.6 m",
"B. 4 m",
"C. 9.1 m",
"D. 5 m",
"E. 7.2 m"
] | A | {"1": "The problem involves three equal-sized circles arranged in a triangular formation, each pair being tangent to each other, and an elastic band is wrapped around them.", "2": "The height from the top of the top circle to the bottom of the bottom two circles is given as 2 meters. We need to find the radius of each ... | short |
bdc8d2b9-cb2d-4e1d-b03d-12673af20fd8 | 339 | Statistics | A bag contains several balls as shown in the video. Which color has a probability of 0.25 of being selected? | [
"A. Yellow",
"B. Purple",
"C. Blue",
"D. Red",
"E. Orange"
] | E | {"1": "Count the number of balls of each color in the bag: Red: 1, Blue: 3, Yellow: 4, Orange: 5, Purple: 7.", "2": "Calculate the total number of balls: 1 + 3 + 4 + 5 + 7 = 20 balls.", "3": "To find the probability of selecting a ball of a specific color, divide the number of balls of that color by the total number of... | medium |
28b6eb8e-e92d-4198-86a3-451a22f2c9bb | 57 | Geometry Area | Find the area of the shaded region ABCGEA? | [
"A. 125 m²",
"B. 112.5 m²",
"C. 275 m²",
"D. 200 m²",
"E. 250 m²"
] | C | {"1": "The problem involves finding the area of the shaded region ABCGEA, where ABCD is a square and AEFD is a rhombus.", "2": "The area of the square ABCD is given as 625 m², which means each side of the square is 25 m (since 25² = 625).", "3": "The area of the rhombus AEFD is given as 500 m². Since AEFD is a rhombus,... | short |
7f4b8fef-1242-4b29-9687-ae2430bf4d61 | 63 | Geometry Area | What is the minimum area of the large triangle? | [
"A. 12",
"B. 6",
"C. 30",
"D. 24",
"E. 27"
] | D | {"1": "We consider a right triangle with an inscribed rectangle whose horizontal side is x and vertical side is y.", "2": "The rectangles top edge is 4 units below the triangles top vertex, and its right edge is 3 units left of the triangles right vertex. By similarity 4/x = y/3, so x·y = 4·3 = 12—the rectangles area."... | medium |
1db5ab5d-c889-446e-b174-869e37e08042 | 354 | Chart | The video shows data on how prices of some essentials rose significantly from 2021 to 2022 due to global inflationary pressures. Later in December 2022, prices for some of those items began to decline, showing early signs of deflation or correction.
Using these data, compare how the prices of the following three categ... | [
"A. +30%, -3%; +40%, -16%; +20%, -11%",
"B. +28%, -3%; +41%, -17%; +19%, -4%",
"C. +28%, -3%; +41%, -16%; +19%, +5%",
"D. +30%, -5%; +45%, -15%; +20%, -10%",
"E. +28%, -3%; +41%, -17%; +19%, +3%"
] | E | {"1": "The video investigates the causes and dynamics of inflation over the past few years, focusing on how different products experienced price surges due to various global and domestic factors such as supply chain disruptions, labor costs, material costs, and corporate pricing strategies. It aims to break down inflat... | long |
cc6f5543-ca7c-4bd7-b304-a7f9263067eb | 50 | Geometry Length | Find an approximate length of EF? | [
"A. 10",
"B. 22",
"C. 20",
"D. 11",
"E. 14"
] | D | {"1": "Define three regions: A = area of the part of the semicircle outside triangle DEF, B = area of the part of triangle DEF outside the semicircle, and C = area of overlap between the triangle and semicircle.", "2": "Given A = B + 47, add C to both sides to get A + C = B + C + 47.", "3": "Observe that A + C is the e... | short |
abc0dfe2-1483-47eb-80b5-0146caa12d9e | 124 | Geometry Length | Find the length of the tangent line segment AB? | [
"A. 6√5",
"B. 18",
"C. 12√2",
"D. 8",
"E. 10√2"
] | B | {"1": "Since AB is a common tangent to both the semicircle and the quarter circle, the two radii to the tangent points are each perpendicular to AB, giving two right angles at A and B.", "2": "At A, draw a horizontal line from A to form a right triangle (blue triangle) with AB as its hypotenuse. At B, consider the righ... | medium |
c4ca4d98-a194-4a15-97f4-9e0c24df2512 | 351 | Chart | Based on the studies conducted by OECD, how does the average teacher's salary compare to similarly educated professionals in Germany versus Hungary? | [
"A. 90/53",
"B. 98/68",
"C. 102/80",
"D. 101/79",
"E. 94/73"
] | E | {"1": "The video is about teacher compensation in the United States and internationally, focusing on the wage gap between teachers and similarly educated professionals.", "2": "It highlights challenges in the U.S. education system and uses comparative data to show how U.S. teacher salaries fall short relative to other ... | long |
044559b1-921a-454e-b09c-7de456a462ec | 9 | Geometry Area | Determine the ratio of the area shaded in yellow and the area shaded in blue? | [
"A. π/8",
"B. 1/2",
"C. 1",
"D. π/2",
"E. 3π/8"
] | C | {"1": "First, consider the semicircle with center O and endpoints A and B, where OB is perpendicular to AO, forming an isosceles right triangle ABO.", "2": "Label the diameter of the semicircle as AC. Since triangle ABO is isosceles and right-angled, AB is equal to AO multiplied by the square root of 2, according to th... | medium |
b2123030-cb8f-45e3-a066-248b0a510fa5 | 252 | Chart | How does China’s investment in the Belt and Road Initiative in 2016 compare to its holdings of U.S. treasuries in the same year? | [
"A. 35:1",
"B. 38:1",
"C. 36:1",
"D. 30:1",
"E. 32:1"
] | D | {"1": "The video examines Chinas changing economic strategy, focusing on its declining holdings of U.S. Treasuries and rising investment in global infrastructure through the Belt and Road Initiative (BRI), explaining the shift from debt accumulation to infrastructure funding.", "2": "Midway through the video, the discu... | long |
88b4f84b-4c92-464b-aad1-b9611edbe5eb | 411 | Statistics | The presenter walks you through two examples that demonstrate how to approach geometric probability problems. Study the method used in these examples carefully. Then, apply a similar approach to solve the final problem presented at the end of the video? | [
"A. 0.33",
"B. 0.77",
"C. 0.55",
"D. 0.22",
"E. 0.66"
] | E | {"1": "The presenter explains two examples involving geometric probability, then presents Example #3, which asks for the probability that a randomly chosen point inside a cylinder lies within one of the spheres it contains.", "2": "The figure shows a cylinder of height 24 units and diameter 8 units. Inside it are three... | long |
23e79ec6-9ad5-4e10-ba2b-524cb201e8de | 297 | Geometry Area | Find the approximate area of rectangle shaded in green? | [
"A. 41 cm²",
"B. 4 cm²",
"C. 90 cm²",
"D. 22 cm²",
"E. 10 cm²"
] | D | {"1": "Let the rectangles width be x and its height be y. The horizontal cut at height y from the bottom leaves an upper right triangle with legs x (horizontal) and (6 - y) (vertical).", "2": "The area of that upper triangle is 16 cm², so (1/2)·x·(6 - y) = 16 ⇒ x·(6 - y) = 32.", "3": "This triangle is similar to a righ... | medium |
a23a86cc-c84d-4138-903d-75902f8a8a0c | 305 | Puzzle | Look at the final example in the video. Which cube accurately forms when the flat pattern on the left is folded? | [
"A. A",
"B. B",
"C. C",
"D. D",
"E. There is insufficient information to solve the problem"
] | B | {"1": "Focus on the distinctive hourglass shape in the net, which is formed by two triangles meeting in the center of one face. Note its orientation relative to the other faces: it is surrounded by black, white, and gray triangles.", "2": "Visualize folding the net. The central face with the hourglass will be adjacent ... | long |
4de25549-109c-46cb-a328-4fd52226bc82 | 338 | Statistics | The video shows a box containing balls of different colors. Two balls are randomly selected from the box without replacement. What is the probability that both selected balls are the same color? | [
"A. 2/7",
"B. 1/4",
"C. 1/3",
"D. 1/5",
"E. 7/15"
] | A | {"1": "There are 4 red balls, two blue balls, and two white balls in the box.", "2": "The probability that both selected balls are the same color = (number of ways to pick two balls of the same color) / (total ways to pick any two balls).", "3": "Total ways to choose any two balls from the eight is C(8,2) = 8·7/2 = 28.... | short |
b5533bc0-7cc9-4629-80f5-f6c84808b09d | 408 | Statistics | Follow the method demonstrated in the examples. Use the same logic to complete the final problem? | [
"A. 0.841",
"B. 0.125",
"C. 0.15",
"D. 0.09",
"E. 0.25"
] | D | {"1": "The video presents several problems about geometric probability. The final problem, labeled Example #5, asks to find the probability that a randomly chosen point in the circle falls within the shaded blue sector.", "2": "The figure shows a full circle inside which a shaded region is formed by a 90° sector minus ... | long |
6076f592-125b-4760-9c1b-8696ea59014c | 24 | Geometry Angle | Find the value of cos PBQ in terms of x? | [
"A. (x² * (3 + 2√3)) / 200",
"B. 1 - (x² * (1 - √3)) / 20",
"C. (x √3) - 2",
"D. 1 - (x² * (2 - √3)) / 200",
"E. (x √3) / 2"
] | D | {"1": "Recall the law of cosines (Alcaxi theorem): in any triangle with sides a, b, c and opposite angles A, B, C, we have c² = a² + b² - 2ab cos(C).", "2": "Apply the law of cosines to the triangle formed by the two sides of length x with included angle 30°: PQ² = x² + x² - 2·x·x·cos(30°) = 2x² - 2x²·(√3/2) = x²(2 - √... | medium |
2a834f16-01fb-4c32-bf8d-c4d2eb908146 | 392 | Topology | The puzzle in the video shows a ring threaded onto a pair of parallel ropes, and the ropes are attached to two sticks, what is the correct sequence of the below steps to free the ring?
(A) Release the not to release the ring
(B) Pull the leather rope forward
(C) Grasp front rope below and loop it around left stick
(D)... | [
"A. CEDBA",
"B. BDCEA",
"C. BCEA",
"D. ECDBA",
"E. DBCEA"
] | E | {"1": "Hook the leather rope behind the left stick with your left index finger (step D).", "2": "Pull the leather rope forward to create slack (step B).", "3": "Grasp the front rope from below and loop it around the left stick (step C).", "4": "Grab the back rope from above and loop it around the left stick (step E).",... | medium |
0cd5d9ad-d08b-493b-a1d1-60c9e38def41 | 193 | Geometry Area | Compute the approximate area of the rectangle? | [
"A. 73.2",
"B. 78.0",
"C. 71.1",
"D. 64.5",
"E. 69.0"
] | C | {"1": "Identify the dimensions needed to calculate the area of the rectangle. We have the radii of three circles: a = 3, b = 2, and c = 1.5. The width of the rectangle is given as d = 6.", "2": "Calculate the length of the rectangle using the formula: Length = a + √[(a+b)² - (a-b)²] + √[(b+c)² - (d-b-c)²] + c.", "3": "... | short |
59a0bb02-faa4-4e1d-a29d-0dc94d508956 | 41 | Counting | Find what fraction of the hexagon is shaded in blue in the second example? | [
"A. 4/5",
"B. 1/2",
"C. 1/4",
"D. 5/11",
"E. 3/4"
] | B | {"1": "Divide the regular hexagon into congruent equilateral triangles by drawing lines from the center to each vertex and the midpoint of each side.", "2": "There are 24 small equilateral triangles in total.", "3": "Of these triangles, 12 are shaded blue.", "4": "Form the shaded fraction: 12 shaded ÷ 24 total = 12/24.... | medium |
f5da5870-988d-49f1-90c1-8f88ffb808a8 | 238 | Arithmetic | In the given video: a quadratic equation is solved. Which method is used to solve the equation? | [
"A. Quadratic Formula",
"B. Using the Square Root Property",
"C. Factoring",
"D. Completing the Square",
"E. Graphing"
] | C | {"1": "The given equation is a quadratic in standard form: x^2 - 5x + 6 = 0. The presenter rewrote the quadratic as a product of two binomials: (x - 3)(x - 2) = 0, since -3 and -2 multiply to +6 and add to -5.", "2": "Apply the zero-product property by setting each factor equal to zero: x - 3 = 0 and x - 2 = 0. Hence, ... | medium |
105028cd-1599-4341-9afe-1730120a84d2 | 220 | Geometry Angle | The video shows quarter circle and two lines inside a square, what is the value of angle specified with pink color? | [
"A. 67.5",
"B. 45",
"C. 112.5",
"D. 90",
"E. 135"
] | A | {"1": "We start by identifying that the diagonal of the square divides it into two right-angled triangles, making the angle between the diagonal and one side of the square 45 degrees.", "2": "The side of the square and the diagonal form the radius of the quarter circle, indicating that these two segments are equal in l... | short |
94a9a7e7-4914-4d76-a800-50deffff3ff9 | 157 | Chart | In which month did the world cocoa prices almost double compared to the previous month? | [
"A. February 2024",
"B. January 2024",
"C. March 2024",
"D. April 2024",
"E. December 2023"
] | D | {"1": "The full video discusses how cocoa prices sharply increased in 2024 due to farming challenges, climate change, and supply shortages, which caused cocoa prices to soar and reshape the chocolate industry.", "2": "Since the question asks about when cocoa prices almost doubled compared to the previous month, we focu... | long |
adf738f2-cc47-4952-b331-39b82a818308 | 56 | Geometry Area | Compute the area of the triangle shaded in blue? | [
"A. 1800",
"B. 600",
"C. 2000",
"D. 1200",
"E. 800"
] | C | {"1": "Construct a large square of side 80 by placing the original 60-by-60 square and two 20-by-20 squares externally along the same diagonal.", "2": "Compute the area of the large square: 80 × 80 = 6400.", "3": "Inside the large square identify three right triangles: the left-lower triangle with legs 80 and 60, the r... | medium |
ee4ecb59-d870-43dd-b92b-3fe51d7db7f9 | 198 | Geometry Angle | Find the angle between the diagonal marked in orange? | [
"A. 30 degree",
"B. 75 degree",
"C. 90 degree",
"D. 60 degree",
"E. 45 degree"
] | D | {"1": "The problem asks for the angle between the diagonal marked in orange, which is formed by face diagonals from two adjacent faces of a cube.", "2": "Connect the endpoints of those two face diagonals that lie on the other corners of the square faces. This third line is also a face diagonal, and together the three d... | short |
e929f11a-4365-4531-afd2-070cfd060cc9 | 378 | Arithmetic | Based on the lecture, can you complete the rest of the solution? | [
"A. 160/3",
"B. 280/3",
"C. 28/3",
"D. 80/3",
"E. 140/3"
] | E | {"1": "We are given the double integral of the function x squared times y cubed over a rectangular region defined by 1 less than or equal to x less than or equal to 2 and 1 less than or equal to y less than or equal to 3.", "2": "First, we integrate with respect to x, treating y as a constant. The integral of x squared... | long |
30b0caf1-ca73-4b69-aa9c-42a89211f113 | 80 | Geometry Length | Find the length of AB? | [
"A. 44",
"B. 16.7",
"C. 22",
"D. 18.5",
"E. 15.5"
] | B | {"1": "In right triangle AED, AE = 7 and ED = 24, so by the Pythagorean theorem AD = √(7² + 24²) = 25.", "2": "Since ABCD is a rectangle, its opposite side BC equals AD, thus BC = 25.", "3": "In right triangle BFC, with BF = 15 and BC = 25 as the hypotenuse, CF = √(25² - 15²) = √(625 - 225) = 20.", "4": "Drop perpendic... | short |
72ef79fb-310d-4b91-b1d0-7436d95e22b7 | 295 | Counting | What are the number of white and grey triangles in Figure 5? | [
"A. 7 and 18",
"B. 14 and 1",
"C. 10 and 15",
"D. 6 and 19",
"E. 15 and 10"
] | E | {"1": "To determine the number of white and gray triangles in Figure 5, we first need to identify the pattern in the sequence of figures.", "2": "Since the number of gray triansgles are the same between Figure 2 and Figure 3, the number of gray triangles remains the same when moving from Figure 4 to Figure 5. Therefore... | medium |
5dfa1d76-11a5-4e2a-9d1b-3456cd158a92 | 173 | Geometry Angle | Find the value of angle denoted as x? | [
"A. 30 degree",
"B. 35 degree",
"C. 60 degree",
"D. 40 degree",
"E. 50 degree"
] | A | {"1": "We start with triangle ABC where a perpendicular is drawn from point A to side BC, meeting at point E. This creates a right angle at E.", "2": "Angle CAE is given as 40 degrees. From point B, a line segment is drawn to AE, intersecting at point D. This divides angle B into two angles of 10 degrees each.", "3": "... | medium |
06397059-f4dc-494f-821e-deb154e3f8b2 | 133 | Chart | How many subscribers did Netflix gain between the start of 2016 and the start of 2020? | [
"A. 200",
"B. 135",
"C. 145",
"D. 150",
"E. 100"
] | E | {"1": "The overall video is about how the streaming industry has evolved, with services like Netflix facing slowing subscriber growth, rising competition, and growing debt.", "2": "Since the question asks about Netflix subscriber growth between 2016 and 2020, we focus on the early-middle portion of the video; around th... | long |
8d1f5ba6-3259-4626-974d-04b1a123060f | 275 | Counting | Find how many different triangles are formed in the last figure? | [
"A. 27",
"B. 18",
"C. 36",
"D. 32",
"E. 34"
] | D | {"1": "Observe that the figure contains two concentric square boxes: an outer square and an inner square.", "2": "Recall the shortcut for a single square box: write down the triangle counts along one side (1, 2, 3, …), find the maximum number N, then total triangles = 2 × N.", "3": "For the outer square, the side trian... | long |
9ada7de7-9920-4478-8237-a1feeb82657f | 217 | Geometry Area | What is the area of the blue shaded area in the given equilateral triangle? | [
"A. 1/3",
"B. 5/9",
"C. 2/9",
"D. 4/9",
"E. 4/9"
] | D | {"1": "Label the original triangle ABC with base BC trisected at points D and E so that BD=DE=EC.", "2": "Label the side AB trisected at points F and G so that AF=FG=GB, and label the side AC trisected at points H and I so that AH=HI=IC", "3": "Draw segments from point I to point E, and this segment is parallel to side... | short |
2af7e676-2c18-4952-9ed7-cb3dabf8bbb8 | 259 | Chart | Estimate the revenue generated by iTunes in 2015, based on the given revenue trend of Apple Pay and the breakdown of the company’s services revenue? | [
"A. 120 million",
"B. 300 million",
"C. 960 million",
"D. 720 million",
"E. 450 million"
] | D | {"1": "The video explores how Apple has entered the finance space with services like Apple Pay, challenging traditional banks. It explains how Apple monetizes digital payments and breaks down how its services revenue is structured, including Apple Pay, the App Store, iTunes, and others.", "2": "Around the 2:25 mark, th... | long |
efb3960a-8810-4d6c-aeed-798fa20fe11f | 129 | Chart | Estimate the number of months it took for the inflation rate to drop to below the federal reserve interest rate after the federal interat rates were raised? | [
"A. 14 months",
"B. 8 months",
"C. 19 months",
"D. 6 months",
"E. 9 months"
] | A | {"1": "The video explains how inflation works, why moderate inflation is important, and how governments manage inflation and deflation risks.", "2": "Since the video explains that interest rates were raised to slow down spending around 4 minutes and discusses inflation trends alongside interest rates, we focus on this ... | long |
37ddd9b8-3ec8-40e3-b1a6-5eca85e3518f | 178 | Chart | What is the ratio of income in September 2010 to September 2011? | [
"A. 6/7",
"B. 5/6",
"C. 4/3",
"D. 6/5",
"E. 3/4"
] | A | {"1": "The video explains different types of charts. After covering bar charts and pie charts, it focuses on a line chart that shows income over the last 3 years, which is the relevant part for this question.", "2": "The chart is titled 'Last 3 Years Income Chart'. The x-axis shows months from January to December, and ... | medium |
155e8fb3-c417-4a54-bd39-ca12eb0c7395 | 304 | Puzzle | For the final example shown, find which cube figures can be formed by folding the net shown on the left? | [
"A. A",
"B. B",
"C. C",
"D. D",
"E. There is insufficient information to solve the problem"
] | C | {"1": "Begin by analyzing the cube net. The net shows three labeled faces: Y, X, and Z arranged in a row with additional blank faces around them. These labeled faces are all adjacent, meaning they will meet at one corner when the net is folded into a cube.", "2": "Visualize how folding the net will bring the faces toge... | long |
e279593f-b6a8-490d-a780-7b1b27f8ec24 | 208 | Geometry Length | What is the distance from point F to the line segment DC? | [
"A. 3.3",
"B. 2",
"C. 3",
"D. 2.5",
"E. 4"
] | B | {"1": "The square ABCD has a side length of 10, and E is the midpoint of side AD, so AE = 5.", "2": "Consider the right triangle AEB. Using the Pythagorean theorem, calculate the hypotenuse EB: EB = √(5^2 + 10^2) = 5√5.", "3": "Fold the square such that point A moves to point F along line EB. Construct line AF and let ... | short |
fe2ac462-4822-4e14-b5a8-3869fdc49a60 | 39 | Arithmetic | What is value of x? | [
"A. 80 degree",
"B. 56 degree",
"C. 40 degree",
"D. 60 degree",
"E. 45 degree"
] | D | {"1": "Note that the two given lines are parallel and the zigzag segments act as transversals cutting through them.", "2": "Through the vertex of the 80° angle, draw a line parallel to the given parallels; through the vertex of the x angle, draw another parallel line.", "3": "By alternate interior angles, the angle adj... | short |
545d0307-86a5-41d0-912c-f346370d2764 | 400 | Topology | You have a metal horseshoe topological puzzle, which consists of two horseshoes linked together with a chain and a ring encircling the chain. The goal is to remove the ring from the puzzle. The following steps describe potential moves to achieve this:
(A) Remove the ring from the middle of the horseshoes
(B) Slide the... | [
"A. FEDCBA",
"B. EFDBCA",
"C. CFEDBA",
"D. FBDBCA",
"E. DCFEBA"
] | A | {"1": "First, place the puzzle horizontally (Step F).", "2": "Hold one horseshoe with each hand to stabilize the puzzle (Step E).", "3": "Move the ring so that it is positioned in the middle of the chain (Step D).", "4": "Turn the horseshoes in opposite directions (Step C).", "5": "This will cause the ring to slide to ... | short |
c31d6ed8-4439-4555-a0aa-492e5068ca24 | 226 | Geometry Area | What is the area of the yellow shaded part in the drawn octagon? | [
"A. 1/2",
"B. 1/8",
"C. 5/8",
"D. 1/4",
"E. 3/8"
] | D | {"1": "Draw all the diagonals of the octagon, which divide it into eight equal sectors.", "2": "Connect points A and B to split the yellow shaded region into two triangles.", "3": "Since line AB is parallel to line CD, moving the triangle along line CD does not change its base or height, and thus its area remains the s... | medium |
4cec7f0e-849d-490d-8aba-3dee1729e71b | 255 | Chart | In 2002, how many times higher was the market concentration in the retail sector compared to the service sector, based on the HHI? | [
"A. 2.2",
"B. 3.5",
"C. 1.9",
"D. 2.7",
"E. 5.0"
] | D | {"1": "The video discusses the history and evolution of antitrust enforcement in the U.S., highlighting how political shifts have influenced regulation of large companies. It references historical examples like Standard Oil and AT&T, and concludes by questioning whether today’s market concentration levels require new a... | long |
14ae99b4-47ee-44f5-93af-c76eb38399a0 | 155 | Geometry Area | Determine what fraction of the quarter circle is shaded in red? | [
"A. There is insufficient information to solve the problem.",
"B. 1/8",
"C. 1/2",
"D. 3/4",
"E. 1/4"
] | C | {"1": "We start with a quarter circle and an inscribed semicircle. The semicircle is tangent to the arc of the quarter circle, and its diameter lies along the two adjacent radii of the quarter circle.", "2": "The problem asks us to find the fraction of the quarter circle that is shaded, which is equivalent to finding t... | medium |
0aec4fee-fe4d-4497-9bac-df28caf9de1e | 211 | Counting | If the area of the shaded region in orange is 9, what is the area of the shaded region in blue? | [
"A. 9",
"B. 3",
"C. 6",
"D. 15",
"E. 12"
] | E | {"1": "Partition the entire rectangle into a grid of equilateral triangles by drawing lines parallel to the sides of the hexagons.", "2": "Along the rectangles boundary, incomplete cells form right triangles, each with half the area of an equilateral triangle.", "3": "Counting the grid cells shows the blue region cover... | short |
86f3b592-f1c4-471b-9603-4c53fa20530d | 33 | Geometry Area | Can you find the area of RSTU? | [
"A. 196",
"B. 200",
"C. 256",
"D. 300",
"E. 225"
] | B | {"1": "We start with a square ABCD with side length 30 and a point P inside the square such that PA = 12 and PB = 26.", "2": "We join point P with the vertices of the square, forming four triangles, and mark the centroids of each triangle as points R, S, T, and U.", "3": "The goal is to find the area of quadrilateral R... | long |
6383f8c7-62d4-4df2-8706-bd3e7e3349b4 | 31 | Arithmetic | Find the sum of speeds during each segment of Bob's journey? | [
"A. 11m/s",
"B. 2.8 m/s",
"C. 3 m/s",
"D. 8 m/s",
"E. 12 m/s"
] | E | {"1": "To find the sum of speeds during each segment of Bob's journey, we first need to calculate the speed for each segment using the formula: speed = distance / time.", "2": "In the first segment, Bob covers 50 meters in 10 seconds. Using the formula, the speed is 50/10 = 5 meters per second.", "3": "In the second se... | long |
bf579f0c-7dfb-4f09-bae1-95396e45516d | 349 | Chart | The Inflation Reduction Act is expected to shift some global manufacturing away from China, especially in sectors like wind energy.
Based on the projections, by what percentage does China’s lead over the Rest of the World (excluding the U.S.) in wind manufacturing change between 2023 and 2030?
Choose the most appropria... | [
"A. Increases by 10%",
"B. Decreases by 15%",
"C. Decreases by 8%",
"D. Decreases by 25%",
"E. Increases by 5%"
] | E | {"1": "The video explores the United States industrial strategy shift through the Inflation Reduction Act, aiming to reduce reliance on China by re-shoring clean energy manufacturing.", "2": "Toward the final quarter of the video, the focus moves from domestic investment efforts to global dynamics, particularly in sect... | long |
35e38fd2-1f27-4f92-93c4-c950055899a8 | 27 | Geometry Area | Estimate the area of the region shaded in blue? | [
"A. 56",
"B. 126",
"C. 285",
"D. 344",
"E. 202"
] | B | {"1": "Let C be the area of the blue shaded central region. Also let A be the area of each corner circular region and B be the area of each of the four side lens regions.", "2": "The total area of the square is R^2, and it is partitioned into 4 corner regions, 4 lenses, and the central region: 4A + 4B + C = R^2.", "3":... | short |
c0d6ba52-ed17-439a-8065-de739bb09f65 | 86 | Puzzle | Find what fraction of the square is shaded in green in the second example? | [
"A. 3/4",
"B. 1/5",
"C. 1/4",
"D. 3/2",
"E. 1/2"
] | E | {"1": "Observe that the figure consists of a square with its inscribed circle, its diagonals drawn, and a semicircle erected on the squares base as diameter.", "2": "The green regions are scattered throughout various parts of the figure.", "3": "By exploiting the figure symmetry, we can transfer the green portions from... | medium |
e8761db0-e393-4d3a-8c70-e789a9d77f40 | 368 | Chart | After the Ukraine-Russia war began, central banks accelerated their gold purchases while ETFs saw heavy outflows. Based on the data provided, approximately how many times larger were the total central bank gold investments in 2022-2023 compared to the ETF outflows during the same period? | [
"A. 6.1",
"B. 4.8",
"C. 5.2",
"D. 8.2",
"E. 3.1"
] | A | {"1": "The overall video discusses the recent surge in global interest in gold, highlighting changing investment patterns. It contrasts traditional reasons for gold price spikes (like economic recessions) with current drivers, including geopolitical uncertainty, distrust in traditional finance, and rising central bank ... | long |
b86c5f6f-1021-43ce-957e-f0117b96f8ac | 371 | Graph Theory | What is the shortest path with minimal cost from Node D to Node G after all iterations? | [
"A. D → C → B → E → G",
"B. D → F → E → G",
"C. D → C → B → E → F → G",
"D. D → F → G",
"E. D → C → G"
] | A | {"1": "List all possible valid direct connection paths from Node D to Node G: D→F→G, D→F→E→G, and D→C→B→E→G.", "2": "Calculate the total cost for each path:", "3": "Path D→F→G: D to F = 3, F to G = 2; Total = 3 + 2 = 5.", "4": "Path D→F→E→G: D to F = 3, F to E = -2, E to G = 4; Total = 3 + (-2) + 4 = 5.", "5": "Path D→... | medium |
0548c035-5c3f-46db-86b3-b74fc34df5d8 | 293 | Arithmetic | Determine the value of A - B? | [
"A. -1",
"B. 4",
"C. 2",
"D. 1",
"E. -2"
] | C | {"1": "Mark the five midpoints of the pentagons sides and draw segments from the interior point to each corner and each midpoint, creating 10 triangles.", "2": "Observe that any two triangles sharing the same side midpoint have equal bases and the same height, so their areas are equal.", "3": "On the side adjacent to r... | short |
78c5c1f5-1e70-4c51-a120-2d7feb1db731 | 321 | Counting | In the final example shown in the video, the structure is made up of identical L-shaped blocks. Based on the examples shown earlier on how to solve this task, how many individual L-shaped blocks make up the entire structure? | [
"A. 8",
"B. 9",
"C. 11",
"D. 12",
"E. 10"
] | E | {"1": "The problem involves counting the number of identical L-shaped blocks that make up a structure.", "2": "The strategy involves visualizing the structure in layers or segments to systematically count the blocks.", "3": "First, identify the top layer of the structure. There are 3 L-shaped blocks clearly visible on ... | long |
4b1e686e-dfe8-4131-a2e3-76a7fa9fc256 | 177 | Statistics | In the first stemplot, what will be the new median if we remove all leaves with value 3 from the stem 13? | [
"A. 124",
"B. 122",
"C. 121",
"D. 123",
"E. 119"
] | E | {"1": "The stem plot shows numbers where each stem (left column) represents the tens digit, and each leaf (right) represents the units digit. So a stem of 10 and a leaf of 0 gives 100, and so on.", "2": "Extract and list all the numbers in ascending order:\n100, 101, 101, 102, 103, 105, 106, 106 (8 leaves)\n111, 112, 1... | long |
57afd2e4-da1f-4f88-8903-7adb96dca354 | 337 | Arithmetic | Determine the total area of the shape? | [
"A. 184",
"B. 202",
"C. 180",
"D. 213",
"E. 150"
] | A | {"1": "Let the side of the blue square be n, so its area is n^2 = 90. Each red square then has side length n/3.", "2": "Let the side of each green square be m (area m^2). Each purple square has side length m/2.", "3": "The total height of the rectangle measured on the left is the sum of purple + green + purple sides, i... | short |
259ecbcf-528c-4427-b190-a91a989bc2c5 | 383 | Arithmetic | Using the steps shown so far, carry out the remaining calculations to find the volume? | [
"A. 16π/9 - ln(2 + √3) - √3 / 3",
"B. 8π/9 - ln(2 + √3) - (2√3) / 3",
"C. 16π/9 - ln(2 + √3) - (2√3) / 3",
"D. 32π/18 + ln(2 + √3) - (2√3) / 3",
"E. 28π/18 - ln(2 + √3) - √3 / 3"
] | C | {"1": "First, we need to understand what the given problem is. The video begins by explaining the problem: computing the volume of the remaining part of a right circular cone after a vertical slice is removed. The cone is defined by the surface z = 2 - √(x² + y²), with its tip at height 2 and base on the xy-plane (z = ... | long |
6b498c15-89aa-413b-af20-1cfb4fc4f30f | 246 | Geometry Area | If the area of each rectangle is 10 squared units, what is the shaded area? | [
"A. 15 sq units",
"B. 12 sq units",
"C. 10 sq units",
"D. 4 sq units",
"E. 5 sq units"
] | C | {"1": "We start by noting that each rectangle has an area of 10 square units.", "2": "To find the shaded area, we draw a line to divide the shaded region into triangles.", "3": "We observe that the area of triangles between two parallel lines remains constant regardless of its position along the line.", "4": "By moving... | short |
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