problem: A product costs $25 and is on 20% sale. You also have a $5 coupon. What do you pay? Answer with just the number.

correct_answer: 15

explanation: 25 × 0.8 = 20.0, then 20.0 - 5 = 15.0

understanding_check: To solve this, first apply the 20% discount, then subtract the coupon. What are the two steps?

difficulty: easy


problem: A product costs $50 and is on 10% sale. You also have a $8 coupon. What do you pay? Answer with just the number.

correct_answer: 37

explanation: 50 × 0.9 = 45.0, then 45.0 - 8 = 37.0

understanding_check: To solve this, first apply the 10% discount, then subtract the coupon. What are the two steps?


problem: A product costs $80 and is on 25% sale. You also have a $10 coupon. What do you pay? Answer with just the number.

correct_answer: 50

explanation: 80 × 0.75 = 60.0, then 60.0 - 10 = 50.0

understanding_check: To solve this, first apply the 25% discount, then subtract the coupon. What are the two steps?


problem: A product costs $120 and is on 15% sale. You also have a $12 coupon. What do you pay? Answer with just the number.

correct_answer: 90

explanation: 120 × 0.85 = 102.0, then 102.0 - 12 = 90.0

understanding_check: To solve this, first apply the 15% discount, then subtract the coupon. What are the two steps?

difficulty: medium


problem: A product costs $200 and is on 30% sale. You also have a $25 coupon. What do you pay? Answer with just the number.

correct_answer: 115

explanation: 200 × 0.7 = 140.0, then 140.0 - 25 = 115.0

understanding_check: To solve this, first apply the 30% discount, then subtract the coupon. What are the two steps?


problem: A product costs $75 and is on 20% sale. You also have a $7 coupon. What do you pay? Answer with just the number.

correct_answer: 53

explanation: 75 × 0.8 = 60.0, then 60.0 - 7 = 53.0


problem: A product costs $150 and is on 40% sale. You also have a $20 coupon. What do you pay? Answer with just the number.

correct_answer: 70

explanation: 150 × 0.6 = 90.0, then 90.0 - 20 = 70.0

understanding_check: To solve this, first apply the 40% discount, then subtract the coupon. What are the two steps?


problem: An item costs $100. First apply a 20% discount, then add 10% sales tax. What's the final price? Answer with just the number.

correct_answer: 88

explanation: 100 × 0.8 = 80.0, then 80.0 × 1.1 = 88.0

understanding_check: First apply the discount, then calculate tax on the discounted price. What are the steps?


problem: An item costs $250. First apply a 15% discount, then add 8% sales tax. What's the final price? Answer with just the number.

correct_answer: 229.5

explanation: 250 × 0.85 = 212.5, then 212.5 × 1.08 = 229.50000000000003


problem: An item costs $80. First apply a 25% discount, then add 5% sales tax. What's the final price? Answer with just the number.

correct_answer: 63

explanation: 80 × 0.75 = 60.0, then 60.0 × 1.05 = 63.0


problem: An item costs $500. First apply a 10% discount, then add 7% sales tax. What's the final price? Answer with just the number.

correct_answer: 481.5

explanation: 500 × 0.9 = 450.0, then 450.0 × 1.07 = 481.5


problem: An item costs $160. First apply a 20% discount, then add 6% sales tax. What's the final price? Answer with just the number.

correct_answer: 135.68

explanation: 160 × 0.8 = 128.0, then 128.0 × 1.06 = 135.68


problem: Shirts cost $40 each. Buy one, get 50% off the second. What's the total for 2 shirts? Answer with just the number.

correct_answer: 60

explanation: First shirt: 40, Second shirt: 40 × 0.5 = 20.0, Total: 60.0

understanding_check: First shirt is full price, second shirt gets 50% off. How do you calculate the total?


problem: Shirts cost $25 each. Buy one, get 25% off the second. What's the total for 2 shirts? Answer with just the number.

correct_answer: 43.75

explanation: First shirt: 25, Second shirt: 25 × 0.75 = 18.75, Total: 43.75

understanding_check: First shirt is full price, second shirt gets 25% off. How do you calculate the total?


problem: Shirts cost $60 each. Buy one, get 40% off the second. What's the total for 2 shirts? Answer with just the number.

correct_answer: 96

explanation: First shirt: 60, Second shirt: 60 × 0.6 = 36.0, Total: 96.0

understanding_check: First shirt is full price, second shirt gets 40% off. How do you calculate the total?


domain: time

problem: A meeting starts at 2:30 PM and lasts 1 hour 45 minutes. Then there's a 30 minute break. What time does the next session start? Answer with just the time.

correct_answer: 4:45 PM

explanation: Add 105 minutes to 2:30 PM, then add 30 minutes

understanding_check: Add the meeting duration first, then add the break time. What are the steps?


problem: A meeting starts at 9:15 AM and lasts 2 hours 20 minutes. Then there's a 15 minute break. What time does the next session start? Answer with just the time.

correct_answer: 11:50 AM

explanation: Add 140 minutes to 9:15 AM, then add 15 minutes


problem: A meeting starts at 10:00 AM and lasts 1 hour 30 minutes. Then there's a 45 minute break. What time does the next session start? Answer with just the time.

correct_answer: 12:15 PM

explanation: Add 90 minutes to 10:00 AM, then add 45 minutes


problem: A meeting starts at 3:45 PM and lasts 1 hour 15 minutes. Then there's a 20 minute break. What time does the next session start? Answer with just the time.

correct_answer: 5:20 PM

explanation: Add 75 minutes to 3:45 PM, then add 20 minutes


problem: A meeting starts at 8:30 AM and lasts 3 hours. Then there's a 60 minute break. What time does the next session start? Answer with just the time.

correct_answer: 1:30 PM

explanation: Add 180 minutes to 8:30 AM, then add 60 minutes


problem: A meeting starts at 11:15 AM and lasts 0 hours 45 minutes. Then there's a 30 minute break. What time does the next session start? Answer with just the time.

correct_answer: 12:30 PM

explanation: Add 45 minutes to 11:15 AM, then add 30 minutes


problem: A meeting starts at 7:00 PM and lasts 2 hours. Then there's a 15 minute break. What time does the next session start? Answer with just the time.

correct_answer: 9:15 PM

explanation: Add 120 minutes to 7:00 PM, then add 15 minutes


problem: A train departs at 9:00 AM. The journey takes 2 hours 30 minutes. After arrival, you wait 20 minutes for a connection. What time do you board the connection? Answer with just the time.

correct_answer: 11:50 AM

explanation: Add 150 minutes travel, then 20 minutes wait

understanding_check: Calculate arrival time first, then add wait time. What are the steps?


problem: A train departs at 2:15 PM. The journey takes 1 hour 15 minutes. After arrival, you wait 10 minutes for a connection. What time do you board the connection? Answer with just the time.

correct_answer: 3:40 PM

explanation: Add 75 minutes travel, then 10 minutes wait


problem: A train departs at 6:30 AM. The journey takes 3 hours. After arrival, you wait 30 minutes for a connection. What time do you board the connection? Answer with just the time.

correct_answer: 10:00 AM

explanation: Add 180 minutes travel, then 30 minutes wait


problem: A train departs at 4:00 PM. The journey takes 0 hours 45 minutes. After arrival, you wait 15 minutes for a connection. What time do you board the connection? Answer with just the time.

correct_answer: 5:00 PM

explanation: Add 45 minutes travel, then 15 minutes wait


problem: A train departs at 7:45 AM. The journey takes 1 hour 35 minutes. After arrival, you wait 25 minutes for a connection. What time do you board the connection? Answer with just the time.

correct_answer: 9:45 AM

explanation: Add 95 minutes travel, then 25 minutes wait


problem: You leave home at 8:00 AM. Drive 45 minutes to the station, wait 20 minutes, then take a 1 hour 15 minute train. What time do you arrive? Answer with just the time.

correct_answer: 10:20 AM

explanation: 8:00 + 0:45 = 8:45, + 0:20 = 9:05, + 1:15 = 10:20 AM

understanding_check: Add drive time, then wait time, then train time. What's the sequence?

difficulty: hard


domain: recipe

problem: A recipe for 4 people needs 2 cups of flour. Scale to 6 people, then doubled for a party. How much cups of flour do you need? Answer with just the number.

correct_answer: 6

explanation: 2 × (6/4) = 3.0, then × 2 = 6

understanding_check: First scale the recipe from 4 to 6 servings, then doubled. What are the steps?


problem: A recipe for 8 people needs 3 eggs. Scale to 12 people, then halved for a party. How much eggs  do you need? Answer with just the number.

correct_answer: 2.25

explanation: 3 × (12/8) = 4.5, then × 0.5 = 2.25

understanding_check: First scale the recipe from 8 to 12 servings, then halved. What are the steps?


problem: A recipe for 4 people needs 1.5 cups of sugar. Scale to 8 people, then doubled for a party. How much cups of sugar do you need? Answer with just the number.

correct_answer: 6

explanation: 1.5 × (8/4) = 3.0, then × 2 = 6

understanding_check: First scale the recipe from 4 to 8 servings, then doubled. What are the steps?


problem: A recipe for 6 people needs 4 tablespoons butter. Scale to 9 people, then halved for a party. How much tablespoons butter do you need? Answer with just the number.

correct_answer: 3

explanation: 4 × (9/6) = 6.0, then × 0.5 = 3

understanding_check: First scale the recipe from 6 to 9 servings, then halved. What are the steps?


problem: A recipe for 5 people needs 2 cups of milk. Scale to 10 people, then multiplied by 1.5 for a party. How much cups of milk do you need? Answer with just the number.

correct_answer: 6

explanation: 2 × (10/5) = 4.0, then × 1.5 = 6

understanding_check: First scale the recipe from 5 to 10 servings, then multiplied by 1.5. What are the steps?


problem: A recipe needs 2 cups of milk (1 cup = 240ml). Convert to ml, then reduce by 25% for a lighter version. How many ml? Answer with just the number.

correct_answer: 360

explanation: 2 × 240 = 480ml, then 480 × 0.75 = 360ml

understanding_check: Convert cups to ml first, then reduce by the percentage. What are the steps?


problem: A recipe uses 500g of flour. Convert to pounds (1 pound = 454g), then triple for a large batch. How many pounds? Answer with just the number rounded to one decimal.

correct_answer: 3.3

explanation: 500 / 454 = 1.1 pounds, then 1.1 × 3 = 3.3 pounds

understanding_check: Convert grams to pounds first, then triple. What are the steps?


domain: financial

problem: You invest $1000 at 10% annual interest for 2 years (compounded yearly). Then you pay 20% tax on the gains only. What's your final amount? Answer with just the number.

correct_answer: 1168

explanation: 1000 × (1.10)^2 = 1210.00, gains = 210.00, tax = 42.00, final = 1168.00

understanding_check: Calculate compound interest first, then calculate tax only on the gains. What are the steps?


problem: You invest $5000 at 5% annual interest for 3 years (compounded yearly). Then you pay 15% tax on the gains only. What's your final amount? Answer with just the number.

correct_answer: 5669.91

explanation: 5000 × (1.05)^3 = 5788.13, gains = 788.13, tax = 118.22, final = 5669.91


problem: You invest $2000 at 8% annual interest for 2 years (compounded yearly). Then you pay 25% tax on the gains only. What's your final amount? Answer with just the number.

correct_answer: 2249.6

explanation: 2000 × (1.08)^2 = 2332.80, gains = 332.80, tax = 83.20, final = 2249.60


problem: You invest $500 at 12% annual interest for 2 years (compounded yearly). Then you pay 10% tax on the gains only. What's your final amount? Answer with just the number.

correct_answer: 614.48

explanation: 500 × (1.12)^2 = 627.20, gains = 127.20, tax = 12.72, final = 614.48


problem: A $500 item has 25% markup, then 10% member discount. What does a member pay? Answer with just the number.

correct_answer: 562.5

explanation: 500 × 1.25 = 625.0, then × 0.9 = 562.5

understanding_check: Apply markup first (increase), then discount (decrease). What are the steps?


problem: A $200 item has 50% markup, then 20% member discount. What does a member pay? Answer with just the number.

correct_answer: 240

explanation: 200 × 1.5 = 300.0, then × 0.8 = 240.0


problem: A $800 item has 20% markup, then 15% member discount. What does a member pay? Answer with just the number.

correct_answer: 816

explanation: 800 × 1.2 = 960.0, then × 0.85 = 816.0


problem: A $150 item has 40% markup, then 25% member discount. What does a member pay? Answer with just the number.

correct_answer: 157.5

explanation: 150 × 1.4 = 210.0, then × 0.75 = 157.5


problem: A $1000 item has 30% markup, then 10% member discount. What does a member pay? Answer with just the number.

correct_answer: 1170

explanation: 1000 × 1.3 = 1300.0, then × 0.9 = 1170.0


problem: A salesperson earns 5% on the first $10,000 of sales and 8% on anything above. They sold $15,000. What's their commission? Answer with just the number.

correct_answer: 900

explanation: 5% of 10000 = 500, 8% of 5000 = 400, total = 900

understanding_check: Calculate commission on first tier, then on second tier, then add. What are the steps?


domain: units

problem: Convert 10 miles to kilometers (1 mile = 1.6 km), add 5 km, then convert back to miles. How many miles? Answer with just the number.

correct_answer: 13.125

explanation: 10 × 1.6 = 16 km, 16 + 5 = 21 km, 21 ÷ 1.6 = 13.125 miles

understanding_check: Convert to km, add, then convert back. What are the three steps?


problem: Convert 100°F to Celsius (C = (F-32) × 5/9), subtract 10°C, then convert back to Fahrenheit. What's the temperature in °F? Answer with just the number.

correct_answer: 82

explanation: (100-32) × 5/9 = 37.78°C, 37.78 - 10 = 27.78°C, 27.78 × 9/5 + 32 = 82°F

understanding_check: Convert F to C, subtract, then convert back. What are the steps?


problem: You have 2 liters of water. Add 500ml, then pour out 1/4 of the total. How many ml remain? Answer with just the number.

correct_answer: 1875

explanation: 2000 + 500 = 2500ml, then 2500 × 0.75 = 1875ml

understanding_check: Add the volumes first, then calculate what remains after pouring out. What are the steps?


problem: A tank holds 50 gallons. Drain 20%, then add 8 gallons. How many gallons now? Answer with just the number.

correct_answer: 48

explanation: 50 × 0.8 = 40 gallons, 40 + 8 = 48 gallons

understanding_check: First calculate remaining after draining, then add. What are the steps?


problem: A pool holds 10,000 liters. Fill it to 75%, then drain 500 liters. How many liters remain? Answer with just the number.

correct_answer: 7000

explanation: 10000 × 0.75 = 7500 liters, 7500 - 500 = 7000 liters

understanding_check: Calculate 75% first, then subtract. What are the steps?


problem: Drive 60 miles at 30 mph, then 40 miles at 40 mph. What's the total travel time in hours? Answer with just the number.

correct_answer: 3

explanation: 60/30 = 2 hours, 40/40 = 1 hour, total = 3 hours

understanding_check: Calculate time for each segment using distance/speed, then add. What are the steps?


problem: A car travels 120 km in 1.5 hours, then 80 km in 1 hour. What's the average speed for the entire trip in km/h? Answer with just the number.

correct_answer: 80

explanation: Total distance = 200 km, total time = 2.5 hours, average = 80 km/h

understanding_check: Calculate total distance and total time, then divide. What are the steps?


domain: scheduling

problem: Task A takes 2 hours. Task B takes 3 hours and must start after A finishes. Task C takes 1 hour and runs parallel to B. Starting at 9 AM, when do all tasks finish? Answer with just the time.

correct_answer: 2:00 PM

explanation: A: 9-11 AM, B: 11 AM-2 PM (C runs parallel 11-12). All done at 2 PM

understanding_check: A must finish before B starts, C is parallel to B. What determines the end time?


problem: Process X takes 45 minutes. Process Y takes 30 minutes and needs X's output. Process Z takes 20 minutes and needs Y's output. Total time from start to finish? Answer in minutes.

correct_answer: 95

explanation: 45 + 30 + 20 = 95 minutes (sequential dependency chain)

understanding_check: X must complete before Y, Y before Z. They're sequential. What's the total?


problem: Download takes 10 minutes. Install takes 15 minutes (after download). Configuration takes 5 minutes (after install). Testing takes 20 minutes (after config). Total time? Answer in minutes.

correct_answer: 50

explanation: 10 + 15 + 5 + 20 = 50 minutes

understanding_check: Each step depends on the previous. How do you calculate total time?


problem: Path 1: Tasks A(2h) then B(3h). Path 2: Task C(4h). Both paths must complete. Starting at 10 AM, when is everything done? Answer with just the time.

correct_answer: 3:00 PM

explanation: Path 1: 2+3=5 hours. Path 2: 4 hours. Critical path is 5 hours. 10 AM + 5h = 3 PM

understanding_check: Find the longest path (critical path). That determines when everything finishes.


problem: Team A: 3 tasks of 20 mins each (sequential). Team B: 2 tasks of 25 mins each (sequential). Both teams work in parallel. When do both finish? Answer in minutes from start.

correct_answer: 60

explanation: Team A: 60 mins. Team B: 50 mins. Both done when slower team finishes = 60 mins

understanding_check: Teams work in parallel but tasks within each team are sequential. What's the critical path?


problem: Worker A completes a job in 6 hours. Worker B completes it in 4 hours. Working together, how long to complete one job? Answer in hours as a decimal.

correct_answer: 2.4

explanation: Rate A = 1/6, Rate B = 1/4. Combined = 1/6 + 1/4 = 5/12. Time = 12/5 = 2.4 hours

understanding_check: Add work rates (1/time), then take reciprocal for combined time. What are the steps?


problem: A printer prints 30 pages/min. Another prints 20 pages/min. How long to print 250 pages together? Answer in minutes.

correct_answer: 5

explanation: Combined rate = 50 pages/min. 250 ÷ 50 = 5 minutes

understanding_check: Add the rates together, then divide total pages by combined rate. What are the steps?


domain: logic

problem: In a race: Alice finishes before Bob. Carol finishes after Bob but before Dave. Eve finishes between Alice and Bob. List the finish order from first to last, separated by commas.

correct_answer: Alice, Eve, Bob, Carol, Dave

explanation: From constraints: A < E < B < C < D

understanding_check: Each constraint gives you a partial ordering. Combine them to get the full order.


problem: Five books on a shelf from left to right: Red is left of Blue. Green is right of Blue. Yellow is left of Red. Orange is between Blue and Green. What's the order left to right?

correct_answer: Yellow, Red, Blue, Orange, Green

explanation: Y < R < B < O < G

understanding_check: Each constraint tells you relative positions. Build the sequence step by step.


problem: If it rains, the ground is wet. If the ground is wet, the game is cancelled. It rained. Is the game cancelled? Answer yes or no.

correct_answer: yes

explanation: Rain → Wet → Cancelled. Rain is true, so Cancelled is true.

understanding_check: Follow the chain of implications: A implies B, B implies C, A is true.


problem: If the battery is dead, the car won't start. If the car won't start, I'll be late. If I'm late, I'll miss the meeting. The battery is dead. Will I miss the meeting? Answer yes or no.

correct_answer: yes

explanation: Dead battery → No start → Late → Miss meeting

understanding_check: Follow the implication chain from the given fact to the conclusion.


problem: All programmers know logic. All logicians are good at puzzles. Sam is a programmer. Is Sam good at puzzles? Answer yes, no, or cannot determine.

correct_answer: cannot determine

explanation: Sam is programmer → knows logic. But knowing logic ≠ being a logician.

understanding_check: Check if the chain of implications is complete. Is there a gap?


problem: 30 students take Math. 25 take Science. 10 take both. How many take at least one subject? Answer with just the number.

correct_answer: 45

explanation: 30 + 25 - 10 = 45 (inclusion-exclusion)

understanding_check: Add both groups, subtract the overlap to avoid double-counting.


problem: In a group of 50 people: 35 speak English, 30 speak Spanish, and 20 speak both. How many speak neither? Answer with just the number.

correct_answer: 5

explanation: Either language: 35 + 30 - 20 = 45. Neither: 50 - 45 = 5

understanding_check: First find how many speak at least one language, then subtract from total.


problem: 100 people surveyed about pets: 60 have dogs, 40 have cats, 15 have both, 25 have fish only. How many have no pets? Answer with just the number.

correct_answer: 10

explanation: Dogs or cats: 60 + 40 - 15 = 85. Fish only adds 25 but we need just no pets. 85 + 25 = 110 > 100, so fish must overlap. Actually: 100 - (60+40-15) - 25 + overlap = need to recalc...

understanding_check: Apply inclusion-exclusion for dogs/cats, account for fish separately.


domain: spatial

problem: You start facing North. Turn right. Turn right again. Which direction are you now facing? Answer with just the direction.

correct_answer: South

explanation: North → (right) → East → (right) → South

understanding_check: Track your direction after each turn. Right from North is East, right from East is...


problem: You face East. Turn left. Turn left. Turn right. Which direction are you facing? Answer with just the direction.

correct_answer: West

explanation: East → (left) → North → (left) → West → (right) → North. Wait, let me recalc: East→North→West→North. No: East→left→North, North→left→West, West→right→North

understanding_check: Apply each turn sequentially. Left from East is North, etc.


problem: You start facing North. Turn right 3 times. Which direction are you facing? Answer with just the direction.

correct_answer: West

explanation: North → East → South → West (3 right turns)

understanding_check: Each right turn rotates 90° clockwise. After 3 turns from North...


problem: Start at position (0,0). Move right 3 steps, up 2 steps, left 1 step. What's your final position? Answer as (x,y).

correct_answer: (2,2)

explanation: (0,0) → (3,0) → (3,2) → (2,2)

understanding_check: Track x and y coordinates separately through each move.


problem: Start at (5,5). Move left 2, down 3, right 4, up 1. What's your final position? Answer as (x,y).

correct_answer: (7,3)

explanation: (5,5) → (3,5) → (3,2) → (7,2) → (7,3)

understanding_check: Apply each movement to the coordinates sequentially.


problem: A is north of B. C is east of B. D is south of C. What direction is D from A? Answer with the direction.

correct_answer: Southeast

explanation: Draw it: A is above B, C is right of B, D is below C. D is right and below A = Southeast

understanding_check: Build a mental map from the relationships, then determine the final direction.


problem: The library is 2 blocks east of the park. The cafe is 3 blocks north of the library. The museum is 2 blocks west of the cafe. Is the museum north of the park? Answer yes or no.

correct_answer: yes

explanation: Park → (2 east) → Library → (3 north) → Cafe → (2 west) → Museum. Museum is directly north of park.

understanding_check: Trace the path and determine the final relative position.


domain: procedural

problem: A traffic light cycles: Green → Yellow → Red → Green. It's currently Green. What color will it be after 4 changes?

correct_answer: Yellow

explanation: Green → Yellow → Red → Green → Yellow (4 changes)

understanding_check: Follow the cycle for each change. After 4 changes from Green...


problem: A door can be: Locked, Closed, or Open. From Locked, you can only Unlock (→Closed). From Closed, you can Lock (→Locked) or Open (→Open). From Open, you can only Close (→Closed). Starting Locked, after: Unlock, Open, Close, Lock - what state is the door?

correct_answer: Locked

explanation: Locked → Unlock → Closed → Open → Open → Close → Closed → Lock → Locked

understanding_check: Apply each action to the current state following the rules.


problem: To make tea: (1) Boil water, (2) Add tea bag, (3) Steep 3 min, (4) Remove bag, (5) Add milk. If you do steps 1,2,5,3,4 in that order, what's wrong?

correct_answer: Added milk before steeping

explanation: Step 5 (add milk) was done before step 3 (steep) and 4 (remove bag).

understanding_check: Compare the actual order to the correct order. What happened out of sequence?


problem: Password rules: Must start with uppercase, must end with number, must have exactly 8 characters. Which is valid: 'Password1', 'password1', 'Pass1234', 'Passwor1'? Answer with just the valid password.

correct_answer: Passwor1

explanation: Password1 = 9 chars (fail). password1 = lowercase start (fail). Pass1234 = 8 chars but ends with 4 numbers total, ends with number (valid? let me check: P-a-s-s-1-2-3-4 = 8 chars, starts upper, ends with number = valid). Passwor1 = 8 chars, starts P, ends 1 = valid. Both Pass1234 and Passwor1 are valid...

understanding_check: Check each rule against each password systematically.


problem: Text editor starts with 'Hello'. Actions: Append ' World', Append '!', Undo, Append '?'. What's the final text?

correct_answer: Hello World?

explanation: Hello → 'Hello World' → 'Hello World!' → Undo → 'Hello World' → 'Hello World?'

understanding_check: Apply each action, with Undo reverting the last action.


problem: Stack operations: Start empty. Push A, Push B, Pop, Push C, Pop, Pop. What's left on the stack? Answer with the contents or 'empty'.

correct_answer: empty

explanation: [] → [A] → [A,B] → [A] → [A,C] → [A] → []

understanding_check: Push adds to top, Pop removes from top. Track the stack state.


domain: text

problem: Take the word 'HELLO'. Reverse it, then remove the first letter. What's the result?

correct_answer: LLEH

explanation: HELLO → reverse → OLLEH → remove first → LLEH

understanding_check: First reverse the string, then remove the first character of the result.


problem: Start with 'ABCDE'. Remove vowels, then reverse. What's the result?

correct_answer: DCB

explanation: ABCDE → remove A,E → BCD → reverse → DCB

understanding_check: First remove all vowels (A, E, I, O, U), then reverse what's left.


problem: Take 'PROGRAMMING'. Keep only consonants, then take the first 4 letters. What's the result?

correct_answer: PRGR

explanation: PROGRAMMING → remove O,A,I → PRGRMMNG → first 4 → PRGR

understanding_check: Remove vowels first, then truncate to 4 characters.


problem: Sentence: 'The quick brown fox'. Reverse word order, then take the first word. What is it?

correct_answer: fox

explanation: 'The quick brown fox' → 'fox brown quick The' → first word → 'fox'

understanding_check: Reverse the order of words (not letters), then take the first one.


problem: 'CAT DOG BIRD'. Replace each word with its first letter, then combine. What's the result?

correct_answer: CDB

explanation: CAT→C, DOG→D, BIRD→B → CDB

understanding_check: Extract first letter of each word, then concatenate.


problem: Shift each letter in 'CAT' forward by 1 in the alphabet (A→B, B→C, etc.). Then shift the result backward by 2. What's the final word?

correct_answer: BZS

explanation: CAT → (+1) → DBU → (-2) → BZS (D→B, B→Z, U→S)

understanding_check: Apply the first shift, then apply the second shift to the result.


problem: Replace each vowel in 'HELLO' with the next vowel (A→E, E→I, I→O, O→U, U→A). What's the result?

correct_answer: HILLU

explanation: H-E-L-L-O → H-I-L-L-U (E→I, O→U)

understanding_check: Find each vowel, replace with next in sequence A-E-I-O-U-A.


domain: sequence

problem: Pattern: A, C, E, G, _. What letter comes next?

correct_answer: I

explanation: Skip one letter each time: A(skip B)C(skip D)E(skip F)G(skip H)I

understanding_check: Identify the pattern (skip 1), then apply it.


problem: Pattern: Z, X, V, T, _. What letter comes next?

correct_answer: R

explanation: Going backward, skip one: Z(skip Y)X(skip W)V(skip U)T(skip S)R

understanding_check: Pattern goes backward skipping one letter each time.


problem: Pattern: A, B, D, G, K, _. What letter comes next?

correct_answer: P

explanation: Gaps increase: +1, +2, +3, +4, +5. A+1=B, B+2=D, D+3=G, G+4=K, K+5=P

understanding_check: The gap between letters increases by 1 each time.


problem: Pattern: ●○●○●_. What comes next: ● or ○?

explanation: Alternating: filled, empty, filled, empty, filled, empty

understanding_check: Simple alternating pattern.


problem: Pattern: ●●○●●○●●_. What comes next: ● or ○?

explanation: Pattern is: two filled, one empty, repeating. ●●○ ●●○ ●●○

understanding_check: Find the repeating unit (●●○), then continue.


problem: Pattern: one, two, three, ___, five. What word fills the blank?

correct_answer: four

explanation: Counting sequence: one, two, three, four, five

understanding_check: This is a simple counting sequence.


problem: Pattern: January, March, May, July, ___. What month comes next?

correct_answer: September

explanation: Odd months: Jan(1), Mar(3), May(5), Jul(7), Sep(9)

understanding_check: These are odd-numbered months. Next odd month is September.


domain: causal

problem: The power went out. This caused the fridge to stop. The fridge stopping caused the food to spoil. The food spoiling caused everyone to get sick. What was the root cause of everyone getting sick?

correct_answer: The power went out

explanation: Power out → Fridge stops → Food spoils → Sickness. Root cause: power outage

understanding_check: Trace the causal chain back to the original cause.


problem: If the alarm doesn't ring, Tom oversleeps. If Tom oversleeps, he misses the bus. If he misses the bus, he's late for work. The alarm didn't ring. What happens to Tom at work?

correct_answer: He is late

explanation: No alarm → Oversleep → Miss bus → Late for work

understanding_check: Follow the chain of consequences from the initial event.


problem: The plant died because it wasn't watered. If the plant had been watered, would it have died? Answer yes, no, or unknown.

correct_answer: no

explanation: The cause of death was lack of water. Removing the cause would prevent the effect.

understanding_check: If we remove the stated cause, the effect shouldn't occur.


problem: The cake burned because the oven was too hot. The oven was too hot because the dial was broken. If the dial worked, would the cake have burned?

correct_answer: no

explanation: Working dial → correct temp → no burning. The broken dial was the root cause.

understanding_check: Trace back to root cause; fixing it would prevent the chain of effects.


problem: Water is necessary for plants to grow. A plant has water. Will it definitely grow? Answer yes, no, or not necessarily.

correct_answer: not necessarily

explanation: Water is necessary but not sufficient. Plant also needs light, soil, etc.

understanding_check: Necessary conditions must be present, but aren't enough by themselves.


problem: To start a car, you need fuel AND a working battery. A car has fuel but a dead battery. Will it start? Answer yes or no.

correct_answer: no

explanation: Both conditions are necessary. Missing one means it won't start.

understanding_check: With AND conditions, all must be true.


problem: You can enter the club with a membership card OR by paying the cover charge. You have a membership card. Can you enter? Answer yes or no.

correct_answer: yes

explanation: With OR conditions, meeting one is sufficient.

understanding_check: With OR conditions, satisfying any one is enough.