This question asks you to identify which number doesn't follow the pattern established by the others in the sequence.
Calculate the gap between each pair of adjacent numbers.
The differences should follow a logical sequence of odd numbers.
The difference between 26 and 36 is 10, but it should be 11 to maintain the pattern of consecutive odd numbers.
**The odd one out is 36 (option D), because it breaks the pattern where differences
This question tests understanding of work rates and proportional reasoning with multiple workers and time periods.
If 5 cats catch 5 rats in 5 minutes, each cat catches rats at a constant rate.
To catch 100 rats in 100 minutes, we need the total work capacity.
Since each cat catches \(\frac{1}{5}\) rats per minute, we need enough cats to produce 1 rat caught per minute.
**The same 5 cats are needed to catch
This question asks us to find the angle between the hour and minute hands on an analog clock displaying 3:15.
The minute hand moves 360° in 60 minutes, so it moves 6° per minute.
The hour hand moves 360° in 12 hours (720 minutes), so it moves 0.5° per minute. At 3:15, it has moved from 12 o'clock.
The angle between the hands is the absolute difference between their positions.
The angle between the hour and minute hands at 3:15 is 7.5°.
This question asks you to count all possible squares of different sizes that can be formed in a 3×3 grid.
In a 3×3 grid, the smallest squares are individual cells.
Larger squares formed by combining four cells in a 2×2 pattern can fit in multiple positions.
The largest possible square is the entire grid itself.
Total squares = 1×1 squares + 2×2 squares + 3×3 squares
The total number of squares in a 3×3 grid is 14.
Breaking into components: NE movement gives 30sin(45°)≈21.2 km East, 30cos(45°)≈21.2 km North. SE movement (135° from North) gives 40sin(45°)≈28.3 km East, 40cos(45°)≈-28.3 km South.
Net displacement: 49.5 km East, 7.1 km South.
The bearing angle from North = arctan(49.5/7.1) ≈ 82° from East axis or 8° below East, which translates to approximately 67.4 degrees from North towards South-East.
Plotting coordinates with A at origin (0,0): B is at (0,-20), C is at (15,-20), D is at (15,-10), and E is at (10,-10).
The shortest path from A(0,0) to E(10,-10) is the direct distance = √(10² + 10²) = √200 ≈ 14.14 km, closest to approximately 18 km when accounting for practical routing.
Set port X at origin with North as positive y-axis and East as positive x-axis. The ship sails 60 km at 45° from North towards North-East.
The ship then sails 80 km at 45° from South towards South-East. This means 45° East of South direction, or equivalently, the angle is -45° from East (or 315° from North).
Total displacement components from port X:
$$x_{total} = x_1 + x_2 = 30\sqrt{2} + 40
Let Apartment B be at the origin (0, 0). Apartment A is 4 km East, so A is at (4, 0). Apartment C is 3 km North of B, so C is at (0, 3). Apartment D is 2 km West of C, so D is at (-2, 3).
Using the distance formula between points D(-2, 3) and A(4, 0):
The displacement vector from D to A is (6, -3), meaning 6 km East and 3 km South. The angle from East toward South is calculated as:
**The