QB_PH_GA_029: Analytical & Spatial Aptitude

What is the angle (in degrees) between the hour hand and the minute hand of an analog clock at 3:30?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Standard Clock Angle Formula**: $\theta = |30 H - 5.5 M|$ where $H = 3$ is hours, $M = 30$ is minutes. 2. **Computation**: $30 H = 30 \times 3 = 90^\circ$ $5.5 M = 5.5 \times 30 = 165^\circ$ $\theta = |90^\circ - 165^\circ| = |-75^\circ| = 75^\circ$ 3. **Visual Verification**: - Minute hand points directly at 6 ($180^\circ$). - Hour hand is halfway between 3 ($90^\circ$) and 4 ($120^\circ$), at $105^\circ$. - Separation: $180^\circ - 105^\circ = 75^\circ$. 4. **Official Answer**: 75 degrees.