GMAT rates and ratios

Average speed is not the average of the speeds

Driving out at 60 km/h and back at 40 km/h does not average 50. Average speed is total distance over total time, and because more time is spent at the slower speed the answer is always below the arithmetic mean — here, 48.

• Compute total distance and total time separately, then divide.
• Where no distance is given, pick a convenient one — the lowest common multiple of the speeds.
• "50" will always be among the options. It is the distractor.

Work and mixtures

• Work adds as rates, not as times. One worker taking 4 hours and another 6 gives a combined rate of 1/4 + 1/6 = 5/12, so 12/5 hours together.
• Mixtures — track the quantity of the thing being mixed, not the total volume. The amount of salt is conserved; the solution volume is not.
• Ratios need a multiplier. 3:2 means 3k and 2k, and k is usually what the question is really after.

Adding times rather than rates is the single most common error in work problems, and it produces an answer that is always too large — a useful sanity check, since two workers must finish faster than either alone.