GMAT Question of the Day

1. 3 pounds
2. 4.5 pounds
3. 6 pounds (correct answer)
4. 9 pounds

Explanation: This is a weighted average mixture problem, where you're combining two items with different costs to achieve a target average cost. The key insight is setting up an equation where the total cost of ingredients equals the total cost of the final mixture. Let's call the unknown pounds of blend X as $x$. You have $x$ pounds at $5/pound plus 6 pounds at $9/pound, and you want the entire mixture to cost $7/pound. Setting up the equation: $$5x + 9(6) = 7(x + 6)$ $ Solving: $$5x + 54 = 7x + 42$$ $$54 - 42 = 7x - 5x$$ $$12 = 2x$$ $$x = 6$$ You can verify: 6 pounds of blend X ($30) + 6 pounds of blend Y ($54) = 12 pounds total costing $84, which is indeed $7 per pound. Answer A (3 pounds) gives you a mixture costing $7.50 per pound—too expensive because you're using too little of the cheaper blend. Answer B (4.5 pounds) yields approximately $7.14 per pound, still too high. Answer D (9 pounds) would create a mixture costing about $6.40 per pound—too cheap because you're using too much of the less expensive blend. Strategy tip: In mixture problems, always check if your answer makes intuitive sense. Since $7 is exactly halfway between $5 and $9, you need equal amounts of each blend to hit that target. This "halfway" pattern is a quick way to spot the answer when the target average falls exactly in the middle of your two values.