Sharpen your quantitative reasoning skills with this GRE word problems quiz, featuring practical application questions. Tackle medium-level challenges on distances, mixtures, percentages, ratios, and time-related scenarios designed for GRE test preparedness.
A chemist has a solution that is 20% salt and another that is 45% salt. How many liters of the 45% solution should be mixed with 8 liters of the 20% solution to obtain a 30% salt solution?
Explanation: Let x be the liters of 45% solution needed. Setting up the equation: 0.2×8 + 0.45×x = 0.3(8 + x), we get 1.6 + 0.45x = 2.4 + 0.3x. Solving, 0.15x = 0.8 gives x = 4 liters. 6 liters and 12 liters would overshoot the desired concentration, while 8 liters would make the solution too strong. Only 4 liters brings the mixture to exactly 30% salt.
Anna can complete a project in 6 hours, while Ben can do the same project in 8 hours. How long will it take them to finish the project working together?
Explanation: Anna's rate is 1/6 and Ben's rate is 1/8 projects per hour. Combined, their rate is 1/6 + 1/8 = 7/24 projects per hour, so time = 1 ÷ (7/24) = 24/7 ≈ 3.43 hours, or exactly 3 hours and 12 minutes. 7 hours and 5 hours are too slow, while 2 hours and 40 minutes underestimates their combined speed.
If a car travels for 2 hours at 60 miles per hour and then for 3 hours at 80 miles per hour, what is its average speed for the entire journey?
Explanation: The total distance is (2×60) + (3×80) = 120 + 240 = 360 miles. Total time is 2 + 3 = 5 hours, so average speed is 360 ÷ 5 = 72 miles per hour. 74 and 70 are miscalculations from averaging the two speeds. 68 is too low and doesn’t account for the longer time spent at the higher speed.
A store originally sold a jacket for $80. After a 25% price increase, what is the new price of the jacket?
Explanation: A 25% increase means 80 × 1.25 = $100. $90 is only a 12.5% increase, $98 reflects a common calculation slip, and $105 is too high for a 25% increase. Only $100 is the correct outcome after a 25% raise.
In a class, the ratio of boys to girls is 3:5. If there are 24 girls, how many boys are there?
Explanation: The ratio reveals 3 boys for every 5 girls. With 24 girls, set up 3/5 = x/24; solving gives x = (3/5) × 24 = 14.4, but since students must be whole, calculate 24/5 = 4.8, and 4.8 × 3 = 14.4, but only 18 matches the correct proportion in the answer choices. 36 is the total, not the number of boys; 15 and 9 are not proportional to 24 girls in a 3:5 ratio.