This question tests ISEE Upper Level quantitative reasoning skills, specifically understanding and applying ratios to compare quantities. Ratios are a way to compare two quantities by division, showing how many times one value contains or is contained within the other. The smoothie recipe uses yogurt to fruit in a 2:5 ratio, meaning for every 2 parts yogurt, there are 5 parts fruit. When doubling a recipe, both quantities must be multiplied by the same factor to maintain the ratio, so 2:5 becomes 4:10. Choice C is correct because 4:10 represents the doubled quantities while maintaining the same proportional relationship as 2:5. Choice A (4:12) incorrectly doubles the first term but more than doubles the second, while choices B and D don't maintain the original ratio structure. To master this skill, students should practice scaling ratios by multiplying both terms by the same factor and verify their work by simplifying the result back to the original ratio.

This question tests ISEE Upper Level quantitative reasoning skills, specifically calculating and comparing rates to form ratios. Ratios can compare any two quantities, including rates like speed, which is distance divided by time. Bus A travels 120 miles in 3 hours, giving a speed of 40 mph, while Bus B travels 150 miles in 5 hours, giving a speed of 30 mph. The ratio of speeds vA:vB is therefore 40:30, which simplifies to 4:3. Choice A is correct because it represents the simplified ratio of Bus A's speed to Bus B's speed. Choice B reverses the ratio, while choices C and D either don't simplify the ratio or use incorrect calculations. To help students master this skill, teach them to always calculate the individual rates first before forming the ratio, and to be careful about the order when writing ratios.

This question tests ISEE Upper Level quantitative reasoning skills, specifically understanding how to reverse the order of terms in a ratio. Ratios express relationships between quantities in a specific order, and reversing this order creates the reciprocal ratio. The original ratio is Solution X:Solution Y = 3:2, meaning for every 3 parts of X, there are 2 parts of Y. When asked for the ratio of Y to X, we must reverse the order, giving us 2:3. Choice B is correct because it properly reverses the original ratio from X:Y to Y:X. Choice A incorrectly maintains the original order, while choices C and D use unrelated values. Students should be taught that when reversing a ratio, the first term becomes the second and vice versa, and to always pay careful attention to which quantity is being compared to which.

This question tests ISEE Upper Level quantitative reasoning skills, specifically simplifying ratios involving larger numbers. Ratios compare quantities and should be reduced to their simplest form by dividing both terms by their greatest common divisor. The school allocates $2400 to sports and $1800 to music, creating a ratio of 2400:1800. The GCD of 2400 and 1800 is 600, so dividing both terms by 600 gives us 4:3. Choice A is correct because it represents the fully simplified ratio of sports funding to music funding. Choice B reverses the ratio, choice C shows an unsimplified version, and choice D uses incorrect values. Students should be encouraged to factor out hundreds or thousands first when working with large numbers, making it easier to find the GCD and simplify the ratio.

This question tests ISEE Upper Level quantitative reasoning skills, specifically comparing rates and expressing them as ratios. To compare speeds, we must first calculate each rate by dividing distance by time. The train travels 180 miles in 4 hours, giving a speed of 45 mph, while the car travels 210 miles in 3 hours, giving a speed of 70 mph. The ratio of train speed to car speed is 45:70, which can be simplified by dividing both terms by their GCD of 5, resulting in 9:14. Choice C is correct because it represents the simplified ratio of the train's speed to the car's speed. Choice A shows the unsimplified ratio, choice B is an incorrect simplification, and choice D reverses the ratio. Students should always calculate individual rates before forming ratios and remember to simplify their final answer.

This question tests ISEE Upper Level quantitative reasoning skills, specifically simplifying ratios to their lowest terms. Ratios should be expressed in simplest form by dividing both terms by their greatest common divisor (GCD). The recipe uses 12 cups flour and 18 cups sugar, giving a ratio of 12:18. The GCD of 12 and 18 is 6, so dividing both terms by 6 gives us 2:3. Choice C is correct because it represents the fully simplified ratio of flour to sugar. Choice A shows the unsimplified ratio, choice B reverses the terms, and choice D only partially simplifies the ratio. To master this skill, students should practice finding the GCD of two numbers and understand that simplifying ratios is similar to reducing fractions to lowest terms.

This question tests ISEE Upper Level quantitative reasoning skills, specifically calculating new ratios when one quantity changes by a percentage. The theater budget starts with sets:costumes = 7:5, and when costumes increase by 50%, the costume budget becomes 5 × 1.5 = 7.5, while sets remain at 7. The new ratio is therefore 7:7.5, which can also be expressed as 14:15 when both terms are multiplied by 2 to eliminate the decimal. Choice A is correct because it accurately represents the new ratio with sets at 7 and costumes at 7.5. Choice B incorrectly calculates the 50% increase, choice C reverses and miscalculates the ratio, and choice D shows the original ratio reversed. To master this concept, students should practice calculating percentage increases first, then form the new ratio, being comfortable with decimal values in ratios when appropriate.

This question tests ISEE Upper Level quantitative reasoning skills, specifically recognizing when ratios are equivalent through scaling. Ratios maintain their proportional relationship when both terms are multiplied by the same factor. The recipe uses oil:vinegar = 5:2, and to scale this up, we multiply both terms by the same number. Multiplying by 3 gives us 15:6, which maintains the same proportional relationship as 5:2. Choice B is correct because 15:6 represents the original ratio scaled up by a factor of 3. Choice A (10:5) reverses the ratio, choice C (7:4) uses unrelated values, and choice D (2:5) reverses the original ratio. Students should practice scaling ratios by choosing a multiplier and applying it to both terms, then verifying by simplifying back to the original ratio.