Advanced SAT Proportional Reasoning and Survey Analysis Practice Questions

Calculate the percentage of consumers preferring brand M: \( \\frac{420}{700} = 0.6 \), or 60%. For 14,000 consumers, the number preferring brand M is \( 0.6 \\times 14000 = 8400 \). The rest prefer brand N, \( 14000 - 8400 = 5600 \). The difference is \( 8400 - 5600 = 2800 \).

Calculate the percentage of consumers preferring brand X: \( \\frac{360}{600} = 0.6 \), or 60%. For 12,000 consumers, the number choosing brand X is \( 0.6 \\times 12000 = 7200 \). The rest choose brand Y, \( 12000 - 7200 = 4800 \). The difference is \( 7200 - 4800 = 2400 \).

First, calculate the percentage of residents who favor the park: \( \\frac{280}{500} = 0.56 \), or 56%. For a population of 8,000, the number of residents favoring the park is \( 0.56 \\times 8000 = 4480 \). The remaining residents favor the mall, so \( 8000 - 4480 = 3520 \). The difference is \( 4480 - 3520 = 960 \).

To find the difference in units sold, first calculate the percentages. Product A received \( \\frac{420}{750} \\approx 0.56 \), or 56%. Product B received \( \\frac{330}{750} \\approx 0.44 \), or 44%. For 12,000 units, Product A would sell \( 0.56 \\times 12000 = 6720 \) units and Product B would sell \( 0.44 \\times 12000 = 5280 \) units. The difference is \( 6720 - 5280 = 1440 \) units.

Calculate the percentage of students preferring online learning: \( \\frac{540}{900} = 0.6 \), or 60%. For 18,000 students, the number preferring online learning is \( 0.6 \\times 18000 = 10800 \). The rest prefer traditional learning, \( 18000 - 10800 = 7200 \). The difference is \( 10800 - 7200 = 3600 \).

First, calculate the percentage of decided voters: \( 100% - 30% = 70% \). Then, find the number of decided voters: \( 0.7 \\times 3000 = 2100 \). The percentage of decided voters for service X is \( \\frac{1800}{2100} \\approx 0.8571 \), or approximately 85.71%. For 90,000 people, the number preferring service X is \( 0.8571 \\times 90000 \\approx 77143 \). The rest prefer service Y, \( 90000 - 77143 = 12857 \). The difference is \( 77143 - 12857 = 64286 \). If the undecided voters (30%) split evenly, the number of undecided voters is \( 0.3 \\times 90000 = 27000 \), with 13,500 going to each service. Adjusted numbers: \( 77143 + 13500 = 90643 \) for service X and \( 12857 + 13500 = 26357 \) for service Y. The adjusted difference is \( 90643 - 26357 = 64286 \).

First, calculate the percentage of decided voters: \( 100% - 15% = 85% \). Then, find the number of decided voters: \( 0.85 \\times 2000 = 1700 \). The percentage of decided voters for product Z is \( \\frac{1200}{1700} \\approx 0.7059 \), or approximately 70.59%. For 60,000 customers, the number preferring product Z is \( 0.7059 \\times 60000 \\approx 42354 \). The rest prefer product W, \( 60000 - 42354 = 17646 \). The difference is \( 42354 - 17646 = 24708 \).

Calculate the percentage of voters favoring policy P: \( \\frac{330}{550} = 0.6 \), or 60%. For 11,000 voters, policy P would get \( 0.6 \\times 11000 = 6600 \) votes. Policy Q would get \( 11000 - 6600 = 4400 \) votes. The difference is \( 6600 - 4400 = 2200 \).

Calculate the percentage of customers preferring product Z: \( \\frac{240}{400} = 0.6 \), or 60%. For 10,000 customers, the number preferring product Z is \( 0.6 \\times 10000 = 6000 \). The rest prefer product W, \( 10000 - 6000 = 4000 \). The difference is \( 6000 - 4000 = 2000 \).

Calculate the percentage of voters favoring candidate C: \( \\frac{570}{950} = 0.6 \), or 60%. For 19,000 voters, candidate C would get \( 0.6 \\times 19000 = 11400 \) votes. Candidate D would get \( 19000 - 11400 = 7600 \) votes. The difference is \( 11400 - 7600 = 3800 \).

First, calculate the percentage of decided voters: \( 100% - 25% = 75% \). Then, find the number of decided voters: \( 0.75 \\times 2500 = 1875 \). The percentage of decided voters for policy P is \( \\frac{1500}{1875} = 0.8 \), or 80%. For 75,000 voters, the number voting for policy P is \( 0.8 \\times 75000 = 60000 \). The rest vote for policy Q, \( 75000 - 60000 = 15000 \). The difference is \( 60000 - 15000 = 45000 \).

First, calculate the percentage of decided voters: \( 100% - 10% = 90% \). Then, find the number of decided voters: \( 0.9 \\times 1500 = 1350 \). The percentage of decided voters for candidate X is \( \\frac{900}{1350} = 0.6667 \), or approximately 66.67%. For 45,000 voters, the number voting for candidate X is \( 0.6667 \\times 45000 \\approx 30000 \). The rest vote for candidate Y, \( 45000 - 30000 = 15000 \). The difference is \( 30000 - 15000 = 15000 \).

Calculate the percentage of users preferring service X: \( \\frac{600}{1000} = 0.6 \), or 60%. For 20,000 users, the number preferring service X is \( 0.6 \\times 20000 = 12000 \). The rest prefer service Y, \( 20000 - 12000 = 8000 \). The difference is \( 12000 - 8000 = 4000 \).

Calculate the percentage of voters for candidate A: \( \\frac{480}{800} = 0.6 \), or 60%. For 16,000 voters, candidate A would get \( 0.6 \\times 16000 = 9600 \) votes. Candidate B would get \( 16000 - 9600 = 6400 \) votes. The difference is \( 9600 - 6400 = 3200 \).

First, calculate the percentage of decided voters: \( 100% - 20% = 80% \). Then, find the number of decided voters: \( 0.8 \\times 1200 = 960 \). The percentage of decided voters preferring product A is \( \\frac{720}{960} = 0.75 \), or 75%. For 30,000 people, the number preferring product A is \( 0.75 \\times 30000 = 22500 \). The rest prefer product B, \( 30000 - 22500 = 7500 \). The difference is \( 22500 - 7500 = 15000 \).