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SAT · Math · Problem-Solving and Data Analysis
Ratios, rates, proportional relationships, and units is part of Problem-Solving and Data Analysis in the SAT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.
Question types you will see here include chained unit conversion, scale and proportion, distance, rate and time and unit rate comparison.
Common traps: multiplying where dividing is needed; using 100 instead of 1000; dropping a factor.
Question 1
The ratio of fiction to nonfiction among the 56 books on a shelf is 5 to 9. How many of the books on a shelf are nonfiction?
16
20
36
51
Answer: C. 36
There are 5 + 9 = 14 parts, so each part is 56 ÷ 14 = 4. The nonfiction make up 9 parts: 36.
Question 2
During a test run, a high-speed train travels at a constant 288 kilometers per hour. What is this speed in meters per second? (1 kilometer = 1,000 meters)
4.8
80
1,036.8
4,800
Answer: B. 80
288 km/h is 288,000 meters in 3,600 seconds, and 288,000 ÷ 3,600 = 80 meters per second (B). A divides by 60 only and never converts kilometers to meters; C multiplies by 3.6 where it should divide; D converts to meters per minute and stops there.
Question 3
A tap alone can fill an empty tank in 6 hours. A drain alone can empty a full tank in 12 hours. If the tap and the drain are both open, how many hours does it take to fill the empty tank?
4
6
9
12
Answer: D. 12
The tap fills 1/6 of the tank per hour and the drain removes 1/12, so the net rate is 1/6 − 1/12 = 1/12 and the time is 12 hours, choice D. Choice A adds the rates as if the drain filled the tank, B ignores the drain, and C averages 6 and 12.
Question 4
A flour mill's silo has a capacity of 5 cubic metres and is filled to 80% of capacity with wheat that has a density of 750 kilograms per cubic metre. The wheat is packed into sacks of 25 kilograms each. How many full sacks can be packed?
30
96
120
150
Answer: C. 120
Wheat volume = 0.80 × 5 = 4 m³, mass = 4 × 750 = 3,000 kg, and 3,000 ÷ 25 = 120 sacks. A is 750 ÷ 25, the sacks per cubic metre. B applies the 80% a second time. D ignores the 80% fill level (3,750 ÷ 25).
Question 5
A money changer deducts a flat fee of 15 dirhams and converts the rest of a customer's dirhams to rupees at 1 dirham = 22.6 rupees. How many rupees does a customer receive for 1,000 dirhams?
43.58
22,261
22,585
22,600
Answer: B. 22,261
After the fee, 985 dirhams are converted: 985 × 22.6 = 22,261 rupees (B). A divides by the rate, converting in the wrong direction; C subtracts the 15-dirham fee as if it were 15 rupees; D ignores the fee.
A few questions show the style. The free scan shows which SAT skills cost you the most points, then builds a plan around them.