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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
The ratio of juniors to seniors among the 30 students on a committee is 3 to 2. How many of the students on a committee are juniors?
Enter your own answer.
Answer: 18
There are 3 + 2 = 5 parts, so each part is 30 ÷ 5 = 6. The juniors make up 3 parts: 18.
Question 3
The ratio of boys to girls in a school robotics club is 4 : 5. The club has 36 members. How many girls are in the club?
4
9
16
20
Answer: D. 20
The ratio has 4 + 5 = 9 parts, so each part is 36 ÷ 9 = 4 members and there are 5 × 4 = 20 girls (D). A is the size of one part, not the number of girls; B divides 36 by 4, using the boys' share as the number of parts; C is the number of boys.
Question 4
A dripping tap leaks water at a constant rate of 15 milliliters per minute. How many liters of water does it leak in one week? (1 liter = 1,000 milliliters)
Enter your own answer.
Answer: 151.2
In one week there are 60 × 24 × 7 = 10,080 minutes, so the tap leaks 15 × 10,080 = 151,200 milliliters, which is 151,200 ÷ 1,000 = 151.2 liters. Leaving out the factor of 24 hours per day gives 6.3 liters, and skipping the final division leaves the answer in milliliters.
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.