IAAT Ratios and Proportional Reasoning 2 — Questions and Answers
Question 1: In a proportion, if a/b = c/d, which of the following must also be true?
- a + b = c + d
- a × d = b × c (Correct answer)
- a − b = c − d
- a ÷ c = d ÷ b
Correct answer: a × d = b × c
In any proportion a/b = c/d, the cross-products are equal: a × d = b × c.
Question 2: A store sells 3 apples for $1.20. At this rate, how much do 10 apples cost?
- $3.60
- $3.80
- $4.00 (Correct answer)
- $4.20
Correct answer: $4.00
Unit price = $1.20 ÷ 3 = $0.40 per apple; 10 × $0.40 = $4.00.
Question 3: The ratio of red marbles to blue marbles is 2:7. If there are 63 blue marbles, how many red marbles are there?
- 14
- 16
- 18 (Correct answer)
- 21
Correct answer: 18
If 7 parts = 63, then 1 part = 9, so 2 parts (red) = 18.
Question 4: Which table of values shows a proportional relationship?
- x: 1,2,3 | y: 3,5,7
- x: 1,2,3 | y: 2,4,6 (Correct answer)
- x: 1,2,3 | y: 1,3,6
- x: 1,2,3 | y: 4,6,8
Correct answer: x: 1,2,3 | y: 2,4,6
In x: 1,2,3 | y: 2,4,6, the ratio y/x = 2 for all pairs, confirming proportionality.
Question 5: If 12 workers can complete a job in 8 days, how many days will 6 workers need to complete the same job?
- 4 days
- 12 days
- 16 days (Correct answer)
- 24 days
Correct answer: 16 days
This is inverse proportion: 12 × 8 = 6 × d, so d = 96 ÷ 6 = 16 days.
Question 6: A photograph is enlarged so that the new width is 15 inches. The original photo was 5 inches wide and 8 inches tall. What is the height of the enlarged photo?
- 18 inches
- 20 inches
- 24 inches (Correct answer)
- 25 inches
Correct answer: 24 inches
Scale factor = 15 ÷ 5 = 3; new height = 8 × 3 = 24 inches.
Question 7: The ratio 8:12 is the same as:
- 1:2
- 2:3 (Correct answer)
- 3:4
- 4:6
Correct answer: 2:3
Dividing both 8 and 12 by their GCF of 4 gives 2:3.
IAAT Ratios and Proportional Reasoning 2
In a proportion, if a/b = c/d, which of the following must also be true?