Half the gnomes have big noses, so 28 / 2 = 14 have big noses. Three - quarters of the gnomes have red hats, so 28 * 3 / 4 = 21 gnomes have red hats. There are 6 gnomes with blue hats and big noses, so there are 14 - 6 = 8 with red hats and big noses. Thus, there are 21 - 8 = 13 gnomes with red hats that have small noses.
The answer: 13
Reverse engineering the question: There are 28 garden gnomes in a yard. Three-fourths of them have red hats, and the rest have blue hats. Half the garden gnomes have big noses instead of small noses. If six gnomes with blue hats have big noses, how many gnomes with red hats have small noses?


Reasoning and answer: Kate bought 7 packs × 18 balls / pack = 126 red bouncy balls. She also bought 6 packs × 18 balls / pack = 108 yellow bouncy balls. Kate bought 126 balls - 108 balls = 18 more red bouncy balls than yellow bouncy balls.
The answer: 18
What was the question?
Question: Kate bought 7 packs of red bouncy balls and 6 packs of yellow bouncy balls. Each pack contained 18 bouncy balls. How many more red bouncy balls than yellow bouncy balls did Kate buy?


Jake delivers 234 x 4 = 936 newspapers in a month. Miranda delivers 234 x 2 = 468 newspapers in a week. So she delivers 468 x 4 = 1872 newspapers in a month. Hence, Miranda delivers 1872 - 936 = 936 newspapers more than Jake in a month.
The answer: 936
Reverse engineering the question: Jake delivers 234 newspapers a week. Miranda delivers twice as many newspapers a week. How many more newspapers does Miranda deliver than Jake in a month?


Reasoning and answer: After keeping 10 cookies for herself, Karen has 50 - 10 = 40 cookies. After giving cookies to her grandparents, Karen has 40 - 8 = 32 cookies. Karen can give each person in her class 32 / 16 = 2 cookies.
The answer: 2
What was the question?
Question: Karen bakes 50 chocolate chip cookies. She keeps 10 for herself, and she gives 8 to her grandparents. If Karen wants to give everyone in her class cookies, and there are 16 people in her class, how many cookies will each person receive?


Each carton has an area of 4 * 4 * 5 = 80 square inches. Each shipping box has an area of 20 * 20 * 20 = 8000 square inches. The total number of cartons that will fit into each box is 8000 / 80 = 100. Since there are 3 widgets in each carton, the total number of cartons in each box will be 3 * 100 = 300.
The answer: 300
Reverse engineering the question: Doris works at the Widget Factory in the packing department. She puts 3 widgets in each carton, which are 4 inches wide, 4 inches long, and 5 inches tall. She then packs those cartons into a shipping box before sending it to the loading bay. The shipping boxes are 20 inches wide, 20 inches long, and 20 inches high. How many widgets get shipped in each shipping box?


John runs at 6 miles per hour for 0.5 hours, for a distance of 6 * 0.5 = 3 miles. Then John runs at 4 miles per hour for 0.5 hours, for a distance of 4 * 0.5 = 2 miles. In total, John runs 3 + 2 = 5 miles.
The answer: 5
Reverse engineering the question:
John jogs at a speed of 4 miles per hour when he runs alone, but runs at 6 miles per hour when he is being dragged by his 100-pound German Shepherd dog. If John and his dog go on a run together for 30 minutes, and then John runs for an additional 30 minutes by himself, how far will John have traveled?