| Gruber's Shortest SAT Test Answer Guide |
Page 15 of 19 7. On a street with 25 houses, 10 houses have fewer than 6 rooms, 10 houses have more than 7 rooms, and 4 houses have more than 8 rooms. What is the total number of houses on the street that are either 6-, 7-, or 8-room houses? 11: You are right. Use Strategy 17, p. 110: In many "logic" problems, it is sometimes easier to use an indirect approach or use the fact that the whole equals the sum of its parts. Use the indirect method: Don't try to get the number of 6-7-8 room houses directly. Instead, find houses that have fewer than 6 rooms (10) and more than 8 rooms (4) and what's left is the 6-7-8 room ones. Use the fact that the whole equals the sum of its parts. The total number of houses is 25 (given) and this must then equal the parts, 10 that have fewer than 6 rooms, plus 4 that have more than 8 rooms, and whatever is remaining that have 6-7-8 rooms. Thus 25 minus 10 minus 4 equals 11 which is the answer.
Incorrect answers: Use Strategy 17, p. 110: In many "logic" problems, it is sometimes easier to use an indirect approach or use the fact that the whole equals the sum of its parts. Use the indirect method: Don't try to get the number of 6-7-8 room houses directly. Instead, find houses that have fewer than 6 rooms (10) and more than 8 rooms (4) and what's left is the 6-7-8 room ones. Use the fact that the whole equals the sum of its parts. The total number of houses is 25 (given) and this must then equal the parts, 10 that have fewer than 6 rooms, plus 4 that have more than 8 rooms, and whatever is remaining that have 6-7-8 rooms. Thus 25 minus 10 minus 4 equals 11 which is the answer.
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