Gruber's Shortest SAT Test Answer Guide
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Gruber's Shortest SAT Test Answer Guide
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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:
Did you answer 14? Did you just say since 10 houses have more than 7 rooms and the rest have more than 8 rooms or less than 4 rooms, that 10 must be the answer (because only 10 houses fall in the 6-7-8 room category)? That's not quite correct.

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.

For all other answers:
No.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.