■ Remember these important tips: If you write in the correct answer but do not fill in the oval(s), you will get the question marked wrong. If you know the correct answer but fill in the wrong oval(s), you will get the question marked wrong. If you do not fully erase an answer, it may be marked wrong. Check your answer grid to be sure you didn’t mark more than one oval per column. Be especially careful that a fraction bar or deci- mal point is not marked in the same column as a digit. Now it is time to do some grid-in practice prob- lems. Be sure to review the strategies listed above to ensure that you fully understand the grid system. Remember: You will never be penalized for an incorrect answer on the grid-in questions—so go ahead and guess. Good luck! –THE SAT MATH SECTION– 172 1 2 3 4 5 6 7 8 9 1 2 4 5 6 7 8 9 0 • / 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 8 9 0 • 1 2 4 5 6 7 8 9 • 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 / 1 2 3 4 5 6 8 9 0 • 1 2 4 5 6 7 8 9 • 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 8 9 0 • .347 34 . 7 34 / 7 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 172 –THE SAT MATH SECTION– 173 ANSWER SHEET 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 173 –THE SAT MATH SECTION– 174 ANSWER SHEET (continued) 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 174 Grid-in Practice Problems 1. The barns in a certain county are numbered con- secutively from 2,020 to 2,177. How many barns are in the county? 2. For some fixed value of x,8(x + 4) = y. After the value of x is increased by 3, 8(x + 4) = z. What is the value of z – y? 3. If 2 8 × 4 2 = 16 x , then x = ? 4. If (y – 1) 3 = 27, what is the value of (y + 1) 2 ? 5. When a is divided by 6, the remainder is 5; and when b is divided by 6, the remainder is 4. What is the remainder when a + b is divided by 6? 6. When a positive integer k is divided by 7, the remainder is 2. What is the remainder when 6k is divided by 3? 7. During course registration, 28 students enroll in biology. After three boys are dropped from the class, 44% of the class consists of boys. What per- cent of the original class did girls comprise? 8. If 3x – 1 = 11 and 4y = 12, what is the value of ᎏ x y ᎏ ? 9. If 1 – x – 2x – 4x = 7x – 1, what is the value of x? 10. If 4x 2 + 20x + r = (2x + s) 2 for all values of x, what is the value of r – s? 11. If (3p + 2) 2 = 64 and p > 0, what is a possible value of p? 12. If (x – 1)(x – 3) = –1, what is a possible value of x? 13. For what integer value of y is y + 5 > 8 and 2y – 3 < 7? 14. If ᎏ 5 3 ᎏ of x is 15, what number is x decreased by 1? 15. Half the difference of two positive numbers is 20. If the smaller of the two numbers is 3, what is the sum of the two numbers? 16. In a club of 35 boys and 28 girls, 80% of the boys and 25% of the girls have been members for more than two years. If n percent of the club have been members for more than two years, what is the value of n? 17. A string is cut into two pieces that have lengths in the ratio of 3:8. If the differences between the lengths of the two pieces of string is 45 inches, what is the length, in inches, of the shorter piece? 18. Fruit for a dessert costs $2.40 a pound. If 10 pounds of fruit are needed to make a dessert that serves 36 people, what is the cost of the fruit needed to make enough of the same dessert to serve 48 people? 19. In the figure below, if line segment AB is parallel to line segment CD and B ෆ E ෆ is perpendicular to E ෆ D ෆ , what is the value of y? AB E F DC y 50° –THE SAT MATH SECTION– 175 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 175 20. In the figure below, what is the value of x? 21. In the figure below, what is the length of line seg- ment AD? 22. If the lengths of two sides of an isosceles triangle are 9 and 20, what is the perimeter of the triangle? 23. If the integer lengths of the three sides of a trian- gle are 5, x, and 10, what is the least possible perimeter of the triangle? 24. If the product of the lengths of the three base sides of a triangle is 120, what is a possible perimeter of the triangle? 25. What is the area of the square below? 26. Through how many degrees does the minute hand of a clock move from 12:25 a.m. to 12:40 a.m. of the same day? 27. A line with a slope of ᎏ 1 3 4 ᎏ passes through points (7,3k) and (0,k). What is the value of k? 28. In the figure below, the slope of line l 1 is ᎏ 5 6 ᎏ and the slope of line l 2 is ᎏ 1 3 ᎏ . What is the distance from point A to point B? 29. The dimensions of a rectangular box are integers greater than 1. If the area of one side of this box is 12 and the area of another side is 15, what is the volume of the box? 30. What is the number of inches in the minimum length of ᎏ 1 4 ᎏ -inch-wide tape needed to cover com- pletely a cube whose volume is 8 cubic inches? 31. What is the greatest of four consecutive even integers whose average is 19? 32. If the average of x, y, and z is 12, what is the aver- age of 3x,3y, and 3z? y A B x l 2 l 1 (3,y 1 ) (3,y 2 ) x 4x – 1 A DEC B 15° 15° 30° 10 10 7 B DC A E 35° 25° 3x° x° –THE SAT MATH SECTION– 176 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 176 33. The probability of selecting a green marble at ran- dom from a jar that contains only green, white, and yellow marbles is ᎏ 1 4 ᎏ . The probability of select- ing a white marble at random form the same jar is ᎏ 1 3 ᎏ . If this jar contains 10 yellow marbles, what is the total number of marbles in the jar? 34. If the operation ⌽ is defined by the equation x ⌽ y = 2x + 3y, what is the value of a in the equation a ⌽ 4 = 1 ⌽ a? 35. x, y,22,14,10, In the sequence above, each term after the first term, x, is obtained by halving the term that comes before it and then adding 3 to that num- ber. What is the value of x – y? 36. If x + 2x + 3x + 4x = 1, then what is the value of x 2 ? 37. What is the least positive integer p for which 441p is the cube of an integer? 38. The average of 14 scores is 80. If the average of four of these scores is 75, what is the average of the remaining 10 scores? 39. If 3 x – 1 = 9 and 4 y + 2 = 64, what is the value of ᎏ x y ᎏ ? 40. If ᎏ p p + × p p + × p p ᎏ = 12 and p > 0, what is the value of p? –THE SAT MATH SECTION– 177 5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 177 . the value of y? AB E F DC y 50° THE SAT MATH SECTION– 175 5658 SAT2 006[04](fin).qx 11/21/05 6:44 PM Page 175 20. In the figure below, what is the value of x? 21. In the figure below, what is the. Half the difference of two positive numbers is 20. If the smaller of the two numbers is 3, what is the sum of the two numbers? 16. In a club of 35 boys and 28 girls, 80% of the boys and 25% of the. is the least possible perimeter of the triangle? 24. If the product of the lengths of the three base sides of a triangle is 120, what is a possible perimeter of the triangle? 25. What is the