sat 6 full tests phần 10 docx

Chapter 4: 1. If X + X/3 + X/4 = Y + Y/3 + Y/4 and Y = 60, what is the value of X? (A) 14.5 (B) 16 (C) 20 (D) 45 (E) 60 The best answer is E. Replace Y with 60 and solve: X + X/3 + X/4 = 60 + 60/3 + 60/4 = 60+20+15 = 95  multiply both sides by 12 to get: 12X + 4X + 3X = 95 x 12 = 1140  19X = 1140  X=60. 2. The price of 15 books is $45. If the price of 8 tapes and 4 books is $44, what is the price of one tape? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 The best answer is B. 15 books cost $45 and therefore one book costs $3. 8(tapes) + 4(3) = $44  8(tapes) = $32  The price of a tape is $4. 3. Tom is three times older than Shelly. If in three years Tom would be twice as old as Shelly, how old is Shelly today? (A) 3 (B) 4 (C) 6 (D) 9 (E) 12 The best answer is A. Let T be the age of tom today and S the age of Shelly. We can write the following equations: T = 3S and (T + 3) = 2(S + 3)  3S + 3 = 2S + 6  S = 3 and so the correct answer is A. 4. How many double-digit numbers are there where the product of their digits is 8? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 The best answer is D. Since there aren’t so many numbers, write them all: 18, 24, 42 and 81 and so the right answer is D. 5. How many odd double-digit numbers, which the sum of their digits is 6, exist? (A) 1 (B) 3 (C) 5 (D) 7 (E) 9 The best answer is B. Since there aren’t many numbers, write them all down: 15, 33 and 51 and so B is the right answer. 6. Inches Centimeters 7 17.78 X 53.34 Using the following conversion table, what is the value of X? (A) 14 (B) 17 (C) 21 (D) 28 (E) 30 The best answer is C. Since 17.78 x 3 = 53.34, X = 7 x 3 using the same ratio. C is the correct answer. 7. The product of two odd integers is between 304 and 337 exclusive. Which of the following cannot be one of the integers? (A) 5 (B) 13 (C) 35 (D) 39 (E) 43 The best answer is E. If the number is too big, for example 43, multiplying it with another odd integer wouldn’t be in the specified range. 43 x 7 = 301, which is under the range. 43 x 9 = 387, which is over the range and therefore 43 cannot be one of the integers. 8. If the average of 6 consecutive numbers is X, what is the average of the two median numbers? (A) X/2 (B) X/3 (C) X – 1 (D) X (E) X + 1 The best answer is D. Since the numbers are consecutive, the average of the two middle numbers is the average of all the numbers. Take 1, 2, 3, 4, 5 and 6 for example: The average is 3.5, now take 3 and 4; their average is also 3.5. In our case the average stays X. 9. If X and Y are different positive integers and 3X + Y = 14, what is the product of all the possible values of X? (A) 6 (B) 8 (C) 14 (D) 20 (E) 24 The best answer is E. Start from the first number: X=1  not possible. X=2  Y=8. X=3  Y=5. X=4  Y=2. X=5  not possible. The product is therefore 2 x 3 x 4 = 24. 10. In the figure above, one side of the square is overlapping with the diameter of the circle. If the radius of the circle is 2, which of the following is the best approximation for the area of the shaded region? (A) 5 (B) 10 (C) 15 (D) 20 (E) 25 The best answer is B. The area of the shaded region is derived from the area of the square minus half the area of the circle. The area of the square is 4 x 4 = 16. The area of the circle is 6.124 2   R and so half the area would be 6.3. The area of the shaded region would be approximately 16 – 6.3 = 9.7 and so B is the closest answer. 11. If 11 12 99  Q , what is the value of Q? (A) 98 (B) 104 (C) 108 Digital and regular camera production of company P during 1998 8 12.5 0 5 10 15 Digital Regular Cameras made [in thousands] (D) 112 (E) 118 The best answer is C. Cross multiply the expression to get 11Q = 12 x 99. Divide both sides by 11 to get: Q = 12 x 9 = 108 and so C is the right answer. 12. What is the perimeter of the triangle in the figure above? (A) 3 + 6 (B) 3(3 + 3 ) (C) 6 3 (D) 9 (E) The data specified is insufficient The best answer is B. This is a special right triangle, its sides are in the ratio of 1:2: 3 . Since the small side is 3, the second side is 6 and the third side is 3 3 . The perimeter of the triangle is therefore 3+6+3 3 = 3(3 + 3 ). 13. According to the chart above, how many more regular cameras than digital cameras were produced by company P during 1998? o 30 3 (A) 2,000 (B) 2,500 (C) 3,200 (D) 4,500 (E) 5,200 The best answer is D. According to the graph 12.5 thousand regular cameras were made and 8 thousand digital cameras, the difference is 4.5 thousand and so D is the right answer. 14. A certain lottery requires guessing 75% of the numbers to win. If the lottery contains 60 numbers, how many numbers should one guess in order to win? (A) 30 (B) 35 (C) 40 (D) 45 (E) 50 The best answer D. In order to win the lottery, one should guess 75% of 60, which is 60 x 3 / 4 = 45 numbers and so the right answer is D. 15. If in the cylinder above, the radius is equal to  2 and the height is 3, what is the volume of the cylinder? (A) 4 (B) 6 (C) 8 (D) 12 (E) 16 The best answer is D. The volume of a cylinder is received by hR  2  , which in our case is 12343 2 2             and so D is the right answer. 16. If X and Y are coordinates, which of the following pairs (X,Y) answer these conditions: X > Y + 2 and X < 7 ? (A) (4, 5) (B) (7, 3) (C) (6, 4) (D) (5, 1) (E) (3, 7) The best answer is D. Look among the answers for two things: X smaller than 7 and X bigger than Y. Take answer D: 5 > 1 + 2 and 5 < 7 and therefore this is the right answer. 17. If X = 2X/Y, then 2Y = (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 The best answer is D. Solve: X = 2X/Y, divide by X to get: 1 = 2/Y  Y=2 and so 2Y = 4. 18. If X + 2Y = 6 and Y = 3 – X/2, what is the value of (X + Y)? (A) 4 (B) 6 (C) 8.5 (D) 10 (E) The answer cannot be determined The best answer is E. The second equation can be written as 2Y = 6 – X, which is equal to the first equation and so we have two variables with only one equation and so more sufficient data is required. 19. If 20% of the liquids in the barrel are X liters and 45% of the liquids are Y liters, which of the following must be true? (A) X = 15 (B) X = Y – 20 (C) 4Y = 9X (D) X + 30 < Y (E) None of the answers above are true The best answer is C. Lets say that there are 100 liters of liquid in the barrel. X = 20%, which is 20 liters and Y = 45 liters. 4 x 45 = 180 liters and so is 9 x 20 and so 4Y = 9X and C is the right answer. 20. In how many ways can 5 kids be chosen out of a group of 6 kids? (A) 15 (B) 8 (C) 10 (D) 6 (E) 5 The best answer is D. When you pick 5 kids one is left out and so picking out 5 is equal to picking out 1 kid. There are 6 combinations of picking up one kid and so the right answer is D. 21. The probability of giving birth to a boy or a girl is equal. What is the probability of receiving 2 girls and a boy (not necessarily in that order)? (A) 1/8 (B) ½ (C) 3/8 (D) ¼ (E) ¾ The best answer is C. Since there are two possibilities in every birth, boy or girl, the number of possibilities in 3 births is 2 x 2 x 2 = 8. There are three possible combinations: girl, girl, boy or girl, boy, girl or boy, girl, girl and therefore the probability is 3/8. 22. A chopper travels 5 miles in 2 minutes, what is its speed in mph? (A) 80 (B) 110 (C) 120 (D) 150 (E) 180 The best answer is D. In one hour there are 60 minutes or 30 2 minutes intervals. In every 2 minute interval, the chopper travels 5 miles and so in 30 intervals it will travel 30 x 5 = 150 miles and its speed would be 15 mph. 23. An agama walks for 5 hours at a rate of 2 mph and 5 additional hours at a rate of 10 mph. What is the agama average speed in mph? (A) 3 (B) 6 (C) 9 (D) 12 (E) 15 The best answer is B. Use the regular average formula and calculate the average rate. The average speed is therefore 6 10 10525     mph and so the right answer is B. 24. If Johnson can run 20 km in one hour, how many km can he run in 24 minutes? (A) 6 (B) 8 (C) 12 (D) 14 (E) 16 The best answer is B. Johnson can run 20 km in one hour, which is 20 km in 60 minutes or 1 km in 3 minutes. In 24 minutes there are 8 3 minutes intervals and so B is the right answer. 25. George can finish a certain job in 8 days and Jerry can finish it in 12 days. How many days would it take them to complete the job together? (A) 6 (B) 7 (C) 24/5 (D) 30/7 (E) 34/11 The best answer is C. George can finish 3 jobs in 24 days (24/8 = 3). Jerry can finish 2 jobs in 24 days (24/12 = 2). Together they can finish (2+3 =5) jobs in 24 days and so it would take them 24/5 days to finish one job and so the right answer is C. [...]... would be represented by multiplying (Y + 2) with X/Y and therefore D is the right answer 24 If 62 P = 12X, which of the following would represent 2X in terms of P? (A) 6 2P-1 (B) 6 P-1 (C) 2P + 1 (D) 6/ (2P – 1) (E) 6 1-2P The best answer is A 2X is simply 12X /6, which is also equal to 62 P / 6 62P / 6 = 62 P x 6- 1 = 62 P-1 and therefore A is the right answer 25 X and Y are both double digit numbers If in each,... the t-shirt both cost 2X + 15.75 = 64 .25  2X = 64 .25 – 15.75 = 48.5  X= $24.5 9 Daniel bought a camera with 3 films for $104 If the camera costs 10 times more then a film, how much will 2 cameras and 2 films cost? (A) $ 56 (B) $112 (C) $158 (D) $1 76 (E) $182 The best answer is E Let X be the price of a film and so the price of a camera is 10X 10X + 3X = 96  13X = 104  X=$8 and a camera costs $80... greater by 3 than the tens digit, what is the greatest possible difference between X and Y? (A) 33 (B) 55 (C) 66 (D) 77 (E) 82 The best answer is C Let’s pick the largest and the smallest numbers: 96 and 30 The difference between them is therefore ( 96 – 30 = 66 ) and so C is the right answer Chapter 6: 1 If 2A + 4B = 15 and A = -B, then 3B = (A) 15 (B) 17.5 (C) 22.5 (D) 25 (E) 27.5 The best answer is C... is either a 4 or a 6, the number must be (A) divisible by 2 (B) divisible by 4 (C) divisible by 6 (D) divisible by 24 (E) odd The best answer is A An even number is a number where the units’ digit is even Since both 4 and 6 are even, the units’ digit must be even and the number is divisible by 2 and so A is the answer 5 If 3X – 7 = 68 , then 86 – 2X = (A) 24 (B) 36 (C) 48 (D) 52 (E) 65 The best answer... divided by 8 the result is Y What is the value of Y? (A) 76 (B) 82 (C) 95 (D) 100 (E) 118 The best answer is A Write the following equations: X + Y = 68 4 and X/8 = Y Replace X with 8Y: 8Y + Y = 68 4  Y = 68 4/9 = 76 7 A photocopying machine has two programs: 1) Unlimited number of copies for $15 per month 2) A basic charge of $12 per month and 10 cents extra for each copy From which number of copies... many liters are in the pool? (A) 5,000 + Z(X – 60 Y) (B) 5,000 – ZX +Y /60 (C) Z/X – Y /60 + 5,000 (D) Z(X – Y) + 5,000 (E) Z(X – Y /60 ) + 5,000 The best answer is E In the beginning there are 5,000 liters in the pool Every second, X liters come in and Y /60 liters come out And therefore after Z seconds there are 5,000 + ZX – ZY /60 liters in the pool, or Z(X – Y /60 ) + 5,000 and so E is the right answer 14... 3R and 2R = 3S, what is the value of X/S? (A) 16/ 81 (B) 3/13 (C) 13/3 (D) 6/ 15 (E) 81/ 16 The best answer is E X = 3Y/2 = 1.5Y = 1.5(1.5Z) = 1.5(1.5(1.5R) = 1.5(1.5(1.5(1.5S))) = S(3/2)4 = S(81/ 16) X/S = (81/ 16) and therefore E is the right answer 20 Which of the following is equal to the sum of two consecutive odd integers? (A) 345 (B) 361 (C) 382 (D) 3 96 (E) 411 The best answer is D Let X be one of... or equal to X For example: [3 .6] = 3 What is the value of [6. 4] x [1/4] + [2] x [7.178] ? (A) 14 (B) 16 (C) 18 (D) 20 (E) 22 The best answer is A The expression is also equal to 6 x 0 + 2 x 7 = 14 and so A is the answer 18 Let ~(A, B)~ be defined as the remainder of the partition A/B What is the value of ~( 163 , 7)~ ? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 The best answer is B 163 divided by 7 is 23 with a remainder... and therefore the area is 42 3  4 3 The area of 4 2 triangles will be 16 3 The ratio is 16 3 : 16 or 3 :1 10 The value of car in 1998 was $50,000 and after three years it dropped to $25 ,60 0 If the value, each year, is always the same fraction of the value reached on the previous year, what is this fraction? (A) ½ (B) 1/3 (C) 5 /6 (D) 4/5 (E) 5/8 The best answer is D The right answer is D, every year... 1/7 is equal to the difference between 1 /6 and 1/8, what can be the value of B? (A) 1/32 (B) 4/13 (C) 9/24 (D) 21/131 (E) 31/ 168 The best answer is E The difference between 1 /6 and 1/8 is (1 /6 – 1/8 = 1/24) One option is adding this difference to 1/7 and the other is to subtract Start with the first option: 1/7 + 1/24 = 24  7 31 and so the right  24  7 168 answer is E 9 Four equilateral triangles . Y/3 + Y/4 and Y = 60 , what is the value of X? (A) 14.5 (B) 16 (C) 20 (D) 45 (E) 60 The best answer is E. Replace Y with 60 and solve: X + X/3 + X/4 = 60 + 60 /3 + 60 /4 = 60 +20+15 = 95 . 6 1-2P The best answer is A. 2X is simply 12X /6, which is also equal to 6 2P / 6. 6 2P / 6 = 6 2P x 6 -1 = 6 2P-1 and therefore A is the right answer. 25. X and Y are both double. 24. If 6 2P = 12X, which of the following would represent 2X in terms of P? (A) 6 2P-1 (B) 6 P-1 (C) 2P + 1 (D) 6/ (2P – 1) (E) 6 1-2P The best answer is A. 2X is simply 12X /6, which