Quantitative comparisons practice phần 8 pps

The best answer is A. Cindy’s initial weight was 50 Kg. The question is how much is 15 out of 50 in percent terms: %30%100 50 15  and therefore column A is greater than column B. 13. A: X B: 15 AI: X percent of X are X/8 0  X The best answer is B. Rewrite the extra data in percent terms: 8 100 XX X  . Multiply both sides by 100 to get: 12.5 X = X 2  X = 12.5 and therefore column B is greater than column A. 14. A: The total decrease in the car’s value B: 60% AI: The value of a car decreased by 20% and then it decreased by 40% more The best answer is B. Let’s say the car cost $100. At first its price decreased to $80, then it decreased by 40%: (0.6 x $80 = $48). The total decrease is (100 – 48 = 52%). The car decreased by 52% and not by 60% and so column B is greater. 15. A: The total increase in the stock’s value B: 40% AI: The value of a certain stock increased by 20% on January and by 20% more on February The best answer is A. Let’s say that the value of the stock was $100. In January it increased to $120. In February it increased to (1.2 x 120 = $144). All together, the stock’s value increased by 44%, which is greater than 40%. 16. A: By how much percent are rollerblades more expansive than ice-skates B: 80% AI: Rollerblades cost 40% more than skateboards and skateboards cost 40% more than ice-skates The best answer is A. Let’s say that ice-skates cost $100 since there are no numbers in the question. Skateboards cost 40% more, thus $140. Rollerblades cost 40% more than $140, which is $196. And therefore rollerblades cost 96% more than ice-skates, which is greater than 80%. 17. A: The average (arithmetic mean) of the rest of the grasshoppers B: 5 Centimeters AI: The average (arithmetic mean) of 15 grasshoppers is 8 centimeters. The average of 5 of the grasshoppers is 10 Centimeters. The best answer B. Let’s say that the average of the rest of the grasshoppers in column A is X. Use the average formula: 643508 8 3510     X X . 3X = 14  3 2 4X , which is a little under 5 and therefore column B is greater. 18. A: The original number of bells that Helen had B: 700 AI: After Helen lost 30% of her bells, she had 500 bells The best answer is A. 500 bells are 70% of the number we are looking for. We can write the following equation: ? 500 100 70   The original number of bells is (50,000)/(70) = A little over 700 and therefore column A is greater. 19. A: The amount of sugar (in liters) in a mix containing 3 liters of strawberry juice and 2 liters of cola B: 1.5 AI: The concentration of sugar in strawberry juice is 20% and in cola it’s 40% The best answer is B. Calculate the amount of sugar in the mix: 20% of 3 liters is 3/5 liters plus 40% of 2 liters, which is 4/5 liters. The total is (3/5 + 4/5 = 7/5 = 1 and 2/5 = 1.4 liters). Column B is greater than column A. 20. A: The probability of guessing the code the safe B: 1/(100,000) AI: The code of a safe has 5 digits. The last digit is 0. The best answer is A. Since we already know the last digit, we need to guess only 4 digits. Each digit can be between 0 and 9. The probability of guessing each digit is 1/10 and therefore the probability of guessing the whole 4 is (1/10) 4 = 1/(10,000), which is greater than the expression in column B. 21. A: 8 2 B: 2 8 The best answer is B. Take the expression in column B and write it as followed: 2 8 = 16 2 , which is greater than column A. 22. A: X B: Y AI: X 2 = 25 and 5Y The best answer is D. X can be either 5 or -5, Y can either be 5 or -5 also and since there can be more than one answers to the problem, the right answer is D. 23. A: X B: 10 AI: X 2 = 81 The best answer is B. X can either be -9 or 9. 10 is larger than both choices and therefore column B is greater than column A. 24. A: Y B: 0.25X AI: X and Y are both negative integers. X/Y > 4 The best answer is B. X/Y > 4  X > 4Y divide both sides by 4: 0.25X > Y and therefore column B is greater than column A. 25. A: X – 5 B: Y + 5 AI: -5 < -X < 5 -20 < -Y < -15 The best answer is B. Simplify the ranges and make them compatible with the question: -5 < -X < 5  5 > X > -5  0 > X – 5 > -10 -20 < -Y < -15  20 > Y > 15  25 > Y + 5 > 20 We can see that the expression in column A is negative while the expression in column B is positive and therefore greater. 26. A: (1/16) 0.5 + (1/25) 0.5 B: (1/16 + 1/25) 0.5 The best answer is A. Column A = (1/16) 0.5 + (1/25) 0.5 = ¼ + 1/5 = 9/20. Column B = (1/16 + 1/25) 0.5 = (41/400) 0.5 = 20 41 . Now, 41 is smaller than 9 and therefore column A is greater. 27. A: (9/144) 0.5 – (1/25) 0.5 B: (9/144 – 1/25) 0.5 The best answer is B. Column A = (9/144) 0.5 – (1/25) 0.5 = 3/12 – 1/5 = 1/20. Column B = (9/144 – 1/25) 0.5 = 20 3 60 9 3600 81 25144 144259 5.05.0                 . We can see that column B is greater than column A. 28. A: 7/1000 B: 0.049/7 The best answer is C. 7/1000 = 0.007. 0.049/7 = 0.007. The columns are equal to one another and so the answer is C. 29. A: 0.6 3 B: 0.6 1/3 The best answer is B. 0.6 is also 3/5. Column A = (3/5) 3 = 9/125. Column B = (3/5) 1/3  we know that a power that is not a fraction makes a fraction smaller, its also good to remember that a power that is a fraction makes a fraction larger and therefore the expression in column B is greater than 3/5 and obviously from 9/125. 30. A: The average of (X + 9Y + 191) and (9X + Y + 347) B: The average of (5X + 4Y + 457) and (5X + 6Y + 87) The best answer is B. Find the average in both columns: Column A = (X + 9Y + 191 + 9X + Y + 347)/2 = (10X + 10Y + 538)/2 = (5X + 5Y + 269). Column B = (5X + 4Y + 457 + 5X + 6Y + 87)/2 = (10X + 10Y + 544)/2 = (5X + 5Y + 272). The best answer is B. 31. A: 3.88 B: 17 The best answer is B. We know that 416  and that 525  and therefore 17, which is found between 16 and 25 will give a result between 4 and 5. Column B is greater than column A. 32. A: Percent increase from 63 to 65 B: Percent increase from 65 to 67 The best answer is A. A = 2/63 and B = 2/65. The denominator is bigger in B and therefore column A is greater. 33. A: X + Y B: X + Z AI: The product of three numbers is 1000 The best answer is D. All we know is that XYZ = 1000, this information is not sufficient to know whether Y is bigger than Z or not. The right answer here is D. 34. A: 0.1 B: 1 25 250        The best answer is C. Column B = 1.0 10 1 250 25 25 250 1         and therefore column A and B are equal. 35. A: 65% of 135 B: 135% of 65 The best answer is C. Remember, don’t calculate- compare. A = 135 100 65  B = 65 100 135  According to the multiplication law, these expressions are equal and thus the answer is C. 36. A: 30% of 25 B: 65% of 15 The best answer is B. A = 5.725 100 30  B = 75.9 100 975 15 100 65  Column B is greater than column A. 37. A: BA  B: BA  AI: A > 0 B < 0 The best answer is B. If A = -B for example, column A = 0 while column B = 2A or 2B. The expression in column B is always positive as opposed to the expression in column A, which can equal zero. 38. A: (X + Y + Z)/3 B: Z AI: X < Y < Z The best answer is B. The expression in column A is actually the average (arithmetic mean), which means that its value is between X and Z, thus smaller than Z. Since the average must be smaller than Z, column B is greater than A. 39. A: The sum of the numbers B: 2188 AI: The average of 12 numbers is 182 The best answer is B. The average (arithmetic mean) of n numbers is their sum divided by n. If the average of 12 numbers is 182, their sum will be 12 x 182 = 2184. Column B is greater than column A. 40. A: (23) -1 B: (24) -1 The best answer is A. A = 1/23 and B = 1/24, in column A 1 is divide into less parts and therefore the result is greater. 41. A: A + B B: 140 AI: A = 20 + 16 + 13 + 11 + 6 + 2 B = 22 + 18 + 13 + 11 + 8 + 4 The best answer is A. Rewrite A and B like this: A = 20 + 16 + 13 + 11 + 6 + 2 B = 4 + 8 + 11+ 13 + 18 + 22 Add them up: A + B = 24 + 24+ 24 + 24 + 24 + 24 A + B = 24 x 6 = 144. Column A is greater than column B. 42. A: 2 x (0.2) B: (0.2) 2 The best answer is A. 2 x (0.2) = 0.4. (0.2) 2 = 0.04. Since 0.4 > 0.04, column A is greater than B. 43. A: Y B: 2X + 3.5 AI: 4Y – 8X = 14 The best answer is C. 4Y – 8X = 14, divide both sides by 4: Y – 2X = 3.5  Y = 2X + 3.5. We can see that the columns are equal to one another. 44. A: 1.5 – 3X B: Y AI: 8Y – 24X = 12 The best answer is D. Take 8Y – 24X = 12 and divide it by 8: Y – 3X = 1.5.  Y = 3X + 1.5. We don’t know if 3X + 1.5 are bigger or smaller than 1.5 – 3X since X can be positive, negative or even zero. The right answer is D. 45. A: 11 out of 12 in percent terms B: 91% The best answer is A. Column A = 12 100,1 %100 12 11  . Stop here. Go to the other column and check if 12 x 91 is greater than 1100: 12 x 91 = 1,092 and therefore it’s more than 91%. Column A is greater than column B. 46. A: X – Y + Z B: 15 AI: Y – X – Z > 15 The best answer is B. Take Y – X – Z > 15 and divide both sides by -1: X – Y + Z < -15 (don’t forget to flip the inequality) We can see that the expression in column A is smaller than that in column B. 47. A: 4/9 + 5/12 B: 4/7 + 5/11 The best answer is B. A = 4/9 + 5/12 = 108 93 108 4548   < 1. B = 4/7 + 5/11 = 77 79 77 3544   > 1 and therefore column B is greater. 48. A: 0 7 B: 7 0 The best answer is B. Zero raised to any positive power is zero, so Quantity A = 0. Any number raised to 0 is unity, so Quantity B = 1. 49. A: 1 B: X AI: 2 1  X The best answer is A. Since X 1 is negative X must the negative. If X is negative, column A is greater. 50. A: 66 B: The average of the six numbers. AI: The sum of 6 even consecutive numbers is 396. The best answer is C. The average is the sum divided by the amount of numbers. The average of the 6 numbers is 396/6 = 66 and therefore the columns are equal to one another. 51. A: X 2 Y 3 B: X 3 Y 2 AI: X < 0 and Y > 0 The best answer is A. Pick up numbers: For example, X= -1 and Y= 2. Column A = 1 x 8 = 8. Column B = -1 x 4 = -4. [...]... column B is greater than column A 53 A: 1 – 4/17 B: 27/ 68 + 17/34 The best answer is B Column A = 1 – 4/17 = 13/17 = 52/ 68 Column B = 27/ 68 + 34/ 68 = 61/ 68 Column B is greater than column A 54 A: (0.99)3(0.99)4 B: (0.99 )8 The best answer is A When dealing with fractions, the smaller the power, the largest the result A = (0.99)7 while B = (0.99 )8 and therefore column A is greater since the power of the... 0.0005 0.00 08 B: 0.0005 A: The best answer is A Move the decimals to the right, keep track of how many you moved Column A = 0.006 6  12 0.0005 0.5 0.00 08 8 Column B =  , which is smaller than 12 and so column A is the 0.0005 5 greatest  71 A: X + X2 – X3 + X 4 B: X 4 – X 2 + X3 – X AI: X = -3 The best answer is B The best way is to replace X with -3 Column A = -3 + 9 – 27 + 81 = 60 Column B = 81 – 9... greater than column A 56 X 2.25  8 X 1.5  16 1.5 B: X  4 A: The best answer is C Take a power of two on both sides to get:  8 X 1.5  16 2 2.25 1.5  8 X 1.5  16 B = X  4   X A= X 2.25 And so column A is equal to column B 57 A: 11 5 B: 100,000 The best answer is A 100,000 can be written as 105 Now, 115 > 105 and therefore column A is greater than column B 58 A: 2Y 2 B: Y The best answer is... =      4  100  4  10  4  10  4 Column A = We can see that column A is greater than column B 65 A: One seventh of 25% of 336 B: One sixth of 20% of 360 The best answer is C 1  25  1  84 00  84  336     12   7  100  7  100  7 1 20 72  1 Column B =   360   2  36    12  6  100 6  6 Column A = We can see that column A = column B and so the answer is C 66 A: 5 ... 177  36 B: 0.63  0.36 A: The best answer is B Column A = 45  96 141   141 0.64  0.36 1 Column B = 177  36 141 , which is a little bigger than 141 and so  0.63  0.36 0.99 column B is greater 68 A: (X2 + Y2) B: (X + Y)2 AI: 0 > X > 1 > Y The best answer is B Column A = X 2 + Y2 Column B = X 2 + Y2 + 2XY, subtract X2 + Y2 from both sides Column A = 0 while column B = 2XY 2XY is greater than zero... B The best way is to replace X with -3 Column A = -3 + 9 – 27 + 81 = 60 Column B = 81 – 9 + 27 – 2 = 97, which is greater than column A 72 A: Y – X B: Y AI: X and Y are positive prime numbers X + Y = 8, Y > X The best answer is B There are two choices: 1 and 7 or 3 and 5 In the first option: X=1, Y=7; Column A = 6 and B = 7 In the second option: X=3, Y=5; Column A = 2 and B = 5 In both cases column... or 5 and 7 In the first option: X=1, Y=11; Column A = 10 and B = 7 In the second option: X=5, Y=7; Column A = 2 and B = 7 The answer is different each time and so the right answer is D 74 A: A + B B: 18 AI: A x B = 17 The best answer is D A and B could be any numbers we want, for example: (1, 17) or (0.17, 100) or any other good combination If we were told that A and B are integers, the answer would . 27/ 68 + 17/34 The best answer is B. Column A = 1 – 4/17 = 13/17 = 52/ 68. Column B = 27/ 68 + 34/ 68 = 61/ 68. Column B is greater than column A. 54. A: (0.99) 3 (0.99) 4 B: (0.99) 8 . numbers B: 2 188 AI: The average of 12 numbers is 182 The best answer is B. The average (arithmetic mean) of n numbers is their sum divided by n. If the average of 12 numbers is 182 , their. 16 + 13 + 11 + 6 + 2 B = 22 + 18 + 13 + 11 + 8 + 4 The best answer is A. Rewrite A and B like this: A = 20 + 16 + 13 + 11 + 6 + 2 B = 4 + 8 + 11+ 13 + 18 + 22 Add them up: A + B = 24