РЕГИОНЫ РОССИЙСКОЙ ФЕДЕРАЦИИ 8 страницаRollerblades 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: 3X = 14 è
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:
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: 82 B: 28
The best answer is B. Take the expression in column B and write it as followed: 28 = 162, which is greater than column A.
22. A: X B: Y AI: X2 = 25 and
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: X2 = 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 è 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 è 5 > X > -5 è 0 > X – 5 > -10 -20 < -Y < -15 è 20 > Y > 15 è 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 = Now,
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 = 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: 0.63 B: 0.61/3
The best answer is B. 0.6 is also 3/5. Column A = (3/5)3 = 9/125. Column B = (3/5)1/3 è 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:
The best answer is B. We know that 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:
The best answer is C. Column B =
35. A: 65% of 135 B: 135% of 65
The best answer is C. Remember, don’t calculate- compare. A = B = 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 = B = Column B is greater than column A.
37. A: B: 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. 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 è 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. è 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 = 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 = B = 4/7 + 5/11 =
48. A: 07 B: 70
The best answer is B. Zero raised to any positive power is zero, so Quantity A = 0.
49. A: 1 B: X AI:
The best answer is A. Since 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: X2Y3 B: X3Y2 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. We can see that column A is positive while B is negative and so A is the right answer.
52. A: The smallest prime number smaller than 4 B: 3
The best answer is B. The smallest prime number smaller than 4 is 1 and not 3 and therefore 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 fraction there is smaller.
55. A: X B: 7 AI:
The best answer is B. If 7 > -7 and so column B is greater than column A.
56. A: B:
The best answer is C. Take a power of two on both sides to get: A = B = And so column A is equal to column B.
57. A: 115 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: B: Y
The best answer is D. For a positive Y, column A is equal to column B. Now, for a negative Y, column A is greater than column B. Since there is more than one answer, the right answer is D.
59. A: X B: 13 AI: XY = 156 Y < 11
The best answer is A. 156 is a multiplication of 12 and 13. Since Y is smaller than 11, X must be larger than 13 in order for the multiplication XY to be equal to 156. Since X > 13, column A is greater than column B.
60. A: 1/X – 1/Y B: (X – Y)/(XY)
The best answer is D. Simplify column B into the following: (X – Y)/(XY) = 1/Y – 1/X. Since we have no further information on X and Y, the answer cannot be obtained and the right answer is D.
61. A: (X – Y)/(XY) B: 0 AI: Y > X > 0
The best answer is B. The easiest way is to plug in numbers. Replace X with 1 and Y with 2. Column A = (1 – 2)/(1 x 2) = -1/2. Column B = 0. Therefore, column B is greater than column A.
62. A: B:
The best answer is B. Simplify both columns. Column A = Column B = We can see that the expression in column B is greater than that in column A.
63. A: B: 1111
The best answer is A. Since its hard calculating the expression in column A, do the following: Multiply 99 with 1111, the result is far less than 999,999 and therefore column A is much bigger than column B.
64. A: One half of 40% of 65 B: One fourth of 35% of 140
The best answer is A. Column A = Column B = 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. Column A = Column B = We can see that column A = column B and so the answer is C.
66. A: B: 6.5
The best answer is B. Simplify the expression in column A:
Column B is greater than column A by 0.5 and so the answer is B.
67. A: B:
The best answer is B. Column A = Column B =
68. A: (X2 + Y2) B: (X + Y)2 AI: 0 > X > 1 > Y
The best answer is B. Column A = X2 + Y2 Column B = X2 + Y2 + 2XY, subtract X2 + Y2 from both sides. Column A = 0 while column B = 2XY. 2XY is greater than zero since X and Y are positive and therefore column B is greater than column A.
69. A: 7/5 B: Y/X AI:
The best answer is A. Take Column A is greater than 1 where column B is smaller than 1 and so the answer is A.
70. A: B:
The best answer is A. Move the decimals to the right, keep track of how many you moved. Column A = Column B =
71. A: X + X2 – X3 + X4 B: X4 – X2 + 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 + 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 B is greater than A and therefore B is the right answer.
73. A: Y – X B: 7 AI: X and Y are positive prime numbers. X + Y = 12, Y > X.
The best answer is D. There are two choices: 1 and 11 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 have been C but no such information was given and so the right answer is D.
75. A: X B: 9/39 AI:
The best answer is C.
Take the expression in column B: 9/39 = 3/13 and so both columns are equal to one another.
A: The length of ST B: 4
The best answer is A. The easiest way to answer this question is to look at ST as the hypotenuse of a triangle. The horizontal distance between S and T is (7 – 3 = 4), the vertical distance is (5 – 2 = 3). We can see that the third side should be 5 in order to validate the Pythagoras principle. Column A(5) is greater than column B(4).
2.
A: 180 degrees B: The measurement of angles 1 and 2 AI: AB is the diameter of the circle
The best answer is C. Angle subtended by the diameter on the circumference = 90o.
3.
A: The measurement of angles 2 and 6 B: The measurement of angles 1 and 5 AI: The illustration is not drawn to scale The best answer is D. All we know about this problem is that angles 1, 2, 5 and 6 sum up to 180 degrees and that is not sufficient. Hence the relationship is indeterminate and the right answer is D.
4.
A: The measurement of angles 3 and 4 B: The measurement of angles 5 and 6
The best answer is A. Angles 3 and 4 are supplementary angles on a straight line and therefore their sum is 180. Angles 5, 6, 1 and 2 sum up to 180 and therefore 5 and 6 by themselves are smaller than 180 degrees.
5.
A: 2BC B: AB + AC AI: Angles 1 and 2 are equal
The best answer is D. The question only implies that the triangle is an isosceles and that is not enough. BC can be as small or big as we want and still the triangle can be an isosceles and therefore the right answer is D.
6. A: The measurement of angles 1 and 2 B: The measurement of angle 4 AI: The illustration is not drawn into scale
The best answer is D. Angles 3 and 4 are vertically opposite angles and so they’re equal to one another. We have no further information about the triangle and relations between the angles there. Angles 1 and 2 can be either larger or smaller than 3 and therefore the answer cannot be determined.
7. A: The length of BC B: The length of AC AI: Angles 1 and 2 are equal. The measurement of angle BAC is 61 degrees.
The best answer is A. Since the triangle is an isosceles and the top angle is 61 degrees, the two base angles are equal to 59.5 degrees. BC is in front of 61 degrees and AC is in front of 59.5 degrees and therefore column A is greater.
8. A: The measurement of angle 1 minus angle 3 B: The measurement of angle 6 minus angle 4
The best answer is C. Angle 3 being an outer angle to the triangle is equal to angles 4 + 5. Angle 1 being an outer angle to the triangle is equal to angles 5 + 6. Angle 1 minus 3 is equal to angle 6 minus angle 4. We can see that the columns are equal to one another.
9. A: Twice the length of AB B: The length of BD AI: The measurement of the angle BAD is 30o.
The best answer is A. Angle subtended by the diameter on the circumference = 90o. In other words AB = 2BD. Column A = 2AB = 4BD. Column B = BD and therefore the answer is A.
10. A: Volume of a cube in which a length of a side is 7 B: Volume of a cube in which a length of a diagonal of a side is
The best answer is A. Column A: The volume given the length of a side is 73. Column B: If side = X, then diagonal of a face = (X2 + X2)1/2 = (2)1/2 X.
11. A: The angle ABC B: 55 degrees AI: Consider an isosceles triangle, AB = BC. AC2 > AB2 + BC2
The best answer is A. Draw a sketch of the triangle. If the triangle was a right triangle (ABC = 900), AC2 = AB2 + BC2. Since the AC2 > AB2 + BC2, the angle at the top (ABC) is larger than 90 degrees and column A is greater than column B.
|
.
, which is a little under 5 and therefore column B is greater.
è The original number of bells is (50,000)/(70) = A little over 700 and therefore column A is greater.
.
is smaller than 9 and therefore column A is greater.
.
and that 
and therefore 17, which is found between 16 and 25 will give a result between 4 and 5.
and therefore column A and B are equal.
. Stop here.
< 1.
> 1 and therefore column B is greater.
is negative X must the negative.
.
.
.
.
.
.
.
.
.
, which is a little bigger than 141 and so column B is greater.
.
, which is smaller than 12 and so column A is the greatest.
.
1.
= 6(2)1/2 è X = 6 and so the volume is 63, which is smaller than the volume in column A.
12.
