РЕГИОНЫ РОССИЙСКОЙ ФЕДЕРАЦИИ 9 страница
A: The measurement of the angle ABC B: The measurement of the angle EDC AI: AC is the diameter of the circle
The best answer is A. Angle subtended by the diameter on the circumference = angle ABC = 90o. Column A is greater than column B.
A: 225o B: The measurement of the angle 4 AI: The illustration is not drawn to scale
The best answer is A. Angle 4 and angle 1 are on the same line and therefore their sum is 180o. And therefore angle 4 must be smaller than 180 degrees, which means that column A is definitely greater than column B.
A: 2Y B: X
The best answer is C. Angle subtended by an arc at the center of a circle is double the angle subtended by the same arc on the circumference, therefore X = 2Y. Column A is equal to column B.
15. A: AB x Z B: AC x Z AI: Angle 1 = angle 2 Z is a number between 0 and 50.
The best answer is C. Since the triangle is an isosceles, AB = BC. When you multiply each of the equal sides by the same number they remain equal to one another and so the two columns are equal.
16. A: The largest angle in the triangle B: 90o AI: consider a right triangle ABC
The best answer is C. Since the triangle is a right triangle, there must be an angle of 90o among the angles. The other angles sum up to 90o and so the largest angle must be the right angle. The columns are equal.
17.
A: 140o B: The sum of angles X and Y AI: Y = The best answer is C. Angle subtended by an arc at the center of a circle is double the angle subtended by the same arc on the circumference, therefore X = 2Y. If Y = Column B = X + Y = 140o and so the columns are equal.
18. A: The area of the square ABCD B: The area of the circle AI: The side of a square is
The best answer is D. The area of the square is The area of the circle is It seems like the area of the circle is greater yet the question didn’t mention that R is not a fraction. If R is a fraction, for example ½, the area of the square would be bigger. The right answer is D.
A: The measurement of X B: The measurement of Y AI: The illustration is not drawn to scale
The best answer is D. The only thing we know for sure is that X and Y are supplementary angles and therefore X + Y = 180. No further information is available and so we cannot determine the relations between X and Y and the right answer is D.
20. A: The ratio between the diameter of circle 1 to the diameter of circle 2 B: AI: The area of circle 1 is twice the area of circle 2
The best answer is C. The area of a circle dependent on the diameter is The area of the first circle is The area of the second circle is We know that Column A is equal to column B.
21. A: The sum of the angles that are equal B: 130o AI: Consider an isosceles triangle, one of the angles is 55o.
The best answer is B. There are two possible angle arrangements in this circle: 55, 55, 70 or 55, 62.5, 62.5. In both cases, the sum of the equal angle does not sum up to 130o or greater and therefore column B is always greater than column A.
A: The length of BD B: The length of BC/2 AI: ABC is a right triangle at B. The area of ABD is 2.25.
The best answer is B. Since ABC is a right triangle, BC2 + 32 = 55 è BC = 4 and therefore column B = 2. The area of ABD is 2.25, write the following equation for the area: (BD x 3)/2 = 2.25 è BD = 1.5. Column A = 1.5 while B = 2 and therefore the answer is B.
23.
A: The area of ABCDE B: 100 AI: The diagonal of the square is BCD is an equilateral
The best answer is A. The ratio between the sides of the square to its diagonal is 1:1: The height of the triangle is ( The area of the square is 100. The area of both is 100 +
24.
A: The circumference of one of the circles B: The perimeter of the triangle ABC AI: The equilateral triangle ABC is formed by connecting the centers of three identical circles. The circles are tangential to one another.
The best answer is B. We know that the circumference of a circle is equal to We can see that each side of the triangle is made up of two radiuses and therefore the perimeter of the triangle is (2R)(3) = 6R. 6.28 > 6 and therefore column B is greater than column A.
25.
A: The area of the triangle ABC B: The area of one of the circles AI: The equilateral triangle ABC is formed by connecting the centers of three identical circles. The circles are tangential to one another.
The best answer is B. The area of a circle is simply All we know about the equilateral triangle is that each of his sides is equal to 2R, but this is sufficient. The height of the ABC is The area of the triangle is base x height divided by two. The area is
26. A: The volume of a cylindrical water tank that has a radius of 3 meters and a height of 5 meters B: The volume of a cylindrical water tank that has a radius of 2 meters and a height of 10 meters
The best answer is A. The volume of a cylinder in general is calculated according to: Column A = Column B = Column A is greater than column B.
27.
A: BE B: ED AI: The measurement of angle ABD is 43 degrees.
The best answer is B. ABC = ABD + DBC è 90o = 43o + DBC è DBC = 47o. ABD and BDE are alternate interior angles and thus equal. BE is in front of a 43o angle. ED is in front of a 47o angle. Therefore, ED is greater since it is located in front of a larger angle.
28. A: The area of the circle B: 507 AI: The circumference of a circle is
The best answer is A. The circumference of the circle is è R = 13. The area of the circle can be easily calculated according to The area = 169 x 3 = 507 and therefore
29. A: Perimeter of a regular octagon with a side of 4.5 B: Perimeter of an equilateral triangle with a side of 12
The best answer is C. An octagon has 8 sides and therefore it has a perimeter of 8 x 4.5 = 36. An equilateral triangle has three sides and therefore it has a perimeter of 12 x 3 = 36. The columns are equal.
30. A: Semi-circumference of a circle with a diameter of 28 inches B: The perimeter of a regular nonagon with a side of 5 inches
The best answer is B. Column A: The circumference of a circle with a diameter of 28 inches is
The semi-circumference is 88/2, thus 44 inches (rounded up). Column B: The perimeter of a regular nonagon (a nonagon has nine sides) is equal to 5 x 9 = 45 inches and therefore column B is greater than column A.
31. A: The perimeter of a regular octagon with a side of 10 B: The perimeter of a regular decagon with a side of 8
The best answer is C. An octagon has 8 sides and therefore its perimeter is 8 x 10 = 80. A decagon has 10 sides and therefore its perimeter is 10 x 8 = 80. 32. A: The volume of a rectangular solid with length of 4 inches, a width of 6 inches and a height of H inches. B: The volume of a rectangular solid with length of 6 inches, a width of 3 inches and a height of Q inches.
The best answer is D. This question takes seconds if you think instead of finding the volumes right away. As you can see each of the columns is dependent on a different variable (H and Q) yet no correlation between the two is given and so the answer would be undeterminable. The right answer in this case is D.
33.
A: X2 + Q2 B: Y2 + Z2
The best answer is C. Since the two triangles are right triangles with a common base, we can use the Pythagoras principle to write the following equations: Let’s name the common base B. B2 = X2 + Q2 and B2 = Y2 + Z2. We can see that the columns are equal to one another.
A: X + Y + Z B: 230o
The best answer is A. All the exterior angles to the quadrilateral equal to 360. We have one exterior angle missing, which can easily be found since her supplementary angle is 55 and so the fourth exterior angle is equal to (180 – 55 = 125o). X + Y + Z + 125 = 360o è X + Y + Z = 360 – 125 = 235o. We can see that column A is greater than column B.
35. A: X3 B: Y4 AI: 3X = 81 4Y = 64
The best answer is B. 3X = 81 è X = 4. 4Y = 64 è Y = 3. Column A = 43 = 64. Column B = 34 = 81. Column B is greater than column A.
36. A: A: The surface area of a cube whose volume is 343 B: 343
The best answer is B. The volume of the cube is 343 and so each of its side is X. X3 = 343 è X = 7. The area of each face is X2 = 49 and since there are 6 faces their area together is 6 x 49 = 294, which is smaller than 343 and so column B is the greatest.
37. A: The measurements of the largest angle in triangle A B: The measurements of the largest angle in triangle B AI: The measures of the angles in triangle A are in the ratio of 2:4:6 The measures of the angles in triangle B are in the ratio of 1:2:6
The best answer is B. Triangle A: Divide 180 by (2 + 4 + 6) to get the basic angular unit in the triangle: 180/12 = 15o. The largest angle in this triangle is 6 units, or 6 x 15o = 90o. Triangle B: Do the same here. The unit is 180/9 = 20o and so the largest angle in this triangle is 6 x 20o = 120o. Column B is greater than column A.
38. A: The median angle in the triangle B: 60o AI: The ratio between the angles in a triangle is 1:5:9
The best answer is C. Divide 180 by (1 + 5 + 9) to get the basic angular unit in the triangle: 180/15 = 12o. The median angle in this triangle is 5 units, or 5 x 12o = 60o. We can see that column A = column B.
1. A: The number of bullets hitting the penny B: 40 AI: The chances of a striking a penny with a gun bullet from 300 yards is 0.04%. A gun man fires 10,000 bullets.
The best answer is B. 0.04% of 10000 = (0.04/100) x 10000 = 4. Therefore Quantity B is greater.
2. A: The number of anticipated winners in the raffle B: 80 AI: The chances of winning the raffle are 0.08%. 10,000 people are participation in the raffle.
The best answer is B. 0.08% of 10000 = (0.08/100) x 10000 = 8 and therefore column B is greater than column A.
3. A: The time it would take Sean to bike 100 miles B: The time it would take Connell to bike 60 miles AI: Sean bikes at 30 mph and Connell bikes at 15 mph.
The best answer is B. Time = Distance / Speed
4. A: The energetic value of one liter of Kerosene B: The energetic value of one liter of HTPB AI: The energetic value of 4 liters of kerosene with 3 liters of HTPB is equal to the energetic value of 2 liters of Kerosene with 7 liters of HTPB.
The best answer is A. Let K represent Kerosene and H represent HTPB. We can write the following equation: 4K + 3H = 2K + 7H Simplify it è 2K = 4H è K = 2H and therefore the value of one liter of Kerosene is twice the value of HTPB and so column A is greater.
5. A: The value of an American dollar B: The value of an Australian dollar AI: The money value of 3 American dollars and 5 Australian dollars is equal to the value of 2 American dollars and 8 Australian dollars
The best answer is A. Let X be the number of American dollars and Y the number of Australian dollars. We can write the following equation: 3X + 5Y = 2X + 8Y. Simplify è X = 3Y and therefore the value of an American dollar is greater than the value of an Australian dollar.
6. A: The value of the largest among the three B: 104 AI: The sum of three consecutive numbers is 312
The best answer is A. Let x-1, x and x+1 be the three consecutive numbers. We know that x-1 + x + x+1 = 312 è 3x = 312 è x = 104. The largest among the three is equal to 105 and therefore column A is greater.
7. A: The average (arithmetic mean) of the first and the last among those numbers B: 54
The best answer is B. AI: The sum of 4 consecutive numbers is 214. Let x, x+1, x+2 and x+3 be the four numbers. We can write the equation: x + x + 1 + x + 2 + x + 3 = 220. è 4x + 6 = 220 è x = 52. The average arithmetic mean of the first and the second is (52 + 55)/2 = 53.5, which is smaller than 54 and so column B is greater.
8. A: The time it takes to run 3 Km at a rate of 150 meters per 10 seconds B: The time it takes to run 2 Km at a rate of 80 meters per 12 seconds
The best answer is B. Time = Distance / rate TimeA = 3000 / 150 = 20 x 10 = 200 seconds. TimeB = 2000 / 80 = 25 x 12 = 300 seconds and therefore column B is greater than column A.
9. A: 25 minutes B: Y AI: X cakes are baked by Z woman in 25 minutes. X cakes are baked by Z + 3 woman in Y minutes.
The best answer is A. The same number of cakes is baked by more women in less time and therefore Y minutes are less than 25 minutes. Column B is the greatest.
10. A: 3 hours and a half B: X AI: Z delivery boys deliver W pizzas in 3 hours and a half. Z delivery boys deliver (W + 3) pizzas in X hours.
The best answer is B. This is a simple reasoning problem, more pizzas delivered by the same number of delivery boys would take more time to deliver and therefore X has to be bigger than 3.5.
11. A: The time in minutes it would take Sandra to walk 10 miles B: The time in hours it would take Christopher to walk 5 miles AI: Sandra walks at a rate of 5 miles per hour while Christopher walks 2.5 miles per one hour.
The best answer is A. Read the columns carefully. Column A is the time in minutes and column B is in hours. Column A = 2 hours = 120 minutes. Column B = 2 hours. 120 > 2 and therefore column A is greater than column B.
Note: people are gonna curse me for that question.
12. A: Time elapsed from 14:12 to 19:03 B: 3 hours and 51 minutes
The best answer is A. Column A: from 14:12 to 15:00 its 48 minutes, from 15:00 to 19:00 its 4 hours and 3 more minutes to 19:03. Altogether, it’s 4 hours and 51 minutes. Column A is greater by one hour exactly from column B.
13. A: The probability of getting an even number in a throw of a dice B: The probability of getting a number greater than 2 in a throw of a dice
The best answer is B. There are 6 options altogether; 3 of them are even numbers: 2, 4 and 6 and therefore the probability is 3/6 = ½. There are 4 numbers greater than 2: 3, 4, 5 and 6 and therefore the probability here is 4/6 = 2/3, which is greater than ½ and so column B is greater than A.
14. A: Timothy’s height B: Avery’s height AI: David is 3 inches taller than Timothy and 4 inches taller than Avery
The best answer is A. Let X be the height of David. Timothy is X – 3 and Avery is X – 4, which means that Timothy is taller than Avery and column A is greater than column B.
15. A: The distance that Martha traveled in kilometers B: The distance that Bertha traveled in miles AI: Martha traveled 6 miles and Bertha traveled 9.6 kilometers Assume that 1 mile is 1.6 kilometers.
The best answer is A. Martha traveled 6 miles, which is (6 x 1.6 = 9.6) kilometers. Bertha traveled 9.6 kilometers, which is 6 miles. 9.6 > 6 and therefore column A is greater.
16. A: The number of minutes that the machine was operational B: 1440N AI: A food processing machine was operating for N Days
The best answer is C. 1 day has 24 hours, which is (24 x 60 = 1440) minutes. The total number of minutes is 1440N. The columns are equal and the right answer is C.
17. A: Frank’s income B: Susan’s new income AI: Before Susan quit her old job, her income was 35% more than Frank’s income. After Susan changed jobs, her new income is 35% less than her old income.
The best answer is A. Since no numbers were given, plug in $100 as Frank’s income. Susan old income was 35% more than $100, thus $135. Susan’s new income is 35% less than $135, which is We can see that her new income is less than Frank’s income and so column A is greater than column B.
18. A: The cost of Z erasers B: ZX/Y AI: Y erasers cost X dollars
The best answer is C. If Y erasers cost X dollars, each single eraser costs X/Y dollars. We want to know how much do Z erasers cost, multiply Z by the cost of one unit. Z erasers cost ZX/Y and so column A = column B.
19. A: Matt’s speed from work back home B: Matt’s speed from home to work AI: Matt goes from home to work in 5 minutes and returns home from work in 25 minutes.
The best answer is D. The question lacks an important detail- we have no way of knowing if Matt goes through the same path from home to work and from work home or if he has a ride in one direction. It is indeterminable and so the right answer is D.
20. A: Number of feet in 999 yards. B: Number of minutes in two days
The best answer is A. Column A: There are 3 feet in every yard and therefore there are 999 x 3 = 2997 feet. Column B: There are 24 x 60 = 1440 minutes in one day and therefore there are 2880 minutes in two days. Column A is greater than column B.
21. A: The length of the longest stick that can fit inside a box whose internal dimensions are 12 cm by 4 cm by 3 cm B: 12 Cm
The best answer is A.
If you try to put the largest stick in the box, you’ll put it from corner to corner and thus you form two right triangles: one with sides of 3,4, 5 and the second is a one with 5, 12 and X. Where X is the size of the stick. Using the Pythagoras principle, X = Column A is greater than column B. Another way to solve this question is by intuition, if one of the sides is 12, you can always put the stick diagonally and therefore a larger stick can be placed in the box.
22. A: Betty’s average speed, in miles per hour B: 40 AI: Betty drove 210 miles from 8:00 A.M. to 13:15 P.M.
The best answer is C. Betty drove from 8:00 to 13:15, which are exactly 5 hours and a quarter. Speed = Distance / Time Speed = 210 / 5.25 = 40 miles per hour. Column A = column B = 40 miles per hour.
23. A: The smallest number greater than 300 in the sequence B: 330 AI: The first term of a sequence is one. Starting with the second term, each term is two less than 4 times the previous term.
The best answer is A. Follow the sequence carefully: The first is 1, the second is 4(1) – 2 = 2. The third term is 4(2) – 2 = 6. The fourth term is 4(6) – 2 = 22. The fifth term is 4(22) – 2 = 86. The fifth term is 4(86) – 2 = 342. Stop here since we passed 300. Since 342 is greater than 330, column A is greater than B.
24. A: The cost of M guitars in dollars B: AI: At Jim’s guitar centre, a guitar costs Q dollars and P cents
The best answer is A. One guitar costs Q dollars + P/100 dollars. M guitars cost We can see that the expression in column B has –PM instead of PM and therefore it is smaller than the expression in column A.
25. A: The ratio between the number of people who jump rope to the number of people who only ran B: 1/2 AI: At the city sports day, 600 people jumped rope, 400 ran and 200 did both
The best answer is A. (600 + 200 = 800) people jumped rope. 400 people only ran. The ratio between the two groups is 800/400 = 2. 2 > ½ and so column A is greater than column B.
26. A: The units’ digit of 115 B: The units’ digit of 511
The best answer is B. Column A: 11 by any power is always a number where the units’ digit is 1. Try some numbers: 111 = 11, 112 = 121 and so on.
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13.
14.
degrees
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, where R is the radius of a circle
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19.
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22.
) and therefore the area of the triangle is equal to 
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, which is approximately 6.28R.
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and therefore the area of the circle is larger and so column B is greater than column A.
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is definitely greater than 507, which makes column A greater than column B.
, which is approximately 88 inches (3.14 x 28).
34.
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This is a hard question to figure out with out a drawing so draw a small sketch of a box:
Cm.
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