РЕГИОНЫ РОССИЙСКОЙ ФЕДЕРАЦИИ 3 страница
59. A: X B: ½ AI: X > 1
The best answer A.
Compare the powers: 3X = 6 è X = 2. Column A is greater than column B.
60. A: 160 B:
The best answer is B. There is only one way to solve this problem (guessing doesn’t count):
Column B is greater than column A.
1. A: B:
The best answer is B. Take each column and reduce it to one variable. Since both sides have the variable ¼ subtract it from both sides. Reduce column A to Column B can be written as Again, it’s still hard to compare and so we’ll find another common denominator.
2. A: B:
The best answer is A. A can be simplified to 8/5. B can be simplified to 16/25, which is definitely smaller than column A.
3. A: B:
The answer is B. We can write column B as 4. A: 14 percent of 50 B: 15 percent of 51
The best answer is B. A can be written as B can be written as
5. A: 17 percent of 300 B: 15 percent of 312
The best answer is A. A can be written as Since the denominator of both columns is the same we can only compare the numerator, divide both numerators by 15 to get: A: 17 x 20, which is 340 and B: 312. We can see that A is greater.
6. A: Q5 B: 3Q2 AI: 2Q3 = -432
The best answer is B. In this question you don’t really need to calculate the actual numbers only pay attention to signs. From the additional data we can conclude that Q is negative since the power is odd. A will result in a negative number but B has an even power and so the result is positive.
7. A: 3X B: X2 AI: X4 = 81
The best answer is D. From the additional data we can conclude that X is 3 or -3. If X = 3, than A Is greater but if X = -3, B is greater and so the answer cannot be determined.
8. A: P2 B: 2P AI: P is a prime number between 1 and 4 inclusive
The best answer is D. Since P can be 2 and also 3, the answer cannot be determined. If P = 2, A = 4 and B = 4 but if P = 3, A = 9 and B = 6 and therefore the answer cannot be determined.
9. A: Y B: 5 AI: -5 < Y < 5
The best answer is B. The range of Y does not include 5 and therefore 5 is a number that is always greater than Y.
10. A: B B: 2 AI: A < B < C A, B and C are positive prime numbers. C = 3
The best answer is C. From the additional data we can conclude that A = 1, B = 2 and C = 3 and therefore both columns are equal.
11. A: The unit’s digit of X B: 3 AI: In a three digit positive integer X, the hundreds’ digit is four times the units’ digit.
The best answer is B. If the hundreds’ digit is four times the units’ digit, then the unit digit can be 2 or smaller (if its 3, than the hundreds’ digit is bigger than 9, which is not possible) and therefore column B must be greater.
12. A: The units’ digit B: 9 AI: In the three digits number Y, the units’ digit is two times greater than the tens’ digit and four times greater than the hundreds’ digit.
The best answer is B. Using the additional information, we have two options: 124 and 248, in both cases 9 is greater than the unit’s digit and so the answer is B.
13. A: The perimeter of a square with an area of 20 B: The perimeter of a square with side 4.5
The best answer is A. The question is about, which square has the largest side. The square of column A has a side of The square of column B has a side of 4.5 and so the area is
14. A: The area of a square with side 2 B: The area of a circle with a radius of 1.5
The best answer is B. The area of the square is 4, compare it with the area of the circle. The area of the circle is
15. A: X + Y B: 2Y AI: 1.5X = Z is negative
The best answer is B. Replace X and Y with Z. X = Z, Y = Column A is equal to Z +
16. A: Q + 2W – P B: 2P + 2Q AI: 0.5Q = 1.5W = 2P
The best answer is Replace Q and W with P. Q = 4P, W = 4P/3. Column A can be written as 4P + 8P/3 – P = P/3. Column B can be written as 2P + 8P = 10P, which is greater than column A.
17. A: The average (arithmetic mean) of the two numbers. B: 3 AI: The product of two integer numbers is 15.
The best answer is D. If the product of the two numbers is 15 then they can be 15 and 1 or 3 and 5, the average of both pairs is bigger than 3 and so it seems like the answer is A. Don’t be mistaken, you were not told that the numbers were positive and so they can also be -5 and -3, with an average smaller than 3.
18. A: The average (arithmetic mean) of the two numbers. B: AI: The product of two positive numbers is 10
The best answer is D. The product of the two numbers is 10 and so they can be 2 and 5, 1 and 10 and even
19. A: The average (arithmetic mean) of the three numbers. B: 5 AI: The product of three integer positive numbers is 12.
The best answer is B. There are many combinations of numbers which their product is 12: (1, 1, 12), (3, 4, 1), and (6, 2, 1). The average of all three combinations is smaller than 5.
20. A: The remainder is when n + 2 is divided by 8 B: 7 AI: The remainder when n-1 is divided by 10 is 0, and the remainder when n+1 is divided by 18 is 4.
The best answer is C. Using the additional data we can conclude that n is equal to 21. According to column A, the remainder is (23/8 = 7), which is equal to column B.
21. A: The remainder is when n - 3 is divided by 6 B: 4 AI: The remainder when n+1 is divided by 9 is 5, and the remainder when n-1 is divided by 5 is 2.
The best answer is C. Using the additional data we can conclude that n is equal to 13. According to column A, the remainder is (10/6 = 4), which is equal to column B.
22. A: The remainder is when n + 7 is divided by 17 B: 9 AI: The remainder when n+3 is divided by 9 is 4, and the remainder when n-1 is divided by 5 is 1.
The best answer is A. Using the additional data we can conclude that n is equal to 37 for example. According to column A, the remainder is (44/17 = 10), which is greater than column B.
23. A: X B: 4 AI: The average (arithmetic mean) grade point average of X students is 86. The average of these X students together with a score of 92 is 88.
The best answer is B. Let’s write the average of the X students with the extra grade:
24. A: Y B: 3 AI: The average (arithmetic mean) age of Y family members is 20. When a new baby was born (assume that his age is 0), the new average Was 15.
The best answer is C. Use the average formula:
25. A: 126 + 127 B:
The best answer is C. Remember, compare don’t calculate. A can be written as 126 + 12 x 126 = 13 x 126, which is equal to column B.
26. A: 87 x 43 B: 412
The best answer is A. A can be written as 23x7 x 22x3 = 227. B can be written as 22x12 = 224, which is smaller than column A.
A: AB B: BO AI: O is the centre of the circle
The best answer is A. Don’t let the proportions of the drawing fool you. Since O is the centre of the circle, both triangles are isosceles and so the angle which is closer to the origin is (180 – 45 – 45 = 90). AB is the side that is in front of the 90 degree angle and so it’s the hypotenuse.
28. A: The original number of Girls in the playground B: 16 AI: After 5 girls leave the playground; there are three times as many boys than girls. After 25 more boys leave the playground, there are twice as many girls than boys.
The best answer is B. Let G be the number of girls and B the number of boys. We can write the following equations: 3(G – 5) = B and 2(B – 25) = G – 5. From these two equations, we can find that G = 15 and so the answer is B.
29. A: The original number of cats in the yard B: The original number of dogs in the yard AI: After 7 dogs leave the yard, there are two times as many cats than dogs. After a further 16 cats leave the yard, there are two and a half as many dogs as cats.
The best answer is A. Let D be the number of dogs in the yard and C the number of cats. We can write the following equations: 2(D – 7) = C and (D – 7) = 2.5(C – 16) Solving these equations, D = 17 and C = 20. And therefore the answer is A.
30. A: The number of yellow papers in the pile B: 120 AI: There are at least 120 blue papers in the piles of papers. The ratio between the number of blue papers to yellow papers is 7 to 6.
The best answer is D. There could be 120 blue papers in the pile and there could also be 500 for example. If there are 120 there’ll be less than 120 yellow papers but if there’ll be 500 for example, there’ll be more than 120 and therefore more sufficient data is required to answer the question.
31. A: The number of cookies in the jar B: 45 AI: There are at least 45 doughnuts in the jar. The ratio between the number of cookies to the number of doughnuts in the jar is 12 to 13.
The best answer is A. The number of doughnuts is more than 45 and using the ratio, the number of cookies is larger than the number of doughnuts and therefore the answer must be A.
32. A: The number of crystal glasses in the kitchen cupboard B: The number of ceramic glasses in the kitchen cupboard AI: There are at least 70 crystal glasses and no more than 70 ceramic glasses in the kitchen cupboard
The best answer is D. The number of crystal glasses is 70 and up and the number of ceramic glasses is 70 and down. There could be 70 of each, which will make C the answer and there could be 50 ceramic and 80 crystal for example and then the answer would be A. Since the answer is not distinct, more data is required.
33. A: The measurement of the angle BAC B: The measurement of the angle ACB
The best answer is D. We are not given any data on the triangle and therefore we cannot determine the size of any angle.
34. A: The measurement of the following angles: BAC and ACB B: 90 degrees AI: The triangle is an isosceles
The best answer is D. Again, the only information is that the triangle is an isosceles, which is insufficient in this case. The measurement of ABC is not necessarily 90 degrees and therefore we cannot determine if BAC + ACB are larger or smaller than 90 degrees.
35. A: The measurement of BAC B: 90 degrees. AI: ABC is a right triangle, where the measurement of ABC is 90 degrees.
The best answer is B. Since the triangle is a right one, the sum of the other two angles sums up to 90 degrees and therefore BAC cannot be 90 degrees by itself.
36. A: -0.00506 B: -0.00605
The best answer is A. In negative numbers, the smaller the number is in absolute value, the larger it is. The absolute value of A is smaller than that of B and therefore it is larger.
37. A: -0.0033 B: -0.000333
The best answer is B. In negative numbers, the smaller the number is in absolute value, the larger it is. The absolute value of B is smaller than that of B since it is closer to zero and therefore it is larger.
38. A: X B: Y AI: -X - Y = 156 X = 2Y
The best answer is B. Replace X with 2Y in the first equation to get: -2Y – Y =156 è Y = -52 And so X = -104. We can see that Y is larger.
39. A: W2 + Y2 B: Q2 + R2 AI: W is positive, Y is negative, Q is positive and R is negative. Y > R > W > Q
The best answer D. Pay no attention to the first line of the extra data since all the variables have a positive power. Take two sets of numbers: Y, R, W and Q = 4, 3, 2 and 1 respectively, in this case, A = 20 and B = 10. Take Y, R, W and Q = -1, -2, -3 and -4 respectively. In this case A = 10 and B = 20 and therefore the answer is not distinct and cannot be determined.
40. A: B:
The best answer B. Simplify each of the statements to the following: A =
1. A: (X + Y)2 B: 2XY
The best answer is D. Open the expression in column A to X2 + 2XY + Y2, now subtract 2XY from both sides and so we compare X2 + Y2 with 0. In all cases except for one (where X and Y are zero) A would be greater than B and so the answer cannot be determined.
2. A: (X + Y)(X – 2Y) B: XY + 8
The best answer is D. Open the parenthesis in column A: X2 – 2XY +YX – 2Y2 = X2 – XY – 2Y2. Subtract XY – 8 from both sides to get: A = X2 – 2XY – 2Y2 – 8 and B = 0. We don’t know anything about X and Y and so the answer cannot be determined properly.
3. A: Y B: 5 AI: In the two digits number XY, the value of the digit X is twice the value of the digit Y.
The best answer is B. There are few possibilities for the number XY: 21, 42, 63 and 84. As you can see, the largest value that Y can be is 4 and therefore 5 is always greater.
4. A: Y B: 4 AI: In the two digits number XY, the value of the digit X is the square root of the digit Y. Y < 5
The best answer is D. There are the following options for the double digit XY: 11 and 24. Since in the first case the answer is B and in the other its C, the final answer should be D.
5.
A: The area of the circle B: AI: The area of the section ABC is The measurement of the angle ABC is 24 degrees.
The best answer is C. Since the measurement of the angle ABC is 24 degrees, there are (360/24 = 15) equivalent sections in the circle and therefore the area of the circle is
6. A: The number of pencils that David bought B: AI: William bought X yellow colored pencils and Y red ones. David bought 15 pencils fewer than two third of the total number of Pencils that William bought.
The best answer is C. Translate the phrase into variables: The number of pencils that David bought is equal to:
7. A: B: The amount of cloths that Tamara bought. AI: Tammy bought S skirts and Q shirts. Tamara bought 12 cloths more than four thirds of the amount Tammy bought. The best answer is B. Translate the phrase into variables. Tamara bought
8. A: Y B: 3 AI:
The best answer is C. The expression given can be simplified to: It turns out that Y = 3 and therefore the answer is C.
9. A: X B: 37 AI:
The best answer is A. Simplify the expression, multiply by 24X to get: -96 + 3X = 16 à X = 37 10. A: The length of side BC B: 14 AI: The perimeter of an isosceles ABC is 36 and the length of side AB is 10.
The best answer is B. There are two options to build the triangle: 10, 10 and 16 or 10, 13 and 13. In either case, 14 is bigger than any of the sides and therefore B is the answer.
11. A: 0 B: The value of Y when X = 4 AI: X = (Y + 2)2
The best answer is C. First, do the obvious and replace X with 4, the expression becomes: 4=(Y+2)2. 2 = Y + 2 à Y = 0.
12. A: The value of X when Y = 7 B: 9.5 AI: X =
The best answer is B. Replace Y with 7 to get: X =
13. A: The time it took car A to travel from point A to point B B: The time it took car B to travel from point A to point B AI: The average speed of car A is 30 miles per hour and the average speed of car B is 25 percent faster. Car A left 12 minutes after car B.
The best answer is A. Don’t be mistaken, some of the given data is irrelevant since it has no correlation with the question. The information given to you on the time of departure should not be used; you are interested in the time between the points. Car A is slower and therefore it would take her more time to get from point A to point B.
14. A: The number of meters traveled by a beetle that traveled for four hours at an average speed of 1.5 meters per minute B: The number of meters traveled by a turtle that traveled for two minutes at an average speed of 2.5 meters per minute
The best answer is A. Use the distance formula; Distance = speed x time. The distance of the beetle is equal to 4 x 1.5 = 6 and the distance of the turtle is 2 x 2.5 = 5 and therefore the answer is A.
15. A: The weight of one ton of feathers B: The weight of one ton of lead
The best answer is C. This question is a little tricky since reading it draws a picture in our head of a stack of feathers verses a stack of lead. Both columns claim the weight of each of the components and therefore the answer is C.
16. A: The number of eggplants in a bag that weighs 4 pounds B: The number of strawberries in a bag that weighs 3 pounds
The best answer is D. You cannot assume that an eggplant weighs more than a strawberry since that information was not given to you in the question. These kinds of questions give us a misleading picture in our head which should be neglected.
17. A: The number of packages that can be made from a pile of 135 pencils B: 12 AI: Each package contains a dozen pencils
The best answer is B. If each package contains a dozen pencils (meaning 12 pencils), than by dividing 135 by 12 we’ll get the number of whole packages that can be made. (135/12 = 11 with a remainder of 3) and therefore 11 packages can be made.
A: The distance from P to Q B: 22 AI: A + 2B = 18
The best answer is B. The distance from P to Q is equal to A + B. We know that A and B are both positive from the drawing and that A + 2B is smaller than 22 and therefore A + B must also me smaller than 22.
A: 14 B: The distance from P to Q back and forth AI: 3A + 3B = 21
The best answer is C. The distance from P to Q is A + B, which is equal to 7 and therefore the distance back and forth is twice 7, thus 14.
20. A: A – B B: B – A AI: A < B
The best answer is B. Pick up numbers, say A=1 and B=2: Column A= -1 and column B=1. Just to be sure pick up negative numbers also, A=-2 and B=-1: column A=-1 and column B=1 and therefore B is the answer.
21. A: X – Y B: Y – X AI:
The best answer is D. For any combination except X=0 and Y=0, the answer would be B yet this combination is valid and so D is the proper answer in this one.
A: The measurement of angle A B: The measurement of angle B AI: The intersection of the two lines is not in the centre of the circle
The best answer is C. When two lines are crossed two identical angles are formed- vertical angles. These angles are equal incoherently to where the intersection is and therefore the answer is C.
23.
A: X B: Y AI: The sum of the variables in the first diagonal equal to those in the second diagonal
The best answer is A. We can write that: ¼ + X = Y + 3/5 à X – Y = 3/5 – ¼ = 7/20, which is positive and therefore X is larger than Y.
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è And so column B is greater.
. We can see that all the variables in column B are greater than those in column A and therefore the answer is B.
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, and therefore column B is greater.
and B can be written as 
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and therefore its perimeter is also greater.
, which is equal to approximately 
and therefore column B is greater.
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and column B is equal to 
, which is greater and so B is the answer.
and 
è 86X + 92 = 88X + 88 è 2X = 4 è X = 2.
è 20Y = 15Y + 15 è Y = 3.
27.
The following questions refer to the figure below (33 – 35):
and B = 
. And therefore the answer is B.
, which can also be written as 
, which can also be written as 
. This expression is definitely greater than that in column A.
è Divide by common variables.
.
, which is between 9 and 9.5 and therefore the answer is B.
18.
22.
