РЕГИОНЫ РОССИЙСКОЙ ФЕДЕРАЦИИ 6 страницаB: 376.5
The best answer is B. Since 375 appears twice, set it as the estimated average. There are two additional numbers: 372 and 378, both have the same deviation from the average in different directions and so the average stays as it is on 375. Column B is greater.
13. A: X B: 4 AI: The average (arithmetic mean) of 10, 24, 25, 30 and X is 15.
The best answer is B. Use the average formula:
14. A: The average height of the remaining 14 buildings B: 36 meters AI: The average height of 15 buildings is 35 meters. One of the buildings, that his height is
The best answer is C. The height of the building that fell is The difference from the average is (35 – 21 = 14) and so the entire average changed by 14/14 = 1 meters up. The new average is 36 meters and so the columns are equal.
15. A: 80 B: The average height of the entire 5 buildings AI: The average height of 3 sky scrapers is 70 meters. The average height of 2 more is 90 meters.
The best answer is A. Calculate the average:
Combinations and Probability
16. A: The number of combinations of arranging 5 people in a row B: The number of combinations of choosing 2 people out of a group of twelve with out referring to order
The best answer is A. Column A = in the first place there are 5 options, in the second there are 4 left and so on. All together, there are 5 x 4 x 3 x 2 x 1 = 120 combinations. Column B = the first is out of 12 and the second pick is out of 11 but the order doesn’t matter and therefore there are 17. A: The probability of picking a red ball and a blue one right after it B: The probability of picking two consecutive blue balls AI: A bucket contains X blue balls and X red ones
The best answer is A. The first pick in both columns is identical in terms of probability. The second pick is the interesting one. Column A: the probability of picking a blue after red is Column B: the probability of picking a blue after blue is The denominator is the same in both yet the numerator in A is greater and so is the column.
18. A: The probability of receiving a sum of 6 with two tosses of fair dices B: The probability of receiving a result of 6 with one dice
The best answer is B. Column A: There are 36 options using two dices, 5 of them will result in the sum of 6: 3-3, 2-4, 4-2, 5-1 and 1-5 and therefore the probability is 5/36. Column B: The probability of receiving 6 is 1/6. 1/6 > 5/36 and so column B is greater.
19. A: The number of three digits numbers that none of the digits repeats itself B: 720
The best answer is B. The first digit can’t be 0 and so there are 9 possibilities. The second digit can be anything but the first, thus 9 possibilities. The third has only 8 left. The number of combinations is 9 x 9 x 8 = 648 and therefore column B is greater. 20. A: The probability of receiving a sum of 10 B: The probability of receiving a sum of 8 AI: Jeremy tosses a dice twice with the following numbers on it: 1, 3, 5, 7, 9 and 11.
The best answer is A. There are 36 results in total (6 x 6). Column A: there are 5 results with a sum of 10: 3-7, 7-3, 5-5, 9-1, 1-9 and so the probability here is 5/36. Column B: there are 4 results with a sum of 8: 1-7, 7-1, 5-3, 3-5 and so the probability here is 4/36, which is smaller. Column A is greater.
21. A: The probability of receiving a sum of 10 B: The probability of receiving a sum of 12 AI: Jeremy tosses a dice twice with the following numbers on it: 1, 2, 4, 6, 8 and 10.
The best answer is B. There are 36 results in total (6 x 6). Column A: there are 4 results with a sum of 10: 4-6, 6-4, 2-8, 8-2. and so the probability here is 4/36. Column B: there are 5 results with a sum of 8: 4-8, 8-4, 6-6, 10-2, 2-10 and so the probability here is 5/36, which is greater. Column B is greater.
22. A: The probability of receiving “heads” at least once B: 5/8 AI: A fair coin is tossed three times
The best answer is A. The probability of receiving “heads” at least once is equal to one minus the probability of not receiving “heads” at all. The required probability is 1 - (0.5 x 0.5 x 0.5) = 7/8. Column A is greater than column B.
23. A: The probability of picking two balls with the same color out of the box one after the other B: ½ AI: A box contains: 3 red balls, 2 blue balls and 4 yellow ones.
The best answer is B. Column A: There are three options: 1. The probability of two red balls: 2. The probability of two blue balls: 3. The probability of two yellow balls: The total probability in column A = Column B is greater than column A.
24. A: The number of possibilities of choosing 11 soccer players from the bench B: 72 AI: There are 13 players on the bench
The best answer is A. This probability is equal to the probability of choosing two players that wouldn’t play. The first player has 13 possibilities and the second has 12, pay attention that the order doesn’t count and therefore there are
25. A: The number of possibilities of choosing 5 basketball players from the bench B: 21 AI: There are 7 players on the bench
The best answer is A. This probability is equal to the probability of choosing two players that wouldn’t play. The first player has 7 possibilities and the second has 6, pay attention that the order doesn’t count and therefore there are
26. A: The probability that Clark will get “heads” twice B: The probability that Louis will get “tails” twice AI: Louis and Clark, each, toss a fair coin twice.
The best answer is C. Column A = 0.5 x 0.5 = 0.25. Column B = 0.5 x 0.5 = 0.25. The columns are equal and therefore the answer is C.
27. A: The probability of failing the test three consecutive times B: The probability of passing the test once out of three times AI: The ratio between passing the test and failing it is 1:3.
The best answer is B. Translate the ratio to probability terms. The probability of passing is ¼ and failing to fail ¾. Column A = (3/4)3 = 27/64. Column B = one minus the probability of failing the test three times = 1 – 27/64 = 37/64, which is greater.
28. A: The probability that 4X is even B: ½ AI: X is a positive integer
The best answer is A. Since X is a positive integer, 2X will always be even no matter if X is even or odd. The probability in column A is 1.
29. A: The probability of receiving a sum of 7 tossing two fair dices B: The probability of receiving a sum of 8 tossing two fair dices
The best answer is B. There are 36 possibilities in total (6 x 6). There are 6 cases in which the sum is 7: 3-4, 4-3, 2-5, 5-2, 1-6, 6-1 and therefore the probability in column A = 6/36 = 1/6. There are 7 cases in which the sum is 8: 1-7, 7-1, 6-2, 2-6, 3-5, 5-3, 4-4 and therefore the probability in column B = 7/36, which is greater than column A.
30. A: The probability that the arrow will miss the target twice and will hit on the third time B: The probability that the arrow will hit the target twice and will miss once AI: The probability of hitting a target with an arrow is 0.6
The best answer is B. The probability of hitting is 0.6 and therefore the probability of missing is (1 – 0.6 = 0.4). The probability in column A = (0.4)(0.4)(0.6) = 0.096. The probability in column B = (0.6)(0.6)(0.4) = 0.144, which is greater than column A and therefore the answer is B.
1. A: The time it would take Ronnie to built 2 doghouses B: The time it would take Bonnie to built 1 doghouse AI: The output of Ronnie is twice the output of Bonnie building Doghouses
The best answer is C. Since the output of Ronnie is twice the output of Bonnie, it takes Ronnie X hours to build a doghouse while it takes Bonnie 2X. Column A = 2X. Column B = 2X. The columns are equal and the answer is C.
2. A: The time it would take Biff to eat 4 ice-creams B: The time it would take George to eat 6 ice-creams AI: Biff can eat 1 ice-cream in the same time that George can 2 ice-creams
The best answer is A. Let’s say it takes Biff X minutes to eat one ice-cream. It takes George X/2 to eat one ice-cream. Column A = 4X. Column B = 3X. Column A takes more time and therefore it’s greater.
3. A: 1 B: The time it would take 17 dogs to bury 17 bones AI: 5 dogs bury 15 bones in 3 hours
The best answer is C.
Time = 1 x 1 = 1 and therefore the columns are equal.
4. A: The number of liters that 7 sprinklers can sprinkle in one hour B: 100 AI: 6 sprinklers can sprinkle 3 liters in 2 minute
The best answer is A.
è Liters = Column A is greater than column B.
5. A: The number of liters that 5 cows can give during half an hour B: The number of liters that 6 cows can give during 20 minutes AI: 3 cows can give 7 liters of milk in one hour
The best answer is A.
Column A: Column B:
6. A: The amount of water in the pool after two hours B: The amount of water in the pool after three hours AI: Pipe A can fill a pool in 4 hours. Pipe B can fill a pool in 6 hours. Pump C can empty a pool in 3 hours. In the morning the pool is half full.
The best answer is B. The output of pipe A is ¼, the output of pipe B is 1/6 and the output of pump C is -1/3. Together, the output is (1/4 + 1/6 – 1/3 = 1/12). Since the entire output is positive the pool will be filled as the time progresses and therefore after 3 hours there’ll be more water in the pool.
7. A: The amount of garbage in the tanker at 12:15 B: The amount of garbage in the tanker at 9:40 AI: A garbage tanker is filled every 30 minutes with 25 Kg of garbage. The tanker is emptied completely every round hour. The whole process starts at 8:00 O’clock.
The best answer is Column A: The garbage tanker is emptied every round hour and therefore at 12:00 it was emptied. At 12:15 it hasn’t been filled yet and so it contains nothing. Column B: The tank was emptied at 9:00 but it was filled at 9:30 and therefore at this hour it contains 25 Kg of garbage, this column is greater.
8. A: The amount of fruit that the orange tree yields during 4 months B: The amount of fruit that the apple tree yields during 8 months AI: The amount of fruits that the apple tree yields every month is by 50% smaller than the amount of fruits that the orange tree yields in a month.
The best answer is C. Let’s say that the apple tree yields X apples in one month è the orange tree yields 2X. Column A = 8X. Column B = 8X and therefore the columns are equal to one another.
9. A: The number of books that Ryan writes during 3 years B: The number of books that Brian writes during 6 years AI: The number of books that Ryan writes each year is by 50% larger than the number of books that Brian writes each year
The best answer is B. Let’s say that Ryan writes X books in one year è Brian writes 1.5X books. Column A = 3X Column B = 6 x 1.5X = 9X and therefore this column is greater.
10. A: The time it would take X and Y to bake 72 cakes B: 3 hours AI: X can bake 6 cakes in one hour. Y can bake 12 cakes in one hour.
The best answer is A. Together, X and Y can bake (6+12 = 18) cakes in one hour. 72 cakes would take (72/18 = 4) hours to bake and therefore column A is greater than column B.
11. A: The time it would take 39 monkeys to eat 63 bananas B: 2.25 hours AI: 13 monkeys eat 7 bananas in 45 minutes
The best answer is C.
135 minutes = two hours and 15 minutes = 2.25 hours and therefore the columns are equal.
12. A: The number of donuts that the officer will eat in 8 hours B: 90 AI: An officer eats 5 donuts during half an hour
The best answer is B.
Column B is greater.
Movement comparison Q.
13. A: 20 meters per second B: 72 Kilometers per hour
The best answer is C. In one kilometer there are 1000 meters and in one hour there are 3600 seconds. One meter per second is equal to 3.6 kilometers per hour. Column A = 20 meters per hour = (20 x 3.6 = 72 kilometers per hour) and therefore both columns are equal.
14. A: 2500 millimeters B: 2.5 meters
The best answer is C. One meter is equal to 100 centimeters. One centimeter is equal to 10 millimeters. 2.5 meters is equal to 2.5 x 1000 = 2500 millimeters and therefore the columns are equal.
15. A: Terry’s speed B: Tania’s speed AI: Terry can walk X miles in Y/3 hours. Tania can walk 2.5X miles in 2Y/5 hours.
The best answer is B. Speed = Distance / Time Column A = X / (Y/3) = 3X/Y. Column B = 2.5X / (2Y/5) = 6.25X/Y. Since X and Y are positive, column B is greater than column A.
16. A: Ruth’s speed B: William’s speed AI: Ruth can swim Q pools in P/4 hours. Tania can swim 1.5Q pools in P/3 hours.
The best answer is B. Speed = Distance / Time Column A = Q / (P/4) = 4X/Y. Column B = 1.5Q / (P/3) = 4.5X/Y. Since Q and P are positive, column B is greater than column A.
17. A: Phil’s driving time from A to B B: Phil’s driving time from B to C AI: Phil drives from A to B at 45 miles per hour and from B to C at 90 miles per hour. The distance from A to B is 3 miles and from B to C is 6 miles.
The best answer is C. Time = Distance / speed Column A: Time = 3/45 = 1/15. Column B: Time = 6/90 = 1/15 and therefore the columns are equal.
18. A: The current’s speed B: The boat’s speed AI: A boat sails with the current of the river for half an hour and travels a Distance of 6 Km. The boat U-turns and travels against the current for Half an hour crossing 2 Km
The best answer is B. Remember, compare don’t calculate. After the boat turned around, it managed to cross 2 Km, which means that her speed is faster than the currents’ speed and therefore column B is greater than column A.
19. A: The fox’s speed [in miles per hour] B: 15 AI: A fox travels during an hour and a half the same distance that he would have traveled in an hour if he’s speed would be 10 miles per hour higher
The best answer is A. Mark X as the fox’s speed. The distances are equal and so we’ll compare them: 1.5X = 1(X + 10) èX = 20 and therefore column B is greater.
20. A: 155 meters per second B: The cruise missile’s velocity AI: A cruise missile is shot from a distance of 7.5 Km and hits its target After one minute.
The best answer is A. Calculate the missile’s speed. Speed = Distance / Time. Speed = (7500 meters) / (60 seconds) = 125 meters per second. Column A is greater than column B.
21. A: The distance that flipper will travel during 5 seconds B: 100 meters AI: Flipper the dolphin swims at a speed of 72 kilometers per hour
The best answer is C. Distance = Speed x Time. Flipper traveled (5 seconds) x (72 Km per hour). One kilometer is 1000 and one hour is 3600 seconds and therefore one meter per second is equal to 3.6 Km per hour. 72 Km per hour = 20 meters per second. Flipper traveled (5)(20) = 100 meters and so the columns are equal.
22. A: The time it would take the turtle to travel 2.5 Km B: 25 hours AI: A turtle walks at a speed of The best answer is A. It takes the turtle (300/60 = 5) minutes to walk His speed is 1/6 meters per minute = 10 meters per hour. 2.5 Km = 2500 meters. The time it would take him to walk that distance is (2500)/(10) = 250 hours. Column A is ten times bigger than column B.
23. A: The average (arithmetic mean) speed of the cheetah during these 8 hours B: 75.7 miles per hour AI: A cheetah runs for 5 hours at a speed of 70 miles per hour and three Hours at an average speed of 90 miles per hour
The best answer is A. Use the simple average formula:
Kinky mixed questions
24. A: 120 degrees B: The measurement of the smaller angle between the clock’s hands at 16:40
The best answer is A. Draw the clock with the relevant time. We can see that the angle is less than 120 degrees because the hour hand is not on 4, it moves a little clockwise. Column A is greater.
25. A: 90 degrees B: The measurement of the smaller angle between the clock’s hands at 12:15
The best answer is A. Draw the clock with the relevant time. We can see that the angle is less than 90 degrees because the hour hand is not on 12, it moves a little clockwise. Column A is greater.
26. A: 120 degrees B: The measurement of the larger angle between the clock’s hands at 12:45
The best answer is B. Draw the clock with the relevant time. We can see that the small angle is less than 120 degrees and more than 90 degrees because the hour hand is not on 12, it moves a little clockwise. The largest angle completes the small angle to 360 degrees and therefore it is more than 120 degrees, thus column B is greater.
27. A: The number of dividers on the perimeter of the circle B: 28 AI: The perimeter of a circle was divided into 28 even arcs using dividers
The best answer is C. Since a circle is a closed shape the number of dividers is equal to the number of spaces. Try working with three spaces, draw a circle; you can see that there are three spacers and three dividers and so is the circle with the 28 spaces.
28. A: The number of poles B: 20 AI: A 20 meters fence is held up with poles located every meter
The best answer is A. Try working with a shorter fence so you can draw a sketch. Let’s try a fence 3 meters long.
As you can see, we used 4 poles for a 3 meters fence and therefore we’ll need 21 poles for the 20 meters fence.
29. A: The time it would take Rufus to drive 140 miles B: 3 hours AI: Rufus’s driving speed is between 40 and 70 miles per hour The best answer is D. If Rufus drives at 40 miles per hour, it would take him 3.5 hours to travel 140 Km and if he travels at 70 miles per hour it would take him 2 hours. Since 3 hours is in the range the answer cannot be determined and the answer is D.
30. A: The time it would take the concord airplane to fly 1000 Kilometers B: 2 hours AI: The concord’s airplane speed is between 200 and 400 meters per second
The best answer is B. If it flies 200 meters per second it would take him (1,000,000 meters)/(200) = 5000 seconds. There are 3600 seconds in one hour and therefore it would take him (5000) / (3600) = approximately 1.4 hours, which is smaller than column A. If it flies 400 meters per second it would take him even less time and so either case, it will pass 1000 Km in less than 2 hours.
31. A: 16 minutes B: The time it would take the gecko to get 7 meters AI: A gecko (house-lizard) travels 2 meters every 2 hours and every third hour, it travels one meter back
The best answer is B. Every three hours, the gecko travels 1 meter. It would take the gecko 15 hours to travel 5 meters and so after 17 hours it will travel 7 meters for the first time. Column B is greater (17 > 16).
32. A: The time it would take Johnny to write 29 pages for the first time B: 6 hours and 30 minutes AI: Johnny writes 5 pages during the first 30 minutes and on the next 30 minutes he throws one page out
The best answer is C. During one hour, Johnny writes 4 pages. After 6 hours, he will write 24 pages. On the next 30 minutes he will write 5 more pages, reaching 29 pages. It takes him 6.5 hours to complete this mission.
33. A: The minimum number of cards that are needed to be taken out of the box in order to get two cards with the same color B: The minimum number of cards that are needed to be taken out of the box in order to get two cards with different colors AI: A box of cards contains 2 blue cards and 2 red ones
The best answer is C. If you take 2 cards out of the box, you could have two options: Two cards in the same color or two cards in different colors but if you take one more card, you’ll have three cards that 2 out of them answer the criteria’s of both columns and therefore the answer is C.
34. A: The number of Jellybeans that Tim has B: 35 AI: Tim has between 6 and 7 boxes of Jellybeans. Each box contains between 5 and 8 Jellybeans.
The best answer is D. Find the range of Jellybeans that Tim has. The minimum number of Jellybeans is 30 and the maximum is 56. Since 35 are in the middle of the range, the answer cannot be determined properly and therefore D is the right answer.
35. A: The number of light bulbs in the shop B: 256 AI: There are between 12 and 18 cases of light bulbs in the shop, each case Contains between 24 and 28 light bulbs.
The best answer is A. Find the range of the number of light bulbs in the shop. The minimum number of bulbs is (12 x 24 = 288) and the maximum is (18 x 28 = 504), both are larger than 256 and therefore column A is always greater than column B.
36. A: The minimum number of balls that Sandra needs to pick in order to get a blue ball B: 15 AI: In a box, there are 5 blue balls, 6 red balls, 2 green balls, 4 black balls and 3 purple ones.
The best answer is A. Sandra, theoretically, can take 15 balls out and still not pick a blue ball since there are 15 balls in different colors. On the 16’Th ball she will surely pick a blue one and so column A (16) is greater than column B (15).
37. A: The number of parts that the yard was divided to B: 24 AI: A yard was divided into many parts by 4 lines lengthwise and 6 lines across
The best answer is A. If a section is divided by 4 lines, there will be 5 spaces and in the same way there will be (4 + 1)(6 + 1) = 35 parts in the yard and not 24. Column A is greater.
38. A: The number of rectangles after the division B: 64 AI: A large piece of plywood is divided into smaller rectangles using 8 lines across and 8 lines lengthwise
The best answer is A. If a section is divided by 2 lines, there will be 3 spaces, thus three parts and in the same way there will be (8 + 1)(8 + 1) = 81 rectangles out of the plywood, which is greater than 64 and so column A is greater.
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and therefore column B is greater.
of the average, fell down.
meters.
meters and so column A is greater.
combinations.
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combinations. Column A is greater than column B.
combinations. The columns are equal to one another.
liters.
è Liters = 
è Liters = 
and therefore column A is greater.
è Time = 
minutes.
è Donuts = 
= 80.
meters during 300 seconds
miles per hour.
