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Welcome to Math Planet Algebra Review Test.  This test is composed of only twelve problems that test your skills of algebra.  You can take this test at any pace you like to.  There is no time limit on this tests.   The result of this test doesn't mean anything.  It is merely for practice and evaluating purposes only.

1. 1729 is the smallest positive integer that is the sum of two different pairs of cubes:
12³ + 1³ and 10³ + 9³. What is the smallest positive integer that is the sum of two different pairs of squares?

1. 2.  A boy and a girl are walking toward each other, boy with the speed of 4 mph and girl with the speed of 3 mph. At one point in time the distance between them is 1 mile. At that time a dog leaves the boy and starts running toward the girl with the speed of 7 mph. As soon as the dog meets the girl, it turns around and runs toward the boy. The dog runs between them in this manner until the boy and the girl meet. What distance has the dog run by the time they all meet?
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3. 3.  A train is ¹/₂ mile long, and is moving with a speed of 45 mph. How long will it take the train to go through a mile-long tunnel?
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5. 4.  Six-digit number is such that its first and fourth, second and fifth, third and sixth digits are the same. Is this number divisible by 7? by 11? by 13?
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7. 5. Which one is bigger: 10²⁰ or 20¹⁰?
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9. 6.  Old man left 19 horses to his sons. According to the will, the oldest son was to receive ¹/₂ of all horses, middle son was to get ¹/₄, and youngest son ¹/₅ of all horses. When the old man died, his three sons could not divide the horses between themselves, so they asked a wise man, who was riding by on his own horse, for an advice. The wise man added his horse to the 19 left by the old man, then gave ¹/₂ (10 horses) to the oldest son, 5 horses to the middle son, 4 horses to the youngest son, and then walked away with his own horse. Did somebody make a mistake?
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11. 7. A and B are located along the river. Two men left A at the same time: one walked along the river, the other one took a boat and rowed up the river. The speed of the boat in the still water is the same as the speed of the walking man. As soon as each man reaches B he turns around and goes back to A. Who will reach A first?
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13. 8. I was n years old in the year N²," said Smith in 1971. When was he born?
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15. 9.  All sides (100 inches long each) of an equlateral triangle are divided into 5 equal parts, and lines that are parallel to the sides, are drawn through the dividing points. In essense, the triangle is divided into smaller similar triangles. If you imagine that all lines are made of one piece of wire, how long will that wire be if you bend it back into a straight line?
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17. 10.  Is it possible to measure 4 gallons of water, if you have only 3 and 5 gallon jugs, and an unlimited supply of water?
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19. 11.  What is the next number in the following sequence:

    1, 3, 7, 12, 18, 26, 35, 45, 56, ...

    • 12. The sum of several consecutive odd integers equals 333. What's the 5th number in the series?

Now you have done the test.  Please click "Preceding Page" at below to see the answers.

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