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Question 1 |

**The sum of two positive integers is 13. The difference between these numbers is 7. What is their product?**

12 | |

22 | |

30 | |

40 |

Question 1 Explanation:

Use the given information to create a system of equations in two variables and then solve with the method of combination or substitution. Translating the problem statement into algebra:

x + y = 13

x − y = 7

The method of substitution can be used here. First solve for x in terms of y:

x = y + 7

Then substitute the right hand side for x in the other equation:

(y + 7) + y = 13

Now combine like terms and solve for y:

2y = 6, y = 3

Then substitute 3 for y in either equation and solve for x:

x + 3 = 13; x = 10.

However, you should notice that the method of combination reduces the number of steps necessary to solve the system. Add the 2 equations together and solve for x:

x + x = 13 + 7; 2x = 20; x = 10

The value of y can then be found. Once the variable values are found, their product can be computed:

x * y = 10 * 3 = 30

x + y = 13

x − y = 7

The method of substitution can be used here. First solve for x in terms of y:

x = y + 7

Then substitute the right hand side for x in the other equation:

(y + 7) + y = 13

Now combine like terms and solve for y:

2y = 6, y = 3

Then substitute 3 for y in either equation and solve for x:

x + 3 = 13; x = 10.

However, you should notice that the method of combination reduces the number of steps necessary to solve the system. Add the 2 equations together and solve for x:

x + x = 13 + 7; 2x = 20; x = 10

The value of y can then be found. Once the variable values are found, their product can be computed:

x * y = 10 * 3 = 30

Question 2 |

**The table above shows the mass, radius, axis period, radius of orbit, and period of revolution of the Sun and the planets in our solar system. Based on the table, if Earth, Mars, or Jupiter was chosen at random, what is the probability that the chosen planet’s mass would be greater than 10 x 10**

^{24}?13% | |

33% | |

66% | |

100% |

Question 2 Explanation:

First, analyze the table and note each planet’s mass:

Earth: 5.98 x 1024 kg

Mars: 6.37 x 1023 kg

Jupiter: 1.90 x 1027 kg

Only Jupiter is greater than 10 x 1024 kg. One out of the three planets is 33.33%.

Earth: 5.98 x 1024 kg

Mars: 6.37 x 1023 kg

Jupiter: 1.90 x 1027 kg

Only Jupiter is greater than 10 x 1024 kg. One out of the three planets is 33.33%.

Question 3 |

**In the given figure, the measure of angle OAC is 60 degrees, and the center of the circle is 0. If the circle has a radius of 6, what is the length of segment DB?**

3 | |

3√2 | |

6 | |

6√2 |

Question 3 Explanation:

Since O is the center, AO = DO = CO = BO = 6. This means we can divide these pieces into isosceles triangles. If triangle AOC is isosceles, and angle OAC = 60°, then angle ACO = 60°. This leaves 180 − 120 = 60 degrees for the third angle AOC. Triangle AOC = equilateral, and angle DOB is vertical with angle AOC and will also equal 60 degrees. Therefore, triangle DOB will also be equilateral, and the length of DB = 6, choice (C).

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