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Number System

Which of these numbers is irrational?
All natural numbers together with 0 form which set of numbers?
P and Q are positive integers such that PQ = 90. Which of these values can NOT be P + Q?
P and Q are positive integers such that PQ = 48. Which of these values can NOT be P + Q?
P and Q are positive integers such that PQ = 96. Which of these values can NOT be P + Q?
P and Q are positive integers such that PQ = 120. Which of these values can NOT be P + Q?
P and Q are positive integers such that PQ = 72. Which of these values can NOT be P + Q?
P and Q are positive integers such that PQ = 84. Which of these values can NOT be P + Q?
In how many distinct ways can 19 be expressed as the sum of two different positive integers?
In how many distinct ways can 13 be expressed as the sum of two different positive integers?
In how many distinct ways can 16 be expressed as the sum of two different positive integers?
In how many distinct ways can 18 be expressed as the sum of two different positive integers?
In how many distinct ways can 22 be expressed as the sum of two different positive integers?
In how many distinct ways can 11 be expressed as the sum of two different positive integers?
What number, when multiplied by 16, gives the same product as 120 multiplied by 252?
What number, when multiplied by 16, gives the same product as 83 multiplied by 304?
What number, when multiplied by 18, gives the same product as 294 multiplied by 339?
What number, when multiplied by 24, gives the same product as 144 multiplied by 279?
What number, when multiplied by 48, gives the same product as 92 multiplied by 276?
What number, when multiplied by 36, gives the same product as 154 multiplied by 252?
What number, when multiplied by 24, gives the same product as 356 multiplied by 234?
What number, when multiplied by 32, gives the same product as 205 multiplied by 352?
If a + b + c = 6 and ab + bc + ca = 5, what is the value of a³ + b³ + c³ – 3abc?
If a + b + c = 8 and ab + bc + ca = 20, what is the value of a³ + b³ + c³ – 3abc?
If a + b + c = 15 and ab + bc + ca = 21, what is the value of a³ + b³ + c³ – 3abc?

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