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Number System

Number System: Formulas, Shortcuts and Solved Examples

The number system is the map of every kind of number you will meet. This lesson…
If x + y + z = 20 and both y and z are positive integers greater than zero, what is the maximum value x can take?
If x + y + z = 12 and both y and z are positive integers greater than zero, what is the maximum value x can take?
Consider this data-sufficiency question: what is the two-digit number? Statement I: the sum of its digits is 11. Statement II: the difference between its digits is 3. Which of these is correct?
If (a² – b²) ÷ (a + b) = 13, what is the value of (a – b)?
If (a² – b²) ÷ (a + b) = 9, what is the value of (a – b)?
Which of these correctly orders the Roman numerals from greatest to least, : C, D, L, and M?
A number is divisible by 6 exactly when which condition holds?
A number is divisible by 3 exactly when which condition holds?
A number is divisible by 4 exactly when which condition holds?
A number is divisible by 8 exactly when which condition holds?
A number is divisible by 11 exactly when which of these conditions holds?
If ab = 0 for two numbers a and b, what can be concluded?
If x and y are both negative numbers, which of these statements is always true?
If n is a negative number, which of these is the least (smallest) value?
For an integer n, if n³ is odd, which of these statements is true?
If y is an even integer, which of these expressions must be odd?
If x is an odd integer, which of these expressions must be even?
Which of these is always odd?
If m and n are both odd numbers, which of these expressions is always even?
If w, x, y, and z are the digits of a 4-digit number written left to right, the number’s value is expressed as what?
If p, q, and r are the digits of a 3-digit number written left to right, the number’s value is expressed as what?
The number π (pi) is best classified as which of these?
Which of these statements about number classification is NOT correct?
Every rational number is also which of these?

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