Flashcards

What are the two main categories of numbers in the real number system, and what distinguishes them?

How can you identify if a number is rational?

What is the defining characteristic of an irrational number?

What is the commutative property, and for which basic operations does it hold?

How does the associative property differ from the commutative property?

What is the identity element for addition and for multiplication?

What is the inverse element for a number under addition and under multiplication?

How does the distributive property combine multiplication and addition?

What is the closure property, and why is it fundamental?

How do the properties of real numbers apply when simplifying the expression 3(x + 4)?

What are the main classifications of numbers in the CAT number system?

How can you quickly test if a number is divisible by 7 using the given shortcut?

What is the relationship between factors and multiples in number theory?

How do you calculate the number of factors of a number given its prime factorization?

What is the key relationship between HCF and LCM for two numbers?

How does the remainder theorem help in solving division problems?

What is digit cyclicity and how is it useful in remainder problems?

How do you calculate the number of trailing zeroes in a factorial?

What is the base system in number theory and why is it important?

How does the Chinese Remainder Theorem help solve simultaneous congruence problems?

What are the most important algebraic identities in number theory context?

Which number system topics should be attempted first in CAT due to their quick solving nature?

What types of number system problems should be skipped or approached cautiously in CAT?

What is the recommended time allocation per number system question in CAT?

What are common traps to avoid in CAT number system questions?

What is the recommended practice approach for mastering number system concepts?

How can elimination techniques using units digits help solve CAT number problems?