HSPT Quantitative Question of the Day

1. (A) is greater than (B) (correct answer)
2. (B) is greater than (A)
3. (A) and (B) are equal
4. The relationship cannot be determined

Explanation: When comparing expressions with exponents and division, you need to evaluate each expression step by step, being careful to apply the order of operations correctly. Let's calculate expression (A): $3^4 \div 9$. First, evaluate the exponent: $3^4 = 3 \times 3 \times 3 \times 3 = 81$. Then divide: $81 \div 9 = 9$. Now for expression (B): $2^6 \div 8$. Calculate the exponent: $2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$. Then divide: $64 \div 8 = 8$. Since 9 > 8, expression (A) is greater than expression (B). Choice A is correct because our calculations show that 9 > 8. Choice B is wrong because it claims the opposite relationship. Choice C incorrectly states the values are equal when 9 ≠ 8. Choice D suggests we can't determine the relationship, but since both expressions contain only constants (no variables), we can always calculate exact values and make the comparison. Study tip: When comparing numerical expressions, always evaluate completely rather than trying shortcuts. Calculate each expression to its final numerical value first, then compare. Also, remember that expressions with larger bases or exponents don't automatically yield larger results—the division or other operations can change the final comparison, so you must work through each step methodically.