HSPT Quantitative Question of the Day

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

Explanation: When comparing numerical expressions, you need to calculate each quantity first, then determine their relationship. Let's evaluate both expressions step by step. For quantity (a): $5^2 - 4^2 = 25 - 16 = 9$. For quantity (b): $3^2 = 9$. Since both quantities equal 9, they are equal to each other. Now let's examine why each answer choice is correct or incorrect. Choice A claims that (a) is greater than (b), but since $9 = 9$, this is false. Choice B states that (b) is greater than (a), which is also false for the same reason. Choice C correctly identifies that (a) and (b) are equal, since both expressions equal 9. Choice D suggests the relationship cannot be determined, but since we can calculate definite values for both expressions, we can definitely determine their relationship. You might also recognize a shortcut here using the difference of squares formula: $5^2 - 4^2 = (5+4)(5-4) = 9 \times 1 = 9$. This confirms our answer without having to calculate $25 - 16$ separately. Study tip: On HSPT quantitative questions, always calculate the actual values when comparing expressions with exponents. Don't try to guess based on the numbers you see - small differences in bases or exponents can dramatically change the results. Also, watch for opportunities to use algebraic shortcuts like the difference of squares formula to save time.