ISEE Upper Level Mathematics Achievement Question of the Day

1. $3$ (correct answer)
2. $-3$
3. $7$
4. $-7$

Explanation: When you encounter absolute value expressions, remember that absolute value represents distance from zero on the number line, so it's always non-negative. The key is to evaluate what's inside each set of absolute value bars first, then apply the absolute value operation. Let's work through this step by step. For the first expression $|(-8) - 5|$, calculate inside the bars: $(-8) - 5 = -13$. So $|(-8) - 5| = |-13| = 13$. For the second expression $|(-3) + (-7)|$, again calculate inside: $(-3) + (-7) = -10$. So $|(-3) + (-7)| = |-10| = 10$. Now subtract: $13 - 10 = 3$, which is answer choice A. Looking at the wrong answers: Choice B ($-3$) likely comes from incorrectly getting $10 - 13 = -3$ by reversing the subtraction order. Choice C ($7$) might result from calculating $|-8 - (-5)| - |-3 - 7|$ by mishandling the signs within the absolute value bars. Choice D ($-7$) could come from making sign errors and then reversing the subtraction, getting the negative of choice C. The most common mistake here is rushing through the operations inside the absolute value bars or forgetting that absolute value always produces a non-negative result. Always work from the inside out: handle parentheses and operations first, then apply absolute value, and finally perform the arithmetic between the absolute value expressions.