Today’s SAT question of the day begins with two numbers, a, and b. The difference between |a| and |b| is 5. The answer choices provide four false statements and one potentially true statement.
To look at things a different way, a – b is 5 and neither a nor b can be negative. This means that a has to be bigger than b, and that a has to be at least 5. (Test it out: for example, if a was 2, could we subtract any positive number and get 5? Nope.)
We have to choose an answer that fits with those two facts. The correct answer can’t suggest that a is not bigger than b, or that a is less than 5. Check each answer choice:
- says that a < 5
- is a possibility – doesn’t contradict a >b and a greater than or equal to 5.
- does not say that a > b
- makes no sense in this situation, and still doesn’t say that the absolute value of a is grear than the absolute value of b
- says that a < 1
Done! We found only one answer that’s a possibility, so we know which one to choose.
As a reminder, absolute value means the number of units between 0 and your number on a number line. -3 is three units from 0, so its absolute value is 3. -95 has an absolute value of 95…as does 95. Absolute value notation looks like |x|, which reads “the absolute value of x”.