AlgebraHardExtreme value of a difference from ranges
Algebra practice question
If 3 < x < 8 and 2 < y < 5, what is the greatest possible integer value of x − y?
Answer: 5
x − y is largest when x is near 8 and y is near 2, approaching (but never reaching) 6. The greatest integer available is 5.
Common wrong answers
- If you answered 1
- 1 is near the minimum of the difference, not the maximum.
- If you answered 3
- 3 uses mid-range values; push x up toward 8 and y down toward 2.
- If you answered 6
- 6 is excluded: x < 8 and y > 2 are strict, so x − y < 6 exactly.
More Algebra questions
- Hard
For how many integer values of x is −2 < (x − 5)/3 ≤ 1 true? - Hard
The system 2x + 3y = 6 and 4x + 6y = k has infinitely many solutions. What is the value of k? - Hard
Which of the following is the complete solution set to |x − 4| < 6? - Hard
A student has $40 to spend on notebooks costing $4 each and pens costing $2 each, and wants at least 12 items … - Hard
What is the least whole number of minutes of international calling in a month for which the total monthly cost… - Hard
How many liters of the 30% acid solution did the technician use?
Not affiliated with the College Board. SAT is a trademark of the College Board.