x and y satisfy |2 − x| ≤ 6 and |y + 2| ≤ 4.
What is the greatest possible value of |xy|?
- A16
- B24
- C32
- D40
- E48
- FThere is no greatest possible value.
Show the answer and worked solution
answer · E
- A16
- B24
- C32
- D40
- E48
- FThere is no greatest possible value.
Unpack each modulus into an interval: |2 − x| ≤ 6 gives −6 ≤ 2 − x ≤ 6, so −4 ≤ x ≤ 8, and |y + 2| ≤ 4 gives −6 ≤ y ≤ 2. The largest |xy| comes from taking each variable at whichever endpoint has the bigger size, so |x| ≤ 8 and |y| ≤ 6, giving |xy| ≤ 48. This is attained at x = 8, y = −6; the tempting pairing x = −4 with y = −6 only gives 24.