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CAT 2001 — QA Question 14

Solving InequalitiesEasy

x and y are real numbers satisfying the conditions 2 < x < 3 and –8 < y < –7. Which of the following expressions will have the least value?

Answer & solution

  • A

    x2y

  • B

    xy2

  • C

    5xy

  • None of these

Solution

Option 2 can easily be eliminated as it will give positive value, while both option 1 and 3 will be negative.

∵ x2 will fall in the range 4 < x2 < 9.

∵ 5x will fall between 10 < 5x < 15.

∴ 5x > x2
 
Also, 5x < 6x < 7x < ... and –8 < y < –7
 
∴ 5xy > 6xy > 7xy > ...

Hence, option (d).

CAT 2001 QA Q14: x and y are real numbers satisfying the conditions 2 < x < 3 and &ndash;8 < y < &ndash;7. Which of the followi — Solution | TheCATExam