CAT Practice : Inequalities

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This is an excellent question to understand how a polynomial behaves when the variable 'x' takes values between roots. Think about how you can make the polynomial take positive and negative values. What values of 'x' should you substitute in the polynomial?

Inequalities - Maximum possible value

    Q.14: If a, b, c are integers such that – 50 < a, b, c < 50 and a + b + c = 30, what is the maximum possible value of abc?
    1. 1000
    2. 5000
    3. 4410
    4. 4560

 

  • Correct Answer
    Choice C. 4410

Explanatory Answer

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Detailed Solution

abc will be maximum when it is positive. So, a, b, c can all be positive or two of the three can be negative and one positive.

When all are positive, max product is when the numbers are 10, 10 and 10.

When two are negative and one positive, the best–case scenario would be when two negative numbers are as low as possible (magnitudes as high as possible) so that the product can be high. Now, in order for the product to be maximum, the positive number should be as high as possible. So, let the positive number be 49. Then the sum of the two negative numbers should be –19. The best– case scenario would be when numbers are 49, –9, –10.

Product would be 4410. Answer choice (c)

Correct Answer: 4410



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Inequalities are crucial to understand many topics that are tested in the CAT. Having a good foundation in this subject will make us tackling questions in Coordinate Geometry, Functions, and most importantly in Algebra much more comfortable.