CAT 2020 Question Paper | Quants Slot 1

CAT Questions

This question is from Quadratic Equations. We have to find the number of solutions of a given Quadratic Equation. But the solutions have to be distinct and must be distinct positive integers. Get as much practice as you can in Quadratic Equations because the benefits of being good at framing equations can be enormous and useful in other CAT topics as well. In CAT Exam

Question 15 : How many distinct positive integer-valued solutions exist to the equation (x² - 7x + 11)^{(x2 - 13x + 42)} = 1?

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Video Explanation

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Explanatory Answer

(x²-7x+11)^{(x^{2}-13x+42)} = 1
Only possible thing is x^2-13x+42 = 0
Or x²-7x+11 = 1
Solving these two x²-13x+42 = 0
(x – 6) (x – 7) = 0
x = 6 or x = 7
x²-7x+10 = 0
(x – 2) (x – 5) = 0
x = 2 or x = 5
At this moment we have 4 values possible, But there is one more way we can arrive this
(-1)^Even = 1
So, x²-7x+11 = -1
(x – 3) (x – 4) = 0
x = 3 or x = 4
So, 4 + 2 = 6 values

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The question is "How many distinct positive integer-valued solutions exist to the equation (x² - 7x + 11)^{(x2 - 13x + 42)} = 1?"

Hence, the answer is, "6"

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