# CAT 2020 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Quants Questions | Question 17

If you are preparing for the CAT exam dilligently, CAT previous year paper is one thing that you just cannot miss! These previous year papers give you a sense of what to expect in the CAT Question Paper and hence, level up your CAT preparation online. Solve this Number Theory question from CAT 2020 Question Paper Slot 2 and start acing your preparation game.
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Question 17 : The number of integers that satisfy the equality (x2 - 5x + 7)x + 1 = 1 is

1. 5
2. 4
3. 3
4. 2

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We can have three possibilities for the equality of form xn = 1
First n = 0, then x = 1 and then x = -1 and n = even (-1)Even
Using first x = -1, and substituting in given equation
(-1)2 -5(-1) + 7 = 8 (Acceptable)
Using second condition, x2
Solving x = 2 or x = 3 (Both are acceptable)
Last condition x2 -5x + 7 = -1
x2 -5x + 8 = 0
No integer values,
So 3 values satisfy the equality

The question is "The number of integers that satisfy the equality (x2 - 5x + 7)x + 1 = 1 is"

##### Hence, the answer is, "3"

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