# CAT 2020 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Quants Questions | Question 18

Struggling with topics like Number Theory while preparing for the CAT exam? Not sure which questions to attempt and which questions to skip? CAT previous year paper can be your saving grace! Ace your online preparation for CAT by solving questions from CAT previous year paper as they'll help you to understand the pattern and the difficulty level of questions you can expect in the CAT Question Paper. Do not put this off for a later time, start by solving this question from Number Theory taken from CAT 2020 Question paper right away! Do not look at the text and video solution before trying it yourself!

Question 18 : In how many ways can a pair of integers (x , a) be chosen such that x2 − 2 | x | + | a - 2 | = 0 ?

1. 7
2. 6
3. 4
4. 5

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|x|2 – 2|x| + |a – 2| = 0
|x|2 – 2|x| + 1 = 0 is the square of a quadratic number
In the above equation the value of constant cannot be more than 1
So |a – 2| = 0 or = 1
|x|2 – 2|x| = 0
|x|2 = 2|x|
x = 0 or 2 or -2
For all these possibilities value of a = 2
|x|2 – 2|x| + 1 = 0
(|x| - 1)2 = 0
|x| = 1
So, x = 1 or x = -1
Then |a – 2| = 1, a = 3 or a = 1
Four combinations of (x,a) are possible already we have 3
Totally 7 pairs

The question is "In how many ways can a pair of integers (x , a) be chosen such that x2 − 2 | x | + | a - 2 | = 0 ?"

##### Hence, the answer is, "7"

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