CAT 2022 Question Paper (Slot 1) - Quant Question 16
Question 16
The largest real value of a for which the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for x is
Solution
In the question, it is given thatĀ the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for any value of x. This is possible when x in |x+a| and x in |x-1| cancels out.
Case 1:
x + a < 0, x - 1Ā $$\ge\ $$ 0
- a - x + x - 1 = 2
a = -3
Case 2:
x + aĀ $$\ge\ $$ 0 and x - 1 < 0
x + a - x + 1 = 2
a = 1
Largest value of a is 1.
The answer is option C.
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