CAT 2021 Slot 1 · Quant · Question 20

CAT 2021 Slot 1 previous year question on Inequalities & Modulus, with the answer and a step-by-step solution.

Inequalities & ModulusAlgebraMultiple choiceMedium
The number of integers n that satisfy the inequalities \left| n-60 \right|<\left| n-100 \right|<\left| n-20 \right| is
  1. A
    19
  2. B
    18
  3. C
    20
  4. D
    21
Pick an option, then check.
Answer & solution

Answer: Option A

From \left| n-60 \right|<\left| n-100 \right|

we get n<80, and from \left| n-100 \right|<\left| n-20 \right| we get n>60.

So 60<n<80, giving the integers 61,62,\ldots ,79, which number 19.

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