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Question

Vinay is taller than Hansika, Hansika is taller than Abhay, Aalok is taller than Ashok and Ashok is taller than Vinay. Who is the shortest in the group ?

This question was previously asked in
UPSSSC PET 2025 Question Paper (07-Sep-2025) (Shift-2)
The correct answer is
Abhay

Understanding Height Comparisons

This problem involves comparing the heights of five individuals: Vinay, Hansika, Abhay, Aalok, and Ashok. We need to use the given statements to establish a height order and find the shortest person.

Analyzing the Statements

Let's break down each statement and represent the height comparison using inequalities. We'll use the notation 'Person 1 > Person 2' to mean 'Person 1 is taller than Person 2'.

  • Statement 1: Vinay is taller than Hansika.
    Representation: $Vinay > Hansika$
  • Statement 2: Hansika is taller than Abhay.
    Representation: $Hansika > Abhay$
  • Statement 3: Aalok is taller than Ashok.
    Representation: $Aalok > Ashok$
  • Statement 4: Ashok is taller than Vinay.
    Representation: $Ashok > Vinay$

Step-by-Step Height Ranking

Now, let's combine these comparisons to create a single height order:

  1. Combine Statements 1 and 2: Since Vinay > Hansika and Hansika > Abhay, we can deduce that Vinay is taller than Hansika, who is taller than Abhay.
    Combined Inequality: $Vinay > Hansika > Abhay$
  2. Combine Statements 3 and 4: Since Aalok > Ashok and Ashok > Vinay, we know Aalok is the tallest among these three, followed by Ashok, and then Vinay.
    Combined Inequality: $Aalok > Ashok > Vinay$
  3. Combine all information: We have $Aalok > Ashok > Vinay$ and $Vinay > Hansika > Abhay$. Linking these together using Vinay as the common point gives us the complete order from tallest to shortest.
    Full Inequality Chain: $Aalok > Ashok > Vinay > Hansika > Abhay$

Identifying the Shortest Person

Looking at the final height order:

$Aalok > Ashok > Vinay > Hansika > Abhay$

This clearly shows that Abhay is shorter than everyone else in the group. Therefore, Abhay is the shortest person.

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