Amit. Basheer, Chris. Dharam and Esso are 5 friends. All of them are of different heights. The tallest person’s position is numbered 1, the next tallest 2, and so on, till the shortest whose position number is 5.

- The sum of Amit’s position number and Esso ‘s position number is equal to the sum of Dharam’s position number and Chris’ position number.
- Chris is not the shortest and Amit is not the tallest.
- Chris is shorter than Amit, and Dharam is shorter than Basheer.

**Q1. **Who is the tallest?

- Basheer
- Amit
- Esso
- Either Basheer or Amit
- Cannot be determined

**Q2. **If Dharam is shorter than Chris, then the sum of the position numbers of which of the following combinations is/are a perfect square?

- Basheer and Amit
- Dharam and Ess0
- Chris and Basheer
- More than one of the above
- None of the above

**Q3. **If Dharam is shorter than Chris. then which of the following is true?

- if made to stand in decreasing order of their heights, no two persons whose names start with consecutive alphabets (as in the alphabetical series) stand adjacent to each other.
- The sum of the position numbers of Chris and Amit is equal to the position number of Esso.
- The sum of the position numbers of Dharam and Esso is a prime number.
- Basheer is not tallerthan Chris.
- None of the above

Amit is not the tallest and Chris is not the shortest. Further, Amit is taller than Chris and Basheer is taller than Dharam. Since Chris is shorter than Amit but not the shortest,

Amit cannot be number 5.

Similarly Chris cannot be number 2.

Basheer cannot be the shortest, since he is taller than Dharam. Dharam cannot be 1.

The possibilities are

Amit (A) —> 2, 3

Basheer (B) —> 1, 2, 3, 4

Chris (C) —> 3, 4

Dharam (D) —> 2, 3, 4, 5

Esso (E) —> 1, 2, 3, 4, 5

Now A + E = C + D.

But C can take only 3 or 4, and neither A nor D can take 1.

Therefore, C+D= (3+2) or(2+3) is not possible, A+ E: (1 +4)

or (4 + 1), and A is neither 1 nor 4.

Therefore, C + D = 3 + 4 is possible.

Hence, A+E= 2+5-------- (1)

C + D = 4 + 3 is possible.

Hence, A + E = 2 + 5 -------- (2)

Therefore, Basheer is 1" in both the cases.

**Q1. **Basheer is the tallest. Choice (1)

**Q2.** Chris + Basheer $= 3 + 1 = 4 = ( 2 ) ^ { 2 }$ and Dharam + Esso $= 4 + 5 = 9 = ( 3 ) ^ { 2 } .$ choice(4)

**Q3. **Statement (1) is not true as the arrangement will be as follows:

Statement (2) is true, since Chris + Amit = 3 + 2 = 5

= Esso’s number. Choice (2)

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