Directions for the following 2 (two) items: Read the following statements SI and S2 and answer the two items t

Question

Directions for the following 2 (two) items: Read the following statements SI and S2 and answer the two items that follow:

S1: Twice the weight of Sohan is less than the weight of Mohan or that of Rohan. 
S2: Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.

Which one of the following statements is correct?

Accepted Answer

Let S, M, and R be the weights of Sohan, Mohan, and Rohan, respectively. Translate the statements into inequalities: S1: "Twice the weight of Sohan is less than the weight of Mohan or that of Rohan." This means: 2S < M (Equation 1) AND 2S < R (Equation 2) S2: "Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan." This means: 2R > M (Equation 3) AND 2R > S (Equation 4) Analyze the options: 1. Is Sohan's weight greatest (Option B)? From Equation 1 (2S < M), it implies S < M. From Equation 2 (2S < R), it implies S < R. Since Sohan's weight is less than both Mohan's and Rohan's, Sohan cannot have the greatest weight. Thus, Option B is incorrect. 2. Now we need to determine if Mohan or Rohan has the greatest weight, or if it cannot be determined. We have the following relationships: S < M/2 S < R/2 M < 2R S < 2R Let's test with numerical examples to see if we can find scenarios where M is greatest and where R is greatest. Scenario 1: Mohan's weight is greatest. Let S = 10. From 2S < M and 2S < R: 20 < M and 20 < R. From 2R > M: M < 2R. Let R = 25. (Satisfies R > 20) Then M < 2 * 25 => M < 50. For M to be greatest, M must be greater than R. So, M > 25. Let M = 30. Check all conditions with S=10, M=30, R=25: 2S < M (20 < 30) - True 2S < R (20 < 25) - True 2R > M (50 > 30) - True 2R > S (50 > 10) - True In this scenario, M (30) is the greatest. So, Option A is possible. Scenario 2: Rohan's weight is greatest. Let S = 10. From 2S < M and 2S < R: 20 < M and 20 < R. From 2R > M: M < 2R. Let M = 25. (Satisfies M > 20) Then 25 < 2R => R > 12.5. Also, we need R > 20 (from 2S < R). For R to be greatest, R must be greater than M. So, R > 25. Let R = 30. Check all conditions with S=10, M=25, R=30: 2S < M (20 < 25) - True 2S < R (20 < 30) - True 2R > M (60 > 25) - True 2R > S (60 > 10) - True In this scenario, R (30) is the greatest. So, Option C is possible. Since we found valid scenarios where Mohan's weight is greatest (Option A) and where Rohan's weight is greatest (Option C), we cannot definitively determine whose weight is greatest. Therefore, the correct statement is that whose weight is greatest cannot be determined. The final answer is D

Answer

Weight of Mohan is greatest

Answer

Weight of Sohan is greatest

Answer

Weight of Rohan is greatest

Answer

Whose weight is greatest cannot be determined

Explanation

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