Statistics and Sets Problems

[swerve]

In a class, the maximum score of a student is 80, and the minimum score of a student is 65. If Kevin's score is neither the maximum nor the minimum, is Kevin's score closer to the minimum score?

1) Kevin's score is greater than 70.
2) The difference between the minimum score and Kevin's score is less than the difference between the maximum score and his score.

The OA is B

Source: Manhattan Prep

[deloitte247]

- The maximum score of a student = 80
- The minimum score of a student = 65
- Kevin's score is neither maximum nor minimum
Target question =>Is Kevin's score closer to the minimum score?

Statement 1 => Kelvin's score is greater than 70
Comparing Kelvin's score to the range of maximum and minimum score, it can be as low as 71 or as high as 79
If Kelvin's score = 71, then it is close to the minimum score
If Kelvin's score = 79, then it is closer to the maximum score
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2 => The difference between the minimum score and Kelvin's score is less than the difference between the maximum score and his score
Let Kelvin's score = k
65 - k < 80 - k
This analysis shows that k is closer to the minimum score because 65 - k is less than 80 - k
Hence, statement 2 alone is SUFFICIENT.

Answer = B