The scores of a math test for five studerits were posted on the bulletin board. The students' names are Fred, Penny, Tom, John and Jake. Fred and Jake scored the same number of points. Pernny did not get the highest soore. John's score was 5 points lower than Tom's. The scores were 71, 53, 87, 53 and 82 . Which student recelved whit score? A. Fred and Jake 53, Penny 82, Tom 71, Johin 87 B. Frat ani Tom 53, John 74, Tom 82, Pemmy 87 C. Fred ani Tom 53, Penny 82, Jake 71, John 87 D. Fred and Jake 53, Penny 71, Tom 87 , John 82

1. The five scores given are \( 71 \), \( 53 \), \( 87 \), \( 53 \), and \( 82 \). 2. The problem states that Fred and Jake received the same score. Since there are two \( 53 \)s, assign: \[ \text{Fred} = 53 \quad \text{and} \quad \text{Jake} = 53. \] 3. The remaining scores are \( 71 \), \( 82 \), and \( 87 \). 4. It is given that Penny did not get the highest score. The highest score is \( 87 \); therefore, Penny’s score must be either \( 71 \) or \( 82 \). 5. The condition “John's score was 5 points lower than Tom's” means if \( \text{Tom} = x \), then: \[ \text{John} = x - 5. \] The pair \((x, x-5)\) must be chosen from the remaining scores \( 71 \), \( 82 \), and \( 87 \). 6. If we set \( \text{Tom} = 87 \) (the highest remaining score), then: \[ \text{John} = 87 - 5 = 82. \] This leaves \( 71 \) for Penny, which is acceptable since \( 71 \) is not the highest score. 7. This assignment results in: \[ \text{Fred} = 53, \quad \text{Jake} = 53, \quad \text{Penny} = 71, \quad \text{Tom} = 87, \quad \text{John} = 82. \] 8. Comparing with the provided options, Option D states: \[ \text{Fred and Jake } 53, \quad \text{Penny } 71, \quad \text{Tom } 87, \quad \text{John } 82. \] This matches our assignment. Thus, the correct answer is Option D.