The scores of a math test for five students were posted on the bulletin board. The students' names are Tom, Penny, Fred, John and Jake. Tom and Jake scored the same number of points. Penny did not get the highest score. John's score was 5 points lower than Fred's. The scores were \( 67,50,87,50 \) and 82 . Which student received what score? A. Tom and Jake 50, Penny 67, Fred 87 , John 82 B. Tom and Jake 50 , Penny 82 , Fred 67 , John 87 C. Tom and Fred 50 , Penny 82 , Jake 67, John 87 D. Tom and Fred 50 , John 67 , Fred 82 , Penny 87

**Step 1: Identify the given information** - The scores available are \(67\), \(50\), \(87\), \(50\), and \(82\). - Tom and Jake got the same score. - Penny did not get the highest score. - John’s score was \(5\) points lower than Fred’s score. **Step 2: Determine the possible score for Tom and Jake** Since Tom and Jake have the same score, they must both receive one of the scores available in duplicate. The score \(50\) appears twice. Therefore, Tom and Jake must both have scored \(50\). **Step 3: Assign scores to the remaining students based on the conditions** After assigning \(50\) to Tom and Jake, the remaining scores are: \[ 67,\quad 87,\quad 82 \] - The highest score is \(87\). Penny cannot have this score. - John’s score is \(5\) points lower than Fred’s score. We need to assign the remaining scores to Penny, Fred, and John. **Step 4: Determine the scores for Fred and John** Consider the condition: \[ \text{John's score} = \text{Fred's score} - 5 \] Check the possible pairings: - If we assign Fred \(87\), then John would be \(87 - 5 = 82\). This pairing works, because both \(87\) and \(82\) are available. - Alternatively, if Fred \(82\) then John would be \(82 - 5 = 77\), which is not available. - The pairing with Fred \(67\) would give John \(62\), which is also not available. Thus, Fred must have scored \(87\) and John \(82\). **Step 5: Assign the remaining score to Penny** The only remaining score is \(67\), which then goes to Penny. This also satisfies the condition that Penny did not get the highest score. **Step 6: Verify the assignments against the answer options** The final assignments are: - Tom: \(50\) - Jake: \(50\) - Penny: \(67\) - Fred: \(87\) - John: \(82\) Comparing these with the given options, we see that **Option A** matches: - Tom and Jake: \(50\) - Penny: \(67\) - Fred: \(87\) - John: \(82\) Thus, the correct answer is: A. Tom and Jake \(50\), Penny \(67\), Fred \(87\), John \(82\).