Yesterday, 28 military band members in rectangular formation played for the prime Minister. As you can see, the formation is made up of 4 columns and 7 rows. If you add up the number of columns to the number of rows, the total is 11. Today, the prime Minister is hosting the American President and there will be 111 band members playing again in rectangular formation. The sum of the number of columns and the number of rows of this rectangular formation will be A) 41 B) 50 C) 48 D) 40 E) 52

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Understand the Problem: Understand the problem and the given information. We are given that 28 military band members are arranged in a rectangular formation with 4 columns and 7 rows. We are also told that the sum of the number of columns and rows is 11. We need to find the sum of the number of columns and rows for a new formation of 111 band members.Determine Factors of 28: Determine the factors of 28 that correspond to the given formation. Since there are 4 columns and 7 rows, and 4 * 7 = 28, we can confirm that the given information is correct.Determine Factors of 111: Determine the possible factors of 111 that could form a rectangular formation. We need to find two numbers that multiply to 111 and also have a sum that is one of the given options (A, B, C, D, E).Factor 111: Factor 111 to find its factors. 111 is 3 * 37, which are both prime numbers. Therefore, the only two factors that can form a rectangular formation are 3 and 37.Add Factors: Add the factors to find the sum of the number of columns and rows. The sum of 3 and 37 is 3 + 37 = 40.Match Given Options: Match the sum to the given options. The sum we found, 40, matches option D.

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