Multiple choice

Directions: The given question is followed by two statements I and II. You have to determine which of the statements is/are necessary/sufficient to answer the question. A bakery uses three types of ingredients in its special cake mixture: flour, sugar, and butter. By weight, the mixture was a% flour, b% sugar, and c% butter. If exactly 2 kilograms of flour and 4 kilograms of butter were used, how many kilograms of sugar were used? I. a = b II. c = 50

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in either statement I alone or statement II alone is sufficient to answer the question.

  4. The data in both statements I and II together is not sufficient to answer the question.

  5. The data in both statements I and II together is necessary to answer the question.
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C Correct answer
AI explanation

The total mixture weight is W, so we have the equations 2 = W*(a/100), 4 = W*(c/100), and the sugar is W*(b/100) = W*(100-a-c)/100. Using statement I alone where a = b, we have c = 100 - 2a, and since 2 = W*(a/100), we get W = 200/a; the sugar is W*(a/100) which equals 2 kg. Using statement II alone where c = 50, we see that the 4 kg of butter represents 50% of the total weight, so W = 8 kg, which means the sugar is the remaining 2 kg to sum to 8 kg. The data in either statement I alone or statement II alone is sufficient to answer the question.

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