Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream? (1) At the picnic, 60 percent of the guests were served a double scoop of ice-cream. (2) A total of 120 scoops of ice-cream were served to all the guests at the picnic.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement (1) gives the percentage but not the total number of guests. Statement (2) gives the total scoops but not the distribution (single vs double). Together, if N is the total guests, 0.6N * 2 + 0.4N * 1 = 120, which simplifies to 1.6N = 120, allowing us to solve for N and then the number of double scoops.

AI explanation

Let the total number of guests be G and the number of guests served a double scoop be D. Statement 1 gives D as 60 percent of G, but without knowing G, D cannot be found. Statement 2 gives the equation 1 times (G minus D) plus 2 times D equals 120 scoops, but with two variables, a single equation cannot be solved. Using both together, substitute 0.6G for D in the second equation to get G minus 0.6G plus 1.2G equals 120, yielding G as 75, and D becomes 45. Therefore, both statements together are sufficient.

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