Multiple choice

A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red? (1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2 : 1. (2) Of the first 6 marbles removed, 4 are red.

  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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (1) gives the ratio of removed marbles (2 red : 1 blue). Since 9 were removed, 6 were red and 3 were blue. Starting with 20 red, 20 - 6 = 14 red remain. Statement (2) only gives info on the first 6, not all 9, so it is insufficient.

AI explanation

Statement one says the 9 removed marbles have a red to blue ratio of 2 to 1, meaning 6 red marbles and 3 blue marbles were removed. This leaves 14 red marbles in the jar, making statement one sufficient. Statement two only provides the colors of the first 6 removed marbles but gives no information about the remaining 3 removed marbles, making it impossible to determine the exact number of red marbles left in the jar. Therefore, statement one alone is sufficient, but statement two alone is not.

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