Multiple choice

Passage

Directions: The following problem consists of a question followed by three statements (I), (II), and (III). You have to determine which statement(s) is/are sufficient /necessary to answer the question.

Three persons X, Y and Z did some work and shared the money among them but not equally. What was the share of X? I. The ratio of the shares of X and Z is 3 : 5, respectively. II. If X gives Rs. 500 from his share to Y, then Y and Z would have equal amount of money. III. X's share is less than Y's share.

  1. Only I and II

  2. Only II and III

  3. Only I and III

  4. Cannot be answered even by using all three statements

  5. All three statements
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives X:Z ratio. Statement II gives a relationship between Y and Z. Statement III gives an inequality. We have no total amount or absolute values for any share, so we cannot determine X's specific share.

AI explanation

Statement 1 establishes the ratio of shares of X and Z as 3 to 5, meaning X has 3x rupees and Z has 5x rupees. Statement 2 states that if X gives 500 rupees to Y, then Y and Z would have equal amounts, leading to the equation Y plus 500 equals 5x, so Y equals 5x minus 500. Even using Statement 3, which only says X's share is less than Y's share, we get the inequality 3x less than 5x minus 500, meaning x is greater than 250, but we still lack a definitive value for x. Because the total amount of money shared among the three is unknown and we only have an inequality, the exact share of X cannot be determined even by using all three statements.

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