Multiple choice

Directions: The question below is followed by statements A and B. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and choose the correct alternative. What are the speeds of two trains 80 m and 85 m long? (A) They take 37.5 seconds to pass each other when running in the same direction. (B) They take 7.5 seconds to pass each other when running in opposite directions.

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

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

  3. Both (A) and (B) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (A) and (B) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be v1 and v2. (A) (80+85)/(v1-v2) = 37.5. (B) (80+85)/(v1+v2) = 7.5. We have two equations with two variables, so both are needed to solve for v1 and v2.

AI explanation

Let the speeds of the two trains be x and y. From statement A, running in the same direction gives a relative speed of (x minus y), so (x minus y) equals (80 plus 85) divided by 37.5. From statement B, running in opposite directions gives a relative speed of (x plus y), so (x plus y) equals (80 plus 85) divided by 7.5. Because each statement provides only one independent equation with two variables, neither is sufficient alone; however, solving the two linear equations together yields the individual values of x and y.

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