Directions Each problem contains a question and two statements A and B giving certain data You have ...........

Math and Mental Ability Data Sufficiency

Directions :

Each problem contains a question and two statements; A and B giving certain data. You have to select the correct answer from option depending on the sufficiency of data given in the statements to answer the question.

Question: A piece of wood is cut into 3 pieces X, Y and Z. Are they of equal length?

A. The sum of the lengths of X and Y is 2/3rd of the original piece.

B. Y and Z are of same length.

Statement A alone is sufficient and statement B alone is not sufficient to answer the question.

Statement B alone is sufficient and statement A alone is not sufficient to answer the question.

Statements A and B together are sufficient but neither statement alone is sufficient to answer the question.

Each statement alone is sufficient to answer the question.

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Explanation:

- Statement A: It tells us that the combined length of X and Y is 2/3rd of the original wood. This does not specify if X, Y, and Z are equal, as it gives no information about Z's length.

- Statement B: It states that Y and Z are of the same length. However, this alone does not prove X, Y, and Z are of equal lengths without knowing how they are related to X.

- Combined:

- From A, if X + Y = 2/3 of original, then Z = 1/3.

- From B, if Y = Z, then X = 1/3 too.

- This shows X = Y = Z.

Thus, only together are A and B sufficient.

Therefore, Option 3 is correct: "Statements A and B together are sufficient but neither statement alone is sufficient to answer the question."