Multiple choice

Directions: The following 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. What is the value of (z - 21)? (1) z2 - 441 = 0 (2) (2z - 42)2 = 0

  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
B Correct answer
Explanation

Statement (1) z^2 - 441 = 0 implies z^2 = 441, so z = 21 or z = -21. Thus (z - 21) could be 0 or -42. Statement (2) (2z - 42)^2 = 0 implies 2z - 42 = 0, so 2z = 42, z = 21. Thus (z - 21) = 0. Statement (2) is sufficient.

AI explanation

Statement 1 simplifies to z squared equals 441, giving roots of z equals 21 or z equals negative 21, which means z minus 21 could be 0 or negative 42, making it insufficient. Statement 2 simplifies to 2z minus 42 equals 0, which means 2z equals 42 and z equals 21. Since z is exactly 21, the value of z minus 21 is uniquely determined to be 0, making statement 2 alone sufficient.

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