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 a3 + b3? (1) ab = 12 (2) a + b = 7

  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
C Correct answer
Explanation

The expression a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2). Since a^2 + b^2 = (a + b)^2 - 2ab, we can rewrite the expression as (a + b)((a + b)^2 - 3ab). Knowing both a + b and ab allows us to calculate the value, so both statements are required.

AI explanation

Using the sum of cubes formula, a cubed plus b cubed equals a plus b multiplied by a squared minus a times b plus b squared, which can be rewritten as a plus b multiplied by the quantity a plus b squared minus 3 times a times b. Statement 1 provides ab equals 12 and statement 2 provides a plus b equals 7. Substituting these values into the rewritten formula yields 7 multiplied by 49 minus 36, so both statements together are required.

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