Lesson: Data Sufficiency Intermeddiate - 09t01

An Example of Quadratics In Data Sufficiency

[Page 9 of 21]

Let's apply what we just learned to a classic GMAT Data Sufficiency example. Do the following problem, then click Continue.

What is the value of x?

  1. x 2 - 9 = 0
  2. x 2 + 6x + 9 = 0
Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient.
Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient.
Both statements TAKEN TOGETHER are sufficient, but NEITHER statement BY ITSELF is sufficient.
EACH statement BY ITSELF is sufficient.
The two statements TAKEN TOGETHER are NOT sufficient.

Countinue

Each statement provides you with a quadratic equation which means that each statement will yield two values for x. The first thing to note is that this Data Sufficiency is a value question, so, as you've learned, to be sufficient a statement must lead to one and only one value.

This is a classic GMAT trap! Statement (1) yields two different values, 3 and –3. Statement (2) also yields two values, but the values are identical.

Solving for x we find that x = –3 or x = –3, so we find one and only one value. Thus, Statement (2) is sufficient.

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