Data Sufficiency Flashcards

Is integer n divisible by 6? (1) n is divisible by 3. (2) n is divisible by 2.

Answer: Both statements together are sufficient, but neither alone.

Divisibility by 6 requires both divisibility by 2 and 3; neither statement alone guarantees this, but together they do.

What is the value of x + y? (1) x − y = 4. (2) 2x + 2y = 20.

Answer: Statement (2) alone is sufficient.

Statement (2): 2(x + y) = 20, so x + y = 10; sufficient alone.

Is quadrilateral ABCD a rectangle? (1) All four angles are equal. (2) All four sides are equal.

Answer: Statement (1) alone is sufficient.

Four equal angles in a quadrilateral means each is 90°, which defines a rectangle; statement (1) is sufficient alone.

A store sold 200 items. What fraction were defective? (1) 40 items were defective. (2) 160 items were non-defective.

Answer: Each statement alone is sufficient.

Statement (1): 40/200 = 1/5; Statement (2): 40 defective (200−160) → 40/200 = 1/5; each alone is sufficient.

What is the area of circle O? (1) The diameter of circle O is 10. (2) The circumference of circle O is 10π.

Answer: Each statement alone is sufficient.

Both the diameter (r=5, area=25π) and circumference (r=5, area=25π) independently determine the area.

Is x > 0? (1) x² = 16. (2) x³ = 64.

Answer: Statement (2) alone is sufficient.

Statement (1): x could be 4 or −4; not sufficient. Statement (2): x³ = 64 means x = 4 only (positive); sufficient.