Sufficiency Analysis Flashcards

Is the 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 is sufficient

Divisibility by 6 requires both divisibility by 2 AND by 3, so both statements together are needed.

What is the value of x + y? (1) x = 5. (2) x − y = 3.

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

From statement 1, x = 5; combined with x − y = 3 gives y = 2, so x + y = 7.

A box contains only red and blue marbles. How many red marbles are in the box? (1) There are 20 marbles total. (2) The ratio of red to blue marbles is 3:2.

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

With 20 total and a 3:2 ratio, red = 12; neither fact alone gives a definite count.

Is rectangle ABCD a square? (1) AB = BC. (2) The diagonal of ABCD is 10.

Answer: Statement 1 alone is sufficient

In a rectangle, if two adjacent sides are equal (AB = BC), all sides are equal, making it a square.

Did the store's revenue increase from January to February? (1) Revenue in January was $10,000. (2) Revenue in February was $11,500.

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

You need both months' revenues to compare and determine if there was an increase.

Is x > 0? (1) x² = 16. (2) x³ = 64.

Answer: Statement 2 alone is sufficient

x³ = 64 means x = 4, which is positive; x² = 16 gives x = ±4, insufficient alone.

How many hours did Maria work last week? (1) Maria earned $480 last week. (2) Maria earns $12 per hour.

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

Dividing total earnings ($480) by hourly rate ($12) gives 40 hours; neither piece alone is sufficient.