Data Sufficiency Flashcards

Is integer n positive? Statement 1: n² > 25 Statement 2: n > −10 Which of the following is correct?

Answer: Even both statements together are not sufficient to answer the question

Statement 1 means |n| > 5, so n could be 6 (positive) or −6 (negative). Statement 2 allows n = −3 (negative) or n = 5 (positive). Combined, n could still be 6 or −6. Neither alone nor together determines the sign of n.

A factory operates 5 days per week. How many widgets does it produce per day? Statement 1: It produces 500 widgets per week. Statement 2: It produces twice as many widgets on Monday as on any other day. Which of the following is correct?

Answer: Statement 1 alone is sufficient to answer the question

The question stem already states the factory works 5 days per week. Statement 1 gives total weekly output (500 widgets), so 500 ÷ 5 = 100 per day. Statement 2 only describes distribution across days, not the total.

Is quadrilateral ABCD a square? Statement 1: All four sides are equal in length. Statement 2: All four interior angles are equal. Which of the following is correct?

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

Statement 1 alone describes a rhombus — equal sides but angles need not be 90°. Statement 2 alone describes a rectangle — all 90° angles but sides may differ. Only when both conditions hold (equal sides AND equal 90° angles) is the shape guaranteed to be a square.

What is the value of x + y? Statement 1: x + 2y = 10 Statement 2: 2x + y = 8 Which of the following is correct?

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

Adding both equations: (x + 2y) + (2x + y) = 10 + 8 → 3x + 3y = 18 → x + y = 6. Neither statement alone gives x + y, but adding them together yields the answer directly without needing individual values of x and y.

Is x > 0? Statement 1: x² = 9 Statement 2: x³ = 27 Which of the following is correct?

Answer: Statement 2 alone is sufficient to answer the question

Statement 1 gives x = 3 or x = −3, so we cannot determine the sign. Statement 2 gives x³ = 27, and since cube roots are unique for real numbers, x = 3 — which is positive. Statement 2 alone is sufficient.

How old is Sarah today? Statement 1: Sarah is 5 years older than her brother Tom. Statement 2: Tom's age equals twice Sarah's age minus 20. Which of the following is correct?

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

S1: Sarah = Tom + 5. S2: Tom = 2 × Sarah − 20. Substituting S1 into S2: Tom = 2(Tom + 5) − 20 → Tom = 10, Sarah = 15. Each statement alone gives one equation with two unknowns; together they form a solvable system.