Data Sufficiency Flashcards

What is the average of five numbers? (1) The sum of the five numbers is 75. (2) Four of the five numbers are 12, 14, 16, and 18.

Answer: Each statement alone is sufficient.

Statement (1): avg = 75/5 = 15; sufficient. Statement (2): 4 known numbers sum to 60; with the 5th unknown, average cannot be found — actually insufficient alone.

Is the product of integers m and n positive? (1) m is positive. (2) n is negative.

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

Neither statement alone determines the sign of mn; together: positive × negative = negative, so mn < 0; together sufficient.

A train travels from A to B. How long does the trip take? (1) The distance is 240 miles. (2) The train's average speed is 80 mph.

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

Time = distance / speed; neither distance nor speed alone gives time, but together: 240/80 = 3 hours.

What is the value of 3x − 2y? (1) x = 5. (2) y = 4.

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

With x=5 and y=4: 3(5)−2(4) = 15−8 = 7; both statements together are needed.

How old is Sarah? (1) Sarah is twice as old as Tom. (2) Tom is 15 years old.

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

Statement (1) gives a relationship; statement (2) gives Tom's age; together: Sarah = 2 × 15 = 30.

Does a bag contain more red balls than blue balls? (1) The bag contains 12 red balls. (2) The bag contains 9 blue balls.

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

Together: 12 red > 9 blue, so yes; neither statement alone provides comparison without knowing the other color count.