Data Sufficiency Flashcards

To find whether a number N is divisible by 6: Statement I: N is divisible by 2. Statement II: N is divisible by 3. Which is sufficient?

Answer: Both statements together

A number is divisible by 6 only when it is divisible by both 2 and 3, so both statements together are required.

What is the value of x? Statement I: x² = 25. Statement II: x > 0. Which is sufficient?

Answer: Both statements together

Statement I gives x = ±5 and Statement II eliminates the negative, so both together uniquely determine x = 5.

Is integer n even? Statement I: n/2 is an integer. Statement II: n + 1 is odd. Which is sufficient?

Answer: Either statement alone

Both statements independently confirm that n is even: n/2 being an integer and n+1 being odd are each equivalent definitions.

What is the area of a rectangle? Statement I: Its perimeter is 24 cm. Statement II: Its length is twice its width. Which is sufficient?

Answer: Both statements together

Using both statements: width = 4 cm and length = 8 cm, giving area = 32 cm²; neither statement alone is sufficient.

Is x > y? Statement I: x + 2 > y + 2. Statement II: x² > y². Which is sufficient?

Answer: Statement I alone

Statement I simplifies directly to x > y by subtracting 2 from both sides, making it sufficient alone.

What is Ram's age? Statement I: Ram is 5 years older than Sam. Statement II: Sam is 20 years old. Which is sufficient?

Answer: Both statements together

Both statements together give Ram's age as 20 + 5 = 25 years; neither alone provides a definite answer.