Mettl Data Sufficiency ā Questions and Answers
Question 1: Is integer n positive? Statement 1: nĀ² > 25 Statement 2: n > ā10 Which of the following is correct?
- Statement 1 alone is sufficient to answer the question
- Statement 2 alone is sufficient to answer the question
- Both statements together are sufficient, but neither alone is
- Even both statements together are not sufficient to answer the question (Correct answer)
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 ā6 (negative). Statement 2 allows n = ā3 (negative) or n = 5 (positive). Combined, n could still be 6 or ā6. Neither alone nor together determines the sign of n.
Question 2: 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?
- Statement 1 alone is sufficient to answer the question (Correct answer)
- Statement 2 alone is sufficient to answer the question
- Both statements together are sufficient, but neither alone is
- Even both statements together are not sufficient to answer the question
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 Ć· 5 = 100 per day. Statement 2 only describes distribution across days, not the total.
Question 3: 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?
- Statement 1 alone is sufficient to answer the question
- Statement 2 alone is sufficient to answer the question
- Both statements together are sufficient, but neither alone is (Correct answer)
- Even both statements together are not sufficient to answer the question
Correct answer: Both statements together are sufficient, but neither alone is
Statement 1 alone describes a rhombus ā equal sides but angles need not be 90Ā°. Statement 2 alone describes a rectangle ā all 90Ā° angles but sides may differ. Only when both conditions hold (equal sides AND equal 90Ā° angles) is the shape guaranteed to be a square.
Question 4: What is the value of x + y? Statement 1: x + 2y = 10 Statement 2: 2x + y = 8 Which of the following is correct?
- Statement 1 alone is sufficient to answer the question
- Statement 2 alone is sufficient to answer the question
- Both statements together are sufficient, but neither alone is (Correct answer)
- Even both statements together are not sufficient to answer the question
Correct answer: Both statements together are sufficient, but neither alone is
Adding both equations: (x + 2y) + (2x + y) = 10 + 8 ā 3x + 3y = 18 ā 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.
Question 5: Is x > 0? Statement 1: xĀ² = 9 Statement 2: xĀ³ = 27 Which of the following is correct?
- Statement 1 alone is sufficient to answer the question
- Statement 2 alone is sufficient to answer the question (Correct answer)
- Both statements together are sufficient, but neither alone is
- Even both statements together are not sufficient to answer the question
Correct answer: Statement 2 alone is sufficient to answer the question
Statement 1 gives x = 3 or x = ā3, so we cannot determine the sign. Statement 2 gives xĀ³ = 27, and since cube roots are unique for real numbers, x = 3 ā which is positive. Statement 2 alone is sufficient.
Question 6: 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?
- Statement 1 alone is sufficient to answer the question
- Statement 2 alone is sufficient to answer the question
- Both statements together are sufficient, but neither alone is (Correct answer)
- Even both statements together are not sufficient to answer the question
Correct answer: Both statements together are sufficient, but neither alone is
S1: Sarah = Tom + 5. S2: Tom = 2 Ć Sarah ā 20. Substituting S1 into S2: Tom = 2(Tom + 5) ā 20 ā Tom = 10, Sarah = 15. Each statement alone gives one equation with two unknowns; together they form a solvable system.
Mettl Data Sufficiency
Is integer n positive?
Statement 1: nĀ² > 25
Statement 2: n > ā10
Which of the following is correct?