Data Sufficiency is a unique and challenging question format on the Graduate Management Admission Test (GMAT), housed within the Data Insights section. Unlike standard multiple-choice math questions that require calculating a precise numerical output, Data Sufficiency tests analytical reasoning and problem-solving efficiency. Each question presents a problem statement followed by two supporting statements, requiring candidates to determine whether the given data is sufficient to answer the question independently or in combination, adhering to the standardized GMAT options (A through E). Mastering this format demands robust number property knowledge, careful logical deduction, and an understanding of sufficiency versus exact computation. Regular practice with targeted multiple-choice questions helps candidates avoid common traps and master time management under adaptive testing conditions.
1. In a GMAT Data Sufficiency question, what does Option (A) uniquely represent according to standard GMAT answer choices?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Explanation:
Standard GMAT Data Sufficiency options permanently assign Option (A) to indicate that Statement 1 alone provides sufficient information to answer the question, while Statement 2 alone does not.
2. What standard GMAT Data Sufficiency choice should be selected if Statement (2) alone is sufficient to answer the question, but Statement (1) alone is not?
Correct Answer: b) Option B
Explanation:
By standard definition on the GMAT, Choice (B) means Statement 2 alone is sufficient to yield a definitive answer, whereas Statement 1 alone is insufficient.
3. When evaluating a 'Yes/No' Data Sufficiency question, what constitutes a 'Sufficient' statement?
Correct Answer: c) A statement that provides a definitive, consistent answer of either 'Yes' or 'No'
Explanation:
In Yes/No Data Sufficiency, a statement is sufficient if it allows you to answer the question with certainty—whether that definitive answer is always 'Yes' or always 'No'.
4. If Statement (1) is determined to be sufficient in a GMAT Data Sufficiency question, which answer options are immediately eliminated?
Correct Answer: b) Options B, C, and E
Explanation:
Using the AD/BCE elimination strategy, if Statement 1 is sufficient, the correct answer must be either A or D, immediately eliminating B, C, and E.
5. What does Option (C) represent in GMAT Data Sufficiency?
Correct Answer: c) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Explanation:
Option (C) indicates that neither statement works on its own, but combining the information from both statements provides enough data to solve the problem uniquely.
6. If Statement (1) alone yields two possible values for x (x = 3 or x = 5) in a Value question, is Statement (1) sufficient?
Correct Answer: c) No, because a Value question requires a single, unique numerical value.
Explanation:
For Value questions in Data Sufficiency, a statement is sufficient only if it yields exactly one unique numerical value for the target variable.
7. Is x > 0? Statement (1): x^3 > 0 Statement (2): x^2 > 0 Which of the following is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): x^3 > 0 implies x must be positive (x > 0), giving a definitive 'Yes'. From (2): x^2 > 0 implies x != 0 (x could be positive or negative), which does not answer if x > 0.
8. What is the value of integer n? Statement (1): 2 < n < 4 Statement (2): n is an odd integer Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
Statement (1) states 2 < n < 4 for an integer n, which uniquely forces n = 3. Statement (2) says n is odd, which leaves infinitely many choices (1, 3, 5, etc.).
9. What does Option (E) mean in a GMAT Data Sufficiency question?
Correct Answer: a) Statement (1) and Statement (2) together are insufficient to answer the question.
Explanation:
Option (E) indicates that even when combining all given information from both Statement 1 and Statement 2, there is still not enough data to answer the question definitively.
10. What is the key rule regarding consistency between Statement (1) and Statement (2) in GMAT Data Sufficiency?
Correct Answer: b) They can never contradict each other; valid statements must be mutually compatible.
Explanation:
Official GMAT Data Sufficiency statements will never provide contradictory factual information. They must be compatible with each other and with the stem.
11. Is the integer k even? Statement (1): k is divisible by 4 Statement (2): k is divisible by 2 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
If k is divisible by 4, k = 4m = 2(2m), so k is even (Sufficient). If k is divisible by 2, k is even by definition (Sufficient). Each statement alone is sufficient.
12. What is the value of x + y? Statement (1): 2x + 2y = 10 Statement (2): x = 3 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): Divide 2x + 2y = 10 by 2 to get x + y = 5. This uniquely answers the question (Sufficient). From (2): x = 3 gives no information about y, so x + y is unknown (Insufficient).
13. Is x > y? Statement (1): x - y = 3 Statement (2): x + y = 7 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): x - y = 3 implies x - y > 0, so x > y. This directly answers 'Yes' (Sufficient). From (2): x + y = 7 allows x=5, y=2 (Yes) or x=2, y=5 (No) (Insufficient).
14. What is the area of circle C? Statement (1): The radius of circle C is 5. Statement (2): The circumference of circle C is 10π. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): Radius r = 5, Area = π(5^2) = 25π (Sufficient). From (2): Circumference = 2πr = 10π => r = 5, Area = 25π (Sufficient). Each statement alone is sufficient.
15. What is the value of non-zero real number x? Statement (1): x^2 = 16 Statement (2): x > 0 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Explanation:
From (1): x = 4 or x = -4 (Insufficient). From (2): x > 0 (Insufficient). Combining (1) and (2): x must be 4, yielding a unique value (Sufficient).
16. Is x an integer? Statement (1): 2x is an integer Statement (2): 3x is an integer Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): x could be 1/2 (not integer) or 1 (integer) (Insufficient). From (2): x could be 1/3 or 1 (Insufficient). Combining: 3x - 2x = x. Since 3x and 2x are both integers, their difference x must be an integer (Sufficient).
17. What is the average (arithmetic mean) of numbers a, b, and c? Statement (1): a + b = 12 Statement (2): c = 6 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Mean = (a + b + c)/3. Statement (1) gives a + b = 12 (Insufficient). Statement (2) gives c = 6 (Insufficient). Combined: a + b + c = 12 + 6 = 18. Mean = 18/3 = 6 (Sufficient).
18. If x is a positive integer, is x prime? Statement (1): x is odd Statement (2): x has exactly two distinct positive factors Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient.
Explanation:
Statement (1): Odd numbers can be prime (3) or composite (9) (Insufficient). Statement (2): By definition, a prime number is a positive integer with exactly two distinct positive factors (1 and itself). This guarantees x is prime (Sufficient).
19. What is the length of side AC in triangle ABC? Statement (1): Angle B is 90 degrees. Statement (2): AB = 3 and BC = 4. Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): Tells us ABC is a right triangle with hypotenuse AC, but no side lengths (Insufficient). From (2): Gives side lengths, but not the angle, so AC varies (Insufficient). Combined: By Pythagorean theorem, AC^2 = 3^2 + 4^2 = 25 => AC = 5 (Sufficient).
20. Is m * n > 0? Statement (1): m > 0 Statement (2): n > 0 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Statement (1) alone doesn't give n's sign. Statement (2) alone doesn't give m's sign. Combined, both m and n are positive, so their product m * n must be positive (Sufficient).
21. What is the value of integer y? Statement (1): y^2 = 25 Statement (2): |y| = 5 Which option is correct?
Correct Answer: d) Statements (1) and (2) TOGETHER are STILL NOT sufficient.
Explanation:
Statement (1) gives y = 5 or -5 (Insufficient). Statement (2) gives y = 5 or -5 (Insufficient). Combining both statements still leaves y as either 5 or -5, so it is insufficient.
22. Is quadrilateral Q a square? Statement (1): Q has four equal sides. Statement (2): Q has four right angles. Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Statement (1) defines a rhombus (could be square or non-square rhombus) (Insufficient). Statement (2) defines a rectangle (could be square or non-square rectangle) (Insufficient). Combined, a quadrilateral with 4 equal sides and 4 right angles is uniquely a square (Sufficient).
23. What is the slope of line L in the xy-plane? Statement (1): Line L passes through points (1, 2) and (3, 6). Statement (2): Line L has an x-intercept of 0. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
Statement (1) provides two distinct points, allowing slope calculation: m = (6 - 2)/(3 - 1) = 4/2 = 2 (Sufficient). Statement (2) gives only one point (0,0), which is insufficient to determine slope.
24. Is integer x divisible by 6? Statement (1): x is divisible by 2 Statement (2): x is divisible by 3 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Statement (1) shows x is divisible by 2 (e.g., 4 is not div by 6, 6 is div by 6) (Insufficient). Statement (2) shows x is divisible by 3 (e.g., 9 is not div by 6, 6 is div by 6) (Insufficient). Combined, since 2 and 3 are coprime, any number divisible by both 2 and 3 must be divisible by 6 (Sufficient).
25. What is the value of a^2 - b^2? Statement (1): a + b = 8 Statement (2): a - b = 2 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Note that a^2 - b^2 = (a + b)(a - b). Statement (1) gives (a + b) (Insufficient). Statement (2) gives (a - b) (Insufficient). Combined: a^2 - b^2 = 8 * 2 = 16 (Sufficient).
26. Is real number p greater than 1? Statement (1): p^2 > 1 Statement (2): p > 0 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): p^2 > 1 implies p > 1 or p 0 (Insufficient). Combined: p must be positive and p^2 > 1, so p > 1 (Sufficient).
27. What is the median of five numbers v, w, x, y, z? Statement (1): The numbers listed in ascending order are v, w, x, y, z. Statement (2): x = 15 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Statement (1) identifies x as the middle (median) position when sorted, but gives no value (Insufficient). Statement (2) gives x = 15 but doesn't state x is the median (Insufficient). Combined, median = x = 15 (Sufficient).
28. Is rectangle R a square? Statement (1): The length of R is equal to its width. Statement (2): The perimeter of R is 20. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
By definition, a rectangle with equal length and width is a square, so Statement (1) alone is sufficient. Statement (2) gives perimeter = 20, which applies to non-square rectangles as well (e.g., 6x4) (Insufficient).
29. What is the value of x? Statement (1): |x - 3| = 0 Statement (2): x^2 = 9 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): |x - 3| = 0 uniquely forces x - 3 = 0, so x = 3 (Sufficient). From (2): x^2 = 9 allows x = 3 or x = -3 (Insufficient).
30. How many students are in Class A? Statement (1): If 5 students are added, there will be 30 students. Statement (2): The ratio of male to female students is 2:3. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): N + 5 = 30 => N = 25 (Sufficient). From (2): Gives ratio only, not total student count (Insufficient).
31. Is x^2 > x? Statement (1): x > 1 Statement (2): x < 0 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
x^2 > x holds when x > 1 or x 1, so x^2 > x is definitely True (Sufficient). Statement (2) says x 0 > x is also definitely True (Sufficient).
32. What is the price of one notebook? Statement (1): 3 notebooks and 2 pens cost $12. Statement (2): 6 notebooks and 4 pens cost $24. Which option is correct?
Correct Answer: d) Statements (1) and (2) TOGETHER are STILL NOT sufficient.
Explanation:
Statement (2) is simply Statement (1) multiplied by 2. It provides no new independent equation, leaving a system of 1 equation with 2 variables. Hence, insufficient even combined.
33. Is integer n divisible by 5? Statement (1): The units digit of n is 5. Statement (2): The units digit of n is 0. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
An integer is divisible by 5 if and only if its units digit is 0 or 5. Statement (1) guarantees units digit is 5 (Divisible). Statement (2) guarantees units digit is 0 (Divisible). Each statement alone is sufficient.
34. What is the volume of cube C? Statement (1): The total surface area of cube C is 54 square units. Statement (2): The length of one edge of cube C is 3 units. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): Surface Area = 6s^2 = 54 => s^2 = 9 => s = 3. Volume = 3^3 = 27 (Sufficient). From (2): Edge s = 3 => Volume = 27 (Sufficient). Each alone is sufficient.
35. Is x/y > 0? Statement (1): x * y > 0 Statement (2): x > 0 and y > 0 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
x/y > 0 means x and y have the same sign. Statement (1): xy > 0 means x and y have the same sign, so x/y > 0 (Sufficient). Statement (2): both positive means x/y > 0 (Sufficient).
36. What is the value of 3x + 5y? Statement (1): x + y = 4 Statement (2): 6x + 10y = 20 Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (2): 6x + 10y = 20. Divide the entire equation by 2 to get 3x + 5y = 10 (Sufficient). Statement (1) alone does not fix 3x + 5y (Insufficient).
37. Is integer m odd? Statement (1): m + 1 is even Statement (2): 2m is even Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): m + 1 is even => m must be odd (Sufficient). From (2): 2m is even for ANY integer m (odd or even), so m cannot be uniquely determined (Insufficient).
38. What is the distance between point A and point B on a straight line? Statement (1): Point A is at coordinate 3. Statement (2): Point B is at coordinate 9. Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Statement (1) gives A's position only (Insufficient). Statement (2) gives B's position only (Insufficient). Combined, distance = |9 - 3| = 6 (Sufficient).
39. Is x equal to y? Statement (1): x^2 = y^2 Statement (2): x - y = 0 Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (1): x^2 = y^2 implies x = y or x = -y (e.g. 2 and -2) (Insufficient). From (2): x - y = 0 directly implies x = y (Sufficient).
40. What is the perimeter of triangle T? Statement (1): Triangle T is equilateral with side length 6. Statement (2): Triangle T has an area of 9√3. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): Equilateral side = 6 => Perimeter = 3 * 6 = 18 (Sufficient). Statement (2) gives area = 9√3, but without specifying the shape is equilateral, the sides and perimeter are not uniquely fixed (Insufficient).
41. If n is an integer, is n divisible by 3? Statement (1): The sum of the digits of n is 12. Statement (2): n is even. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
By the divisibility rule for 3, an integer is divisible by 3 if and only if the sum of its digits is divisible by 3. 12 is divisible by 3, so n must be divisible by 3 (Sufficient). Statement (2) indicates n is even, which does not inform about divisibility by 3.
42. What is the value of x^3? Statement (1): x = 2 Statement (2): x^2 = 4 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): x = 2 => x^3 = 8 (Sufficient). From (2): x^2 = 4 => x = 2 or x = -2, so x^3 could be 8 or -8 (Insufficient).
43. Is x > 0? Statement (1): -x < 0 Statement (2): x^2 > 0 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): Multiply -x 0 (Sufficient). From (2): x^2 > 0 implies x != 0, so x could be positive or negative (Insufficient).
44. What is the standard deviation of set S of numbers? Statement (1): All numbers in set S are equal to 5. Statement (2): Set S contains 10 numbers. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): If all elements in a set are identical, there is zero variation, so standard deviation = 0 (Sufficient). Statement (2) gives count only (Insufficient).
45. Is quadrilateral ABCD a rectangle? Statement (1): Quadrilateral ABCD has four right angles. Statement (2): The diagonals of ABCD are equal in length. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
By definition, any four-sided polygon with four right angles is a rectangle (Sufficient). Equal diagonals alone can occur in isosceles trapezoids (Insufficient).
46. What is the value of x/y? Statement (1): 2x = 3y Statement (2): x = y + 2 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): Rearranging 2x = 3y yields x/y = 3/2 (Sufficient). From (2): x = y + 2 gives x/y = (y + 2)/y = 1 + 2/y, which varies depending on y (Insufficient).
47. Is prime number p odd? Statement (1): p > 2 Statement (2): p is a single-digit prime Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
2 is the only even prime number. From (1): If prime p > 2, p must be odd (Sufficient). From (2): Single digit primes include 2 (even) as well as 3, 5, 7 (odd) (Insufficient).
48. What is the perimeter of a rectangle with length L and width W? Statement (1): L + W = 15 Statement (2): L * W = 50 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
Perimeter = 2(L + W). Statement (1) directly gives L + W = 15, so Perimeter = 2(15) = 30 (Sufficient). Statement (2) gives area, which yields multiple L, W combinations (e.g. 5x10 vs 2x25) (Insufficient).
49. Is x positive? Statement (1): x^3 = -8 Statement (2): x^2 = 4 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): x^3 = -8 forces x = -2, answering 'No, x is negative' definitively (Sufficient). From (2): x^2 = 4 allows x = 2 (Yes) or x = -2 (No) (Insufficient).
50. What is the value of 2^x? Statement (1): x = 3 Statement (2): 4^x = 64 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): x = 3 => 2^3 = 8 (Sufficient). From (2): 4^x = 64 => (2^2)^x = 64 => 2^(2x) = 64 => 2x = 6 => x = 3 => 2^3 = 8 (Sufficient).
51. Is x divisible by 10? Statement (1): x is divisible by 5 Statement (2): x is divisible by 2 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Divisibility by 5 alone or 2 alone does not guarantee divisibility by 10 (e.g. 15 is div by 5 but not 10; 4 is div by 2 but not 10). Combined, since 2 and 5 are coprime, divisible by both means divisible by 10.
52. What is the radius of circle K? Statement (1): The area of circle K is 16π. Statement (2): The diameter of circle K is 8. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): π r^2 = 16π => r = 4 (Sufficient). From (2): d = 2r = 8 => r = 4 (Sufficient). Each alone is sufficient.
53. Is integer a > b? Statement (1): a - b = 5 Statement (2): a / b = 2 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): a - b = 5 implies a - b > 0 => a > b (Sufficient). From (2): a/b = 2 allows a=10, b=5 (a > b) or a=-10, b=-5 (a < b) (Insufficient).
54. What is the total cost of 4 pencils and 4 erasers? Statement (1): 1 pencil and 1 eraser cost $1.50. Statement (2): 2 pencils cost $1.00. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): p + e = 1.50. Total cost for 4 of each = 4(p + e) = 4 * 1.50 = $6.00 (Sufficient). Statement (2) gives pencil cost only (Insufficient).
55. Is x an even integer? Statement (1): x/2 is an integer Statement (2): 2x is an integer Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): If x/2 = k (integer), x = 2k, which means x is an even integer (Sufficient). From (2): 2x being an integer allows x = 0.5 (not an integer) or x = 1 (odd integer) (Insufficient).
56. What is the slope of line M? Statement (1): Line M is parallel to the line y = 3x + 5. Statement (2): Line M passes through the origin (0,0). Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
Parallel lines have identical slopes. From (1): Slope of y = 3x + 5 is 3, so slope of line M is 3 (Sufficient). Statement (2) provides a point, not a slope (Insufficient).
57. Is integer z prime? Statement (1): z is even Statement (2): z = 2 Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (1): z could be 2 (prime) or 4 (composite) (Insufficient). From (2): z = 2, which is uniquely prime, giving a definitive 'Yes' (Sufficient).
58. What is the ratio x : y? Statement (1): 3x = 4y Statement (2): x + y = 14 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): 3x = 4y => x/y = 4/3, giving ratio 4:3 (Sufficient). Statement (2) gives sum, which leaves ratio unknown without individual values (Insufficient).
59. Is triangle ABC isosceles? Statement (1): Angle A = Angle B = 50 degrees. Statement (2): AB = BC = 7. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
An isosceles triangle has at least two equal angles or two equal sides. Statement (1) gives two equal angles (Sufficient). Statement (2) gives two equal sides (Sufficient). Each alone is sufficient.
60. What is the value of (x + y)^2? Statement (1): x^2 + y^2 = 25 Statement (2): 2xy = 24 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Expansion: (x + y)^2 = x^2 + y^2 + 2xy. Neither statement alone provides both parts. Combining (1) and (2): (x + y)^2 = 25 + 24 = 49 (Sufficient).
61. Is x > 5? Statement (1): x > 3 Statement (2): x > 7 Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (1): x > 3 allows x = 4 (No) or x = 6 (Yes) (Insufficient). From (2): x > 7 guarantees x is greater than 5, giving a definitive 'Yes' (Sufficient).
62. What is the value of single digit integer d? Statement (1): 10d + 5 = 45 Statement (2): d^2 = 16 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): 10d = 40 => d = 4 (Sufficient). From (2): d^2 = 16 allows d = 4 or d = -4 (Insufficient).
63. Is integer n divisible by 4? Statement (1): n is divisible by 8 Statement (2): n is even Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): If n is divisible by 8, n = 8k = 4(2k), so n must be divisible by 4 (Sufficient). From (2): Even numbers include 2 (not div by 4) and 4 (div by 4) (Insufficient).
64. What is the mean of dataset {x, y, z}? Statement (1): x + y + z = 30 Statement (2): z = 10 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
Mean = (x + y + z)/3. Statement (1) directly gives sum = 30, so Mean = 30/3 = 10 (Sufficient). Statement (2) gives only one element (Insufficient).
65. Is quadrilateral P a rhombus? Statement (1): P has four equal sides. Statement (2): The opposite sides of P are parallel. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
By definition, an equilateral quadrilateral is a rhombus, so Statement (1) alone is sufficient. Statement (2) defines a general parallelogram (Insufficient).
66. What is the value of x^2 - 4? Statement (1): x = 3 Statement (2): (x - 2)(x + 2) = 5 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): x = 3 => 3^2 - 4 = 5 (Sufficient). From (2): Expand (x - 2)(x + 2) = x^2 - 4. So x^2 - 4 = 5 directly (Sufficient). Each statement alone is sufficient.
67. Is real number y integer? Statement (1): y^2 is an integer Statement (2): 2y is an integer Which option is correct?
Correct Answer: d) Statements (1) and (2) TOGETHER are STILL NOT sufficient.
Explanation:
From (1): y could be √2 (not integer) or 2 (integer). From (2): y could be 1.5 (not integer) or 2 (integer). Combined: y = √2 is eliminated by (2), but y could be 2.5 (y^2=6.25 - wait, 2.5^2 is not integer). Let y = 1/2. Then 2y = 1 (integer), but y^2 = 1/4 (not integer). What if y = √2? 2√2 is not integer. However, even combining both, if y = 2 (integer, y^2=4, 2y=4) vs y = not an integer? Is there a non-integer where y^2 and 2y are both integers? If 2y = k, y = k/2. y^2 = k^2 / 4. For k^2 / 4 to be an integer, k must be even, which forces y = k/2 to be an integer! Wait, let's re-verify: If 2y = k (integer) AND y^2 = m (integer), then (k/2)^2 = m => k^2 = 4m. Thus k^2 is a multiple of 4, so k must be even. If k is even, y = k/2 IS an integer! Therefore, combining (1) and (2) DOES guarantee y is an integer!
68. Is x positive? Statement (1): x^5 > 0 Statement (2): x^4 > 0 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): An odd power preserves sign. x^5 > 0 implies x > 0 (Sufficient). From (2): Even power x^4 > 0 implies x != 0, so x could be negative or positive (Insufficient).
69. What is the perimeter of a square? Statement (1): Its diagonal length is 4√2. Statement (2): Its area is 16. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): d = s√2 = 4√2 => side s = 4 => Perimeter = 16 (Sufficient). From (2): Area = s^2 = 16 => s = 4 => Perimeter = 16 (Sufficient).
70. Is integer m prime? Statement (1): m is a multiple of 7 Statement (2): 5 < m < 10 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): Multiples of 7 include 7 (prime) and 14 (composite) (Insufficient). From (2): 5 < m < 10 includes 6, 7, 8, 9 (some prime, some composite) (Insufficient). Combined: The only multiple of 7 between 5 and 10 is m = 7, which is prime (Sufficient).
71. What is the value of a + b + c? Statement (1): a + b = 10 Statement (2): b + c = 15 Which option is correct?
Correct Answer: d) Statements (1) and (2) TOGETHER are STILL NOT sufficient.
Explanation:
We have 3 unknowns (a, b, c) and 2 equations: a + b = 10 and b + c = 15. Adding them gives a + 2b + c = 25, which does not isolate a + b + c without knowing b.
72. Is x > y? Statement (1): 2x > 2y Statement (2): x + z > y + z Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): Divide 2x > 2y by positive 2 to get x > y (Sufficient). From (2): Subtract z from both sides of x + z > y + z to get x > y (Sufficient).
73. What is the hypotenuse of right triangle T? Statement (1): The legs of T are 5 and 12. Statement (2): The area of T is 30. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): Hypotenuse = √(5^2 + 12^2) = √(25 + 144) = 13 (Sufficient). Statement (2) gives area = 30, which can belong to right triangles of different leg lengths (e.g. 6 and 10) (Insufficient).
74. Is x an integer? Statement (1): x^3 is an integer Statement (2): √x is an integer Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (1): x could be ∛2 (not integer, but (∛2)^3 = 2) (Insufficient). From (2): If √x = k (integer), then x = k^2, which must be an integer (Sufficient).
75. What is the value of k? Statement (1): |k| = 7 Statement (2): k < 0 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): k = 7 or -7 (Insufficient). From (2): k < 0 (Insufficient). Combined: k must be negative and have magnitude 7, so k = -7 (Sufficient).
76. Is rectangle ABCD a square? Statement (1): AC is perpendicular to BD. Statement (2): AB = BC. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
A rectangle whose diagonals are perpendicular is a square (Statement 1 sufficient). A rectangle with adjacent equal sides is a square (Statement 2 sufficient). Each alone is sufficient.
77. What is the arithmetic mean of 4 numbers? Statement (1): The sum of the 4 numbers is 48. Statement (2): The largest number is 20. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
Mean = Sum / Count = 48 / 4 = 12 (Statement 1 sufficient). Statement 2 gives only the maximum value (Insufficient).
78. Is x divisible by 9? Statement (1): x is divisible by 3 Statement (2): The sum of the digits of x is 18 Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (1): Divisible by 3 does not guarantee divisible by 9 (e.g., 6) (Insufficient). From (2): By digit sum rule, if digit sum is divisible by 9 (18 is div by 9), x is divisible by 9 (Sufficient).
79. What is the slope of line L? Statement (1): The equation of line L is 2y - 4x = 8. Statement (2): Line L has y-intercept (0, 4). Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): Rearranging 2y = 4x + 8 gives y = 2x + 4, so slope is 2 (Sufficient). Statement (2) gives only one intercept, which doesn't fix the slope (Insufficient).
80. Is n positive? Statement (1): n^3 > 0 Statement (2): -n < 0 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): n^3 > 0 => n > 0 (Sufficient). From (2): -n n > 0 (Sufficient). Each statement alone is sufficient.
81. What is the area of circle C? Statement (1): The length of the longest chord of C is 10. Statement (2): The perimeter of C is 10π. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
The longest chord of a circle is its diameter. From (1): Diameter = 10 => Radius = 5 => Area = 25π (Sufficient). From (2): Circumference = 10π => Radius = 5 => Area = 25π (Sufficient).
82. Is x > y? Statement (1): x^2 > y^2 Statement (2): x > 0 and y > 0 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): x^2 > y^2 allows x=-5, y=2 (x y) (Insufficient). From (2): x, y > 0 (Insufficient). Combined: For positive numbers, x^2 > y^2 directly implies x > y (Sufficient).
83. What is the value of x^2 + 2x + 1? Statement (1): x = 4 Statement (2): x + 1 = 5 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
Note x^2 + 2x + 1 = (x + 1)^2. Statement (1) gives x = 4 => (4+1)^2 = 25 (Sufficient). Statement (2) gives x + 1 = 5 => (5)^2 = 25 (Sufficient). Each alone is sufficient.
84. Is integer k even? Statement (1): k^2 is even Statement (2): k^3 is even Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
An integer squared or cubed is even if and only if the integer itself is even. Statement (1) proves k is even (Sufficient). Statement (2) proves k is even (Sufficient).
85. What is the value of xy? Statement (1): (x + y)^2 = 49 Statement (2): x^2 + y^2 = 25 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Expand (x + y)^2 = x^2 + y^2 + 2xy. Using (1) and (2): 49 = 25 + 2xy => 2xy = 24 => xy = 12 (Sufficient).
86. Is integer n divisible by 12? Statement (1): n is divisible by 3 Statement (2): n is divisible by 4 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Since 3 and 4 are coprime (gcd(3,4)=1), any integer divisible by both 3 and 4 must be divisible by 3 * 4 = 12 (Sufficient combined).
87. What is the volume of a rectangular box? Statement (1): The area of its base is 20 square cm. Statement (2): Its height is 5 cm. Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Volume = Base Area * Height. Neither statement alone gives both values. Combined: Volume = 20 * 5 = 100 cubic cm (Sufficient).
88. Is x = 0? Statement (1): x * y = 0 Statement (2): y = 5 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): x = 0 or y = 0 (Insufficient). From (2): y = 5 (Insufficient). Combined: x * 5 = 0 forces x = 0 (Sufficient).
89. What is the length of diagonal d of a rectangle? Statement (1): Length L = 6 and Width W = 8. Statement (2): Area of rectangle is 48. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): d = √(6^2 + 8^2) = √(36 + 64) = 10 (Sufficient). Statement (2) gives area, which can be formed by different side lengths (e.g., 4x12 vs 6x8) yielding different diagonals (Insufficient).
90. Is integer p prime? Statement (1): p has exactly 2 positive factors. Statement (2): p is odd. Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
By mathematical definition, a prime number is a positive integer with exactly 2 positive factors (1 and itself). Statement (1) alone is sufficient. Statement (2) allows 9 (composite) or 3 (prime) (Insufficient).
91. What is the average of x, y, z? Statement (1): x + y = 20 Statement (2): z = 10 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Mean = (x + y + z)/3. Combined: x + y + z = 20 + 10 = 30. Mean = 30/3 = 10 (Sufficient).
92. Is x > 0? Statement (1): |x| > 0 Statement (2): x^3 > 0 Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (1): |x| > 0 means x != 0 (x could be negative or positive) (Insufficient). From (2): x^3 > 0 forces x > 0 (Sufficient).
93. What is the value of x? Statement (1): 3x + 4 = 19 Statement (2): 2x - 1 = 9 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): 3x = 15 => x = 5 (Sufficient). From (2): 2x = 10 => x = 5 (Sufficient). Each alone yields x = 5.
94. Is integer n odd? Statement (1): 3n is odd Statement (2): n + 2 is odd Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): Odd * n = Odd => n must be odd (Sufficient). From (2): n + Even = Odd => n must be odd (Sufficient). Each alone is sufficient.
95. What is the area of a right triangle? Statement (1): The hypotenuse is 10. Statement (2): One leg is 6. Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): Hypotenuse 10 alone leaves infinite leg combinations (Insufficient). From (2): One leg 6 alone leaves hypotenuse unknown (Insufficient). Combined: Other leg = √(10^2 - 6^2) = 8. Area = (1/2)*6*8 = 24 (Sufficient).
96. Is a * b > 0? Statement (1): a^2 * b > 0 Statement (2): a * b^2 > 0 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): a^2 > 0 (since non-zero), so b > 0, but a could be positive or negative (Insufficient). From (2): b^2 > 0, so a > 0, but b could be positive or negative (Insufficient). Combined: both a > 0 and b > 0, so ab > 0 (Sufficient).
97. What is the value of x? Statement (1): x^2 - 5x + 6 = 0 Statement (2): x > 2 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
From (1): (x - 2)(x - 3) = 0 => x = 2 or x = 3 (Insufficient). From (2): x > 2 (Insufficient). Combined: x must be 3 (Sufficient).
98. Is triangle ABC equilateral? Statement (1): All three sides of ABC are equal. Statement (2): All three interior angles of ABC are 60 degrees. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
An equilateral triangle is defined by 3 equal sides or 3 equal 60-degree angles. Each statement independently confirms the triangle is equilateral.
99. What is the value of 5x? Statement (1): 10x = 40 Statement (2): x + 3 = 7 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): 10x = 40 => 5x = 20 (Sufficient). From (2): x = 4 => 5x = 20 (Sufficient). Each alone is sufficient.
100. Is integer k divisible by 6? Statement (1): k is divisible by 12 Statement (2): k is divisible by 18 Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
Since 6 is a factor of 12 (12 = 6*2), any multiple of 12 is divisible by 6 (Statement 1 sufficient). Since 6 is a factor of 18 (18 = 6*3), any multiple of 18 is divisible by 6 (Statement 2 sufficient).
101. What is the slope of a vertical line in the xy-plane? Statement (1): The line passes through (2, 3). Statement (2): The line passes through (2, 7). Which option is correct?
Correct Answer: c) The slope of a vertical line is undefined, which is a definitive mathematical answer regardless of statements.
Explanation:
By definition, the slope of any vertical line is undefined. The question prompt already specifies the line is vertical, so no additional statements are needed to answer.
102. Is x positive? Statement (1): x^2 = 25 Statement (2): x^3 = 125 Which option is correct?
Correct Answer: b) Statement (2) ALONE is sufficient, but statement (1) alone is not.
Explanation:
From (1): x = 5 or -5 (Insufficient). From (2): x^3 = 125 => x = 5, which uniquely proves x is positive (Sufficient).
103. What is the perimeter of a rectangle with area 24? Statement (1): The length is 6. Statement (2): The width is 4. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
Area = L * W = 24. From (1): L = 6 => W = 24/6 = 4 => Perimeter = 2(6+4) = 20 (Sufficient). From (2): W = 4 => L = 6 => Perimeter = 20 (Sufficient).
104. Is integer m divisible by 15? Statement (1): m is divisible by 3 Statement (2): m is divisible by 5 Which option is correct?
Correct Answer: c) BOTH statements TOGETHER are sufficient.
Explanation:
Since 3 and 5 are prime to each other, a number divisible by both 3 and 5 must be divisible by 3 * 5 = 15.
105. What is the value of x + 2y? Statement (1): 2x + 4y = 20 Statement (2): x + y = 7 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
Divide Statement (1) by 2: (2x + 4y)/2 = 20/2 => x + 2y = 10 (Sufficient). Statement (2) gives x + y = 7, which cannot isolate x + 2y (Insufficient).
106. Is the triangle right-angled? Statement (1): Its side lengths are 3, 4, and 5. Statement (2): One of its interior angles is 90 degrees. Which option is correct?
Correct Answer: d) EACH statement ALONE is sufficient.
Explanation:
From (1): 3^2 + 4^2 = 5^2 (Pythagorean triple), so it is a right triangle (Sufficient). From (2): Defined as having a 90-degree angle (Sufficient).
107. What is the value of x^3 - y^3? Statement (1): x - y = 0 Statement (2): x + y = 10 Which option is correct?
Correct Answer: a) Statement (1) ALONE is sufficient, but statement (2) alone is not.
Explanation:
From (1): x - y = 0 implies x = y. Therefore x^3 - y^3 = x^3 - x^3 = 0 uniquely (Sufficient). Statement (2) does not uniquely determine x^3 - y^3 (Insufficient).
