Sample questions of Data Sufficiency

SAMPLE QUESTIONSDirections: Each of the following MAT sample data sufficiency problems contains a question followed by two statements, numbered (A) and (B). You need not solve the MAT sample data sufficiency problem; rather you must decide whether the information given is sufficient to solve the problem. The correct answer to a question is if statement (A) ALONE is sufficient to answer the question but statement (B) alone is not sufficient; if statement (B) ALONE is sufficient to answer the question but statement (1) alone is not sufficient; if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient; if EACH statement ALONE is sufficient to answer the question; if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question. Quantity A: (-6)4 Quantity B: (-6)5 if the quantity A is greater; if the quantity B is greater; if the two quantities are equal; if the relationship cannot be determined from the information given. Ans : A Quantity A: Time to travel 95 miles at 50 miles per hour Quantity B: Time to travel 125 miles at 60 miles per hour Quantity A is greater Quantity A equals Quantity B Quantity B is greater Relationship Indeterminate Ans : C Quantity A: (9/13)2 Quantity B: (9/13)1/2 Quantity A equals Quantity B Relationship Indeterminate Quantity B is greater Quantity A is greater Ans : C Quantity A: 4 / 100 Quantity B: 0.012 / 3 Quantity B is greater Quantity A equals Quantity B Quantity A is greater Relationship Indeterminate Ans : C x = 2y + 3 y = -2 Quantity A: x Quantity B: -1 if the quantity in Column A is greater if the quantity in Column B is greater if the two quantities are equal if the relationship cannot be determined from the information given Ans : C x + 2y > 8 Quantity A: 2x + 4y Quantity B: 20 if the quantity in Column A is greater if the quantity in Column B is greater if the two quantities are equal if the relationship cannot be determined from the information given. Ans : D Quantity A: The number of months in 7 years Quantity B: The number of days in 12 weeks if the quantity in Column A is greater if the quantity in Column B is greater if the two quantities are equal if the relationship cannot be determined from the information given Ans : C Quantity A: 1-1/27 Quantity B: 8/9 + 1/81 if the quantity in is greater if the quantity in is greater if the two quantities are equal if the relationship cannot be determined from the information given. Ans : A r/>s/>0/> Quantity A: rs/r Quantity B: rs/s if the quantity A is greater if the quantity B is greater if the two quantities are equal if the relationship cannot be determined from the information given. Ans : B Quantity A: 0.83 Quantity B: 0.81/3 Quantity B is greater Relationship Indeterminate Quantity A is greater Quantity A equals Quantity B Ans : A Quantity A: s Quantity B:7 if the quantity in Column A is greater; if the quantity in Column B is greater; if the two quantities are equal; if the relationship cannot be determined from the information given Ans : D Quantity A: (0.82)2(0.82)3 Quantity B:(0.82)6 if the quantity in Column A is greater; if the quantity in Column B is greater; if the two quantities are equal; if the relationship cannot be determined from the information given. Ans : A For all real numbers a, let a* = 1 - a. Quantity A: ((-1)*)* Quantity B: 2* if the quantity in Column A is greater; if the quantity in Column B is greater; if the two quantities are equal; if the relationship cannot be determined from the information given. Ans : C Quantity A: (x - 1)(x)(x + 1) Quantity B:(x)(x)(x) if the quantity in Column A is greater; if the quantity in Column B is greater; if the two quantities are equal; if the relationship cannot be determined from the information given. Ans : D Quantity A: (3 x 4 x 17) / (121 x 100) Quantity B: (4 x 5 x 19) / (1000 x 121) Quantity A is greater Quantity A equals Quantity B Relationship Indeterminate Quantity B is greater A Consider a triangle PQR. Quantity A: length of PQ + length of QR Quantity B: length of PR Quantity A is greater Quantity B is greater Relationship Indeterminate Quantity A equals Quantity B Ans : A Quantity A: (27 - 13) (296 + 534) Quantity B: (27 + 13) (534 + 296) Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Quantity A is greater Ans : D Quantity A: A = 1.1 Quantity B: 12.11/2 Relationship Indeterminate Quantity B is greater Quantity A equals Quantity B Quantity A is greater Ans : B 100 < y < 200 and 100 < z < 210 Quantity A: y Quantity B: z Quantity A is greater Quantity A equals Quantity B Quantity B is greater Relationship Indeterminate Ans : D y2 + z2 = 34 and yz = 15 Quantity A: y2 + 2yz + z2 Quantity B: (y + z)2 Quantity B is greater Relationship Indeterminate Quantity A is greater Quantity A equals Quantity B Ans : D Quantity A: (y + 5)2 Quantity B: (y - 5)2 Quantity B is greater Relationship Indeterminate Quantity A equals Quantity B Quantity A is greater Ans : B Quantity A: (1/25)1/2 + (1/144)1/2 Quantity B: [(1/25) + (1/144)]1/2 Relationship Indeterminate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Ans : A y2 + z2 = 34 and yz = 15 Quantity A: y2 + 2yz + z2 Quantity B: (y + z)2 Quantity A is greater Relationship Indeterminate Quantity A equals Quantity B Quantity B is greater Ans : C 100 < y < 200 and 100 < z < 210 Quantity A: y Quantity B: z Quantity A is greater Quantity A equals Quantity B Quantity B is greater Relationship Indeterminate Ans : D Quantity A: (y + 5)2 Quantity B: (y - 5)2 Quantity A equals Quantity B Quantity A is greater Relationship Indeterminate Quantity B is greater Ans : C Consider a rectangle. The length of its shorter side is 8, and the length of its diagonal is 16. Quantity A: 30o Quantity B: measure of angle formed by diagonal and shorter side Quantity A is greater Quantity A equals Quantity B Quantity B is greater Relationship Indeterminate Ans : C The sum of three consecutive even numbers is 18. Quantity A: Their average Quantity B: 6 Relationship Indeterminate Quantity A is greater Quantity A equals Quantity B Quantity B is greater Ans : C x - y > 10 Quantity A: y - x Quantity B: 12 Quantity B is greater Quantity A is greater Quantity A equals Quantity B Relationship Indeterminate Ans : A x = 0, y > 0 Quantity A: xy Quantity B: yx Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Ans : C 30.Diagram is illustrative and is not drawn to scale. Quantity A: Measure of angle 3 - Measure of angle 2 Quantity B: Measure of angle 5 - Measure of angle 6 Relationship Indeterminate Quantity A equals Quantity B Quantity B is greater Quantity A is greater Ans : B Quantity A: 29 Quantity B: 92 Quantity B is greater Quantity A is greater Relationship Indeterminate Quantity A equals Quantity B Ans : B 0 < -x < 10 11 < -y < 20 Quantity A: x Quantity B: y Relationship Indeterminate Quantity A equals Quantity B Quantity B is greater Quantity A is greater Ans : D Diagram is illustrative and is not drawn to scale. Given angles 1 and 2 are equal, length of side AB = x, length of side BC = y, length of side AC = z. Quantity A: x + y Quantity B: y + z Quantity A is greater Quantity A equals Quantity B Quantity B is greater Relationship Indeterminate Ans : B Diagram is illustrative and is not drawn to scale. In triangle ABC, AB = AC and measure of angle 1 = 100o. Quantity A: Measure of angle 2 + Measure of angle 3 Quantity B: 90o Quantity B is greater Relationship Indeterminate Quantity A is greater Quantity A equals Quantity B Ans : A x and y are both positive and x/y > 5 Quantity A: 0.2x Quantity B: y Quantity A is greater Quantity B is greater Relationship Indeterminate Quantity A equals Quantity B Ans : A Diagram is illustrative and is not drawn to scale. Given AB = AC and angle BAC = 60o Quantity A: Length of side AB Quantity B: Length of side BC Quantity A equals Quantity B Quantity B is greater Relationship Indeterminate Quantity A is greater Ans : A y2 = 36 Quantity A: y Quantity B: 6 Relationship Indeterminate Quantity A is greaterQuantity B is greater Quantity A equals Quantity B Ans : A Diagram is illustrative and is not drawn to scale. Quantity A: Measure of angle 1 + Measure of angle 2 + Measure of angle 4 Quantity B: 180o Relationship Indeterminate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Ans : D Diagram is illustrative and is not drawn to scale. In triangle ABC, angle A = 60o and AB = AC. Quantity A: Measure of angle 1 + Measure of angle 2 Quantity B: 120o Relationship Indeterminate Quantity A is greater Quantity A equals Quantity B Quantity B is greater Ans : C Diagram is illustrative and is not drawn to scale. Quantity A: Measure of angle 2 + Measure of angle 3 Quantity B: 180o Quantity B is greater Quantity A is greater Quantity A equals Quantity B Relationship Indeterminate Ans : C Diagram is illustrative and is not drawn to scale. AB is the diameter of the circle. Quantity A: Measure of angle 1 Quantity B: Measure of angle 2 Relationship Indeterminate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Ans : D Diagram is illustrative and is not drawn to scale. Quantity A: Measure of angle 1 + Measure of angle 3 Quantity B: Measure of angle 2 + Measure of angle 4 Relationship Indeterminate Quantity A is greater Quantity A equals Quantity B Quantity B is greater Ans : A Diagram is illustrative and is not drawn to scale. In triangle ABC, AB = AC and measure of angle 1 = 100o. Quantity A: Measure of angle 2 + Measure of angle 3 Quantity B: 90o Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Quantity A is greater Ans : A Diagram is illustrative and is not drawn to scale. Given angles 1 and 2 are equal, length of side AB = x, length of side BC = y, length of side AC = z. Quantity A: x + y Quantity B: y + z Quantity B is greater Quantity A equals Quantity B Quantity A is greater Relationship Indeterminate Ans : B x and y are both positive and x/y > 5 Quantity A: 0.2x Quantity B: y Quantity B is greater Relationship Indeterminate Quantity A equals Quantity B Quantity A is greater Ans : D yz < 0 Quantity A: (y - z)2 Quantity B: y2 + z2 Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Ans : A For any positive integer n, n! is the product of all positive integers less than or equal to n. Quantity A: 20! / 17! Quantity B: 80! / 78! Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Ans : A 2 < z < 4 Quantity A: π2z3 Quantity B: π3z2 Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Ans : D Amy, Beth and Charlie divided a pizza amongst themselves. Amy took 30% of the pizza and ate (3/4) of what she took. Beth took 20% of the pizza. Charlie ate (2/5) of what he took. Quantity A: The amount Amy ate Quantity B: The amount Charlie ate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Ans : A p > 0 > q Quantity A: p + q Quantity B: pq The quantity in Column A is greater. The quantity in Column B is greater. The quantities are equal. The relationship cannot be determined from the information given. Ans : D Quantity A: The average (arithmetic mean) of x and y Quantity B: The average (arithmetic mean) of x - 1 and y + 1 The quantity in Column A is greater. The quantity in Column B is greater. The quantities are equal. The relationship cannot be determined from the information given. Ans : C The integer (x - 1) is a prime number between 40 and 50. Quantity A: The sum of all different prime factors of x Quantity B: 14 The quantity in Column A is greater. The quantity in Column B is greater. The quantities are equal. The relationship cannot be determined from the information given. Ans : B A < C B > D > 0 Quantity A: A - B Quantity B: C - D The quantity in Column A is greater. The quantity in Column B is greater. The quantities are equal. The relationship cannot be determined from the information given. Ans : B In a particular jellybean jar, the number of red jellybeans exceeds the number of white ones by a ratio of 3:2. If two red jellybeans were removed, the ratio of red to white jellybeans would be 1:1. Quantity A: The number of white jellybeans in the jar Quantity B: 4 The quantity in Column A is greater. The quantity in Column B is greater. The quantities are equal. The relationship cannot be determined from the information given. Ans : C Is x equal to 0? Quantity A: (x + 1)2 = 12 Quantity B: x2 + 3x = 0 Quantiy A on its own is sufficient to answer the question but Quantiy B on its own is not. Quantiy B on its own is sufficient to answer the question but Quantiy A on its own is not. Both statements together are sufficient to answer the question but neither statement is sufficient on its own. Either statement on its own is sufficient to answer the question Both statements put together are still insufficient to answer the question Ans : C Is p a positive number? Quantity A: p3 > 0 Quantity B: 10p > 1 Quantiy A on its own is sufficient to answer the question but Quantiy B on its own is not. Quantiy B on its own is sufficient to answer the question but Quantiy A on its own is not. Both statements together are sufficient to answer the question but neither statement is sufficient on its own. Either statement on its own is sufficient to answer the question Both statements put together are still insufficient to answer the question Ans : D Lioudmila took a test where there were two types of questions, type I and type II. 2 points were awarded for getting a type I question correct. 5 points were awarded for getting a type II question correct, and there is no penalty for getting questions wrong. How many type I questions did she answer correctly? Quantity A: She answered 11 questions correctly. Quantity B: She was awarded 43 points. Quantiy A on its own is sufficient to answer the question but Quantiy B on its own is not. Quantiy B on its own is sufficient to answer the question but Quantiy A on its own is not. Both statements together are sufficient to answer the question but neither statement is sufficient on its own. Either statement on its own is sufficient to answer the question Both statements put together are still insufficient to answer the question Ans : C a and b are integers. What are the values of a and b? Quantity A: 2a.3b = 144 Quantity B: 2a+1.3b-1 = 96 Quantiy A on its own is sufficient to answer the question but Quantiy B on its own is not. Quantiy B on its own is sufficient to answer the question but Quantiy A on its own is not. Both statements together are sufficient to answer the question but neither statement is sufficient on its own. Either statement on its own is sufficient to answer the question Both statements put together are still insufficient to answer the question Ans : D Is x bigger than 5? Quantity A: 2x + 9 < 4y + 1 Quantity B: 8y + 2 < 5x + 7 Quantiy A on its own is sufficient to answer the question but Quantiy B on its own is not. Quantiy B on its own is sufficient to answer the question but Quantiy A on its own is not. Both statements together are sufficient to answer the question but neither statement is sufficient on its own. Either statement on its own is sufficient to answer the question Both statements put together are still insufficient to answer the question Ans : C