Advanced Data Sufficiency Practice Set

  1. If x and y are positive even integers, is (40x)x divisible by y?

    2. y is a multiple of 160.

  2. If a ≠ 0, and is

    1. a2 − 2a − 3 = 0
    2. b2 − 4b + 4 = 1
  3. The diameter AD of semicircle DPA is one side of quadrilateral ABCD. One side adjacent to AD is measure 7, and the side opposite AD is measure 16.

    In the figure above, what is the area of semicircle DPA?

    1. The area of quadrilateral ABCD is 140.
    2. The length of the line segment whose endpoints are B and D is 25.

  4. Is x divisible by 39?

    1. x divided by 65 results in a remainder of 7.
    2. x divided by 36 results in a remainder of 15.

  5. If a and b are positive integers with different units digits, and b is the square of an integer, is a also the square of an integer?

    1. The units digit of a + b is 8.
    2. b = 121

  6. What is the value of 8x + y?

    1. 3x − 2y + z = 10
    2. 2(x + 3y) − (y + 2z) = −25

  7. If b and c are two-digit positive integers and b − c = 22d, is d an integer?

    1. The tens digit and the units digit of b are identical.
    2. and x is an integer.

  8. The integers x and y are positive, x > y + 8, and y > 8. What is the remainder when x2 − y2 is divided by 8?

    1. The remainder when x + y is divided by 8 is 7.
    2. The remainder when x − y is divided by 8 is 5.

  9. If x > y > 0, does 3x+1 + 3(2y) = 12v?

    2. 2(3x+2) + 9(2y+1) = 72v
  10. The hypotenuse of right triangle ABE is also side EB of square BCDE.

    In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

    1. The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is
    2. The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

  11. In the sequence T, the first term is the non-zero number a, and each term after the first term is equal to the non-zero number r multiplied by the previous term. What is the value of the fourth term of the sequence?

    1. The sum of the first two terms of the sequence is 16.
    2. The 18th term of the sequence is 81 times the 14th term of the sequence.

  12. A person is to be selected at random from the group T of people. What is the probability that the person selected is a member of club E?

    1. The probability that a person selected at random from group T is not a member of club D and is not a member of club E is
    2. The probability that a person selected at random from group T is a member of club D and not a member of club E is

  13. The population of Town X on January 1, 2010, was 56 percent greater than the population of the same town on January 1, 2005. The population of Town X on January 1, 2015, was 75 percent greater than the population of the same town on January 1, 2010. What was the population of Town X on January 1, 2005?

    1. The population of Town X on January 1, 2015, was 21,840.
    2. The increase in the population of Town X from January 1, 2010, to January 1, 2015, was 4,880 greater than the increase in the population of Town X from January 1, 2005, to January 1, 2010.

  14. What is the value of x − 3z?

    1. x + 4y = 3
    2. x2 + 4xy − 3xz − 12yz = 24
  15. Triangle OAC lies within a circle such that vertex O is also the center of the circle and vertices A and C lie on the circumference of the circle. The measure of angle A is 60 degrees. Arc ABC is defined by the central angle AOC. Point D lies on the circumference of the circle outside arc ABC.

    In the figure above, the center of the circle is O, and the measure of angle CAO is 60 degrees. What is the perimeter of triangle OAC?

    1. The length of arc CDA is 16π greater than the length of arc ABC.
    2. The area of triangle OAC is

  16. If x and y are integers and 3x > 8y, is y > −18?

    1. −9 < x < 20

  17. Over the course of 5 days, Monday through Friday, Danny collects a total of 76 baseball cards. Each day, he collects a different number of cards. If Danny collects the largest number of cards on Friday and the second largest number of cards on Thursday, did Danny collect more than 8 cards on Thursday?

    1. On Friday, Danny collected 49 cards.
    2. On one of the first 3 days, Danny collected 6 cards.

  18. If y = x2, is the equation (25y)(4120) = 1620x true?

    1. (4 − x)(12 − x) = 0
    2. (x − 4)(x − 8)(x − 24) = 0

  19. The ratio of the number of students in an auditorium who are seniors to the number of students in the auditorium who are not seniors is 7:5. How many students are there in the auditorium?

    1. The ratio of the number of students who are seniors who are taking history to the number of students who are not seniors who are taking history is 21:5.
    2. Of the students in the auditorium who are seniors, are taking history; of the students in the auditorium who are not seniors, are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

  20. If y > 0, is

    1. x(x + y) − 4y(x + y) < 0
    2. 5(y + 8) < 20y − 3x + 40