Hard GRE Practice Questions

413 free hard-difficulty GRE questions, drawn live from KomFi's calibrated bank. These are the items that separate top scorers — every one carries a full explanation and trap analysis once you sign in.

1. DUAL-SCALE GRAPH: Helix Biotech — Headcount and Revenue per Employee, 2022–2026 Left axis: Employees (bars). R
2. Solve for x: x - 5 = √(x - 3)
3. Which of the following must be a factor of the integer n if n^2 is divisible by 72?
4. Common information: n is an integer and 2^n = k. Quantity A: 2^n+1 + 2^n+1 Quantity B: 2^n+2 How do the two qu
5. 0 < a < b < 1. Quantity A: dfracab Quantity B: dfraca+1b+1
6. A fair six-sided die (faces 1 through 6) is rolled twice, and the two results are recorded. Quantity A: The pr
7. Solve for x: |2x - 3| = |x + 6|
8. Which of the following describes all real values of x for which |2x - 5| > 9?
9. If 5 people are to be seated in a row of 5 chairs, but two people, A and B, must not sit in the two end chairs
10. If n is a positive integer such that n has an odd number of positive divisors, which of the following must be
11. Given that x > 0 and x + dfrac1x = 3. Quantity A: x^2 + dfrac1x^2 Quantity B: x^3 + dfrac1x^3 Which of the fol
12. A real number x satisfies |2x - 7| < 5. Which of the following expressions must be positive for EVERY x in thi
13. A function is defined by f(x) = √(25 - x^2). For how many integer values of x is f(x) a real number?
14. In a study, the variable x satisfies |2x - 5| < 7. Indicate ALL values that COULD be a value of x. (A) -1 quad
15. Which of the following is true about the price per ounce of the two brands?
16. Common information: x is a nonzero number and -1 < x < 1. Quantity A: x^3 Quantity B: x^5 How do the two quant
17. A data set consists of 5 numbers whose average (arithmetic mean) is 12. Quantity A: The median of the data set
18. In a certain sequence, a₁ = 2 and a_n = 3a_n-1 - 2. What is the value of a₅?
19. A store marks up an item by p% over its cost, then sells it at a discount of p% off the marked price. The fina
20. In the xy-plane, line k passes through the points (-2, 5) and (4, -7). Line m is perpendicular to line k and p
21. Let x and y be real numbers with x+y=10. Indicate ALL values that the product xy could take.
22. A jar contains red and blue marbles only. If two marbles are drawn at random without replacement, the probabil
23. In triangle ABC, two of the side lengths are 8 and 5. Indicate ALL integer values of the third side c for whic
24. It is given that 0 < a < b. Quantity A: dfracab Quantity B: dfraca+3b+3
25. Given that n is an integer and n^2 ≤ n. Quantity A: n Quantity B: 0 Which of the following is true?
26. A dual-scale graph shows a retailer's monthly performance for four months. LEFT axis (bars) is Units Sold; RIG
27. Common information: p is a prime number greater than 3. Quantity A: the remainder when p^2 is divided by 12 Qu
28. In a circle, central angle AOB and inscribed angle ACB intercept the same minor arc AB. Quantity A: The measur
29. How many distinct 4-digit integers can be formed using the digits 0, 1, 2, 3, 4, 5 such that no digit is repea
30. Common information: A quantity grows by 20% and then the result decreases by 20%. Quantity A: The final value

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