📝 Representative GRE Practice Questions with Detailed Solutions
Below are representative high-yield problems calibrated to 2026 test difficulty:
1. Quantitative Reasoning, Discrete Problem (Medium)
Question:
If $n$ is an integer and $99 < n^2 < 200$, how many different values can $n$ have?
- (A) 2
- (B) 4
- (C) 6
- (D) 8
- (E) 10
Step-by-Step Solution:
We need integer values of $n$ where $n^2$ falls between 99 and 200.
- $10^2 = 100$ (Valid)
- $11^2 = 121$ (Valid)
- $12^2 = 144$ (Valid)
- $13^2 = 169$ (Valid)
- $14^2 = 196$ (Valid)
- $15^2 = 225$ (Exceeds 200)
- Positive integers: ${10, 11, 12, 13, 14}$ ($5$ values)
- Negative integers: ${-10, -11, -12, -13, -14}$ ($5$ values)
- Total distinct values: $5 + 5 = 10$
Correct Answer: (E) 10
Common Trap: Students frequently forget negative integers and erroneously select (A) or 5.
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2. Quantitative Reasoning, Data Interpretation / Sets (Hard)
Question:
In a survey of 500 students, 60% play cricket, 50% play football, and 30% play both. What percentage of students play neither cricket nor football?
- (A) 10%
- (B) 20%
- (C) 30%
- (D) 40%
- (E) 50%
Step-by-Step Solution:
Using the principle of inclusion-exclusion for overlapping sets:
$$\text{Total} = \text{Cricket} + \text{Football} - \text{Both} + \text{Neither}$$
$$100% = 60% + 50% - 30% + \text{Neither}$$
$$100% = 80% + \text{Neither}$$
$$\text{Neither} = 20%$$
Correct Answer: (B) 20%
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3. Verbal Reasoning, Text Completion (Medium)
Question:
The scientist’s reputation for __________________ was well-earned; every experiment was documented with obsessive precision, and no conclusion was ever advanced without exhaustive supporting data.
- (A) diligence
- (B) creativity
- (C) equivocation
- (D) prescience
- (E) ingenuity
Solution:
The contextual clues in the sentence are "obsessive precision" and "exhaustive supporting data". These directly describe thorough, painstaking effort.
- (A) diligence = careful, persistent, and thorough effort (Correct)
- (C) equivocation = ambiguity (Contradicts clue)
- (D) prescience = foresight (Irrelevant to experimental documentation)
Correct Answer: (A) diligence
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4. Verbal Reasoning, Sentence Equivalence (Hard)
Question:
While the politician’s public speeches were filled with __________________ promises, his private memos revealed a far more pragmatic and cautious approach to governance.
Select the TWO answer choices that produce sentences that are equivalent in meaning.
- [A] grandiose
- [B] modest
- [C] quixotic
- [D] feasible
- [E] visionary
- [F] restrained
Solution:
The trigger word "While" sets up a direct contrast between the public speeches and the private memos ("pragmatic and cautious"). We need two synonyms that mean unrealistic or excessively lofty:
- (A) grandiose = excessively ambitious or overblown
- (C) quixotic = exceedingly idealistic and impractical
Correct Answers: [A] grandiose and [C] quixotic
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