Free GRE Exam Questions That Helps Candidates Pass

For a square with side ss and diagonal dd, the Pythagorean relation gives d=s2d = s\sqrt{2}. With d=10d=10, solve s=102=1022=52s = \dfrac{10}{\sqrt{2}} = \dfrac{10\sqrt{2}}{2} = 5\sqrt{2}. The area is s2=(52)2=25⋅2=50s^2 = (5\sqrt{2})^2 = 25 \cdot 2 = 50. Choice B. A quick memory aid is the formula Area=d22\text{Area} = \dfrac{d^2}{2} for squares, derived from s2=(d/2)2s^2 = (d/\sqrt{2})^2. Using this shortcut: 102/2=100/2=5010^2/2 = 100/2 = 50. Common pitfalls include forgetting to square the radical or misapplying d=2sd=2s (which would describe a degenerate rectangle, not a square). On test day, pick the method that minimizes arithmetic: either compute ss then square, or apply the direct area–diagonal formula, both yielding the same clean result.

The sentence shows reversal: once dismissed, now supported because results aligned with predictions. The blank must mean “in agreement.” “Congruent” means in harmony or agreement—correct. “Discrepant,” “antithetical,” and “inconsistent” all mean conflicting, which would contradict the support. GRE items often use contrast cues like “once … but later.” Here, “gained traction … with her predictions” signals alignment. Substituting “congruent” produces logical sense. Always check for polarity: negative terms must be consistent with dismissal, while the new evidence is positive.

Let initial green GG and white WW satisfy G:W=3:7G:W=3:7 with G+W=80G+W=80. The ratio parts sum to 3+7=103+7=10, so each part represents 80/10=880/10=8 marbles. Thus G=3⋅8=24G=3\cdot 8=24 and W=7⋅8=56W=7\cdot 8=56. We add xx green marbles; whites remain 5656. We want the new ratio (G+x):W=1:1⇒G+x=W (G+x):W = 1:1\Rightarrow G+x = W. Substitute G=24G=24: 24+x=56⇒x=3224 + x = 56 \Rightarrow x = 32. None of the options shows 32—double-check arithmetic. Recompute: W=56W=56, G=24G=24. To equalize, add 56−24=3256-24=32 greens. Since 32 is not a listed choice, ensure no misread: total 80, ratio 3:7 is correct. The required addition is indeed 32. If the closest option is 30 (C), that would not make 1:1; it would yield G′=54,W=56G'=54, W=56, still short. The mathematically correct answer is 32. If forced to choose among given options, none is correct. On the GRE, such mismatches are rare; when they occur in practice, trust the algebra and re-read the stem. The correct computation shows that 32 green marbles must be added to reach a 1:1 ratio.

(Note: The correct value is 32; options appear to contain an error.)

Denominator: 1x+1y=y+xxy\tfrac{1}{x}+\tfrac{1}{y}=\tfrac{y+x}{xy}. Thus expression = 2/(x+yxy)=2⋅xyx+y=2xyx+y2 / \big(\tfrac{x+y}{xy}\big) = 2 \cdot \tfrac{xy}{x+y} = \tfrac{2xy}{x+y}. Option A. Common pitfalls include forgetting to flip the fraction when dividing or dropping the factor 2. A check: pick easy values x=1,y=1x=1,y=1. Original = 2/(1+1)=12/(1+1)=1. Our simplified form: 2(1)(1)/(1+1)=2/2=12(1)(1)/(1+1)=2/2=1. Match confirmed. On the GRE, fraction-within-fraction simplifications are frequent. Strategy: combine the denominator first, then invert. Plugging test values verifies correctness quickly.

The contrast sets up method-focused, impersonal critique versus personalized attacks. The blank must capture cool analytical distance. “Dispassionate” means impartial and free from strong emotion—precisely the stance described. “Vitriolic” and “incendiary” both suggest harsh, inflammatory tone typical of ad hominem polemics—opposite of the sentence’s praise. “Histrionic” implies theatrical overreaction, again contrary to analytic restraint. On GRE Verbal, look for antithesis cues like “Unlike …” and match the virtue praised—in this case, sobriety and focus on ideas—to a term that denotes emotional restraint. Paraphrasing yields: “critiques are dispassionate … dissecting assumptions,” which preserves coherence and aligns with the methodological emphasis.