Experience the Quality With Free GRE Exam Questions That Helps Candidates Pass

Total of four numbers = 4×15=604 \times 15 = 60. Total of three numbers = 3×14=423 \times 14 = 42. The fourth number = 60−42=1860 - 42 = 18. So the correct answer is 18, not 20. Choice B. Verify: numbers sum to 60; if one is 18, the other three sum 42, giving mean 14. Correct. Common mistake: forgetting to multiply mean by count to get sum. GRE arithmetic mean problems nearly always reduce to sum differences.

Prime factorizations: 8=2³, 9=3², 12=2²·3. LCM uses the highest exponents: 2³ and 3² → 8·9=72. But we must also check 12: 12=2²·3, already divides 72. So LCM=72. Correct answer is A, not C. Double-check: 72/8=9, integer; 72/9=8, integer; 72/12=6, integer. So 72 works and is least. Pitfall: multiplying all three numbers (864), which is far larger than necessary. GRE LCM problems are best solved via prime factorization.

Total balls =4+6+5=15= 4+6+5=15. Total unordered pairs =(152)=105=\binom{15}{2}=105. Pairs of the same color:

Red–Red: (42)=6\binom{4}{2}=6

Blue–Blue: (62)=15\binom{6}{2}=15

Green–Green: (52)=10\binom{5}{2}=10

Sum =6+15+10=31= 6+15+10=31.

Therefore, pairs of different colors =105−31=74= 105 - 31 = 74. Probability =74/105= 74/105. This fraction is already in lowest terms (74 = 2×372 \times 37; 105 = 3×5×73 \times 5 \times 7). An equivalent route uses the complement with sequential probabilities: P(different) =1−[415⋅314+615⋅514+515⋅414]=1−31105=74105= 1 - \big[\tfrac{4}{15}\cdot\tfrac{3}{14} + \tfrac{6}{15}\cdot\tfrac{5}{14} + \tfrac{5}{15}\cdot\tfrac{4}{14}\big] = 1 - \tfrac{31}{105} = \tfrac{74}{105}. Common pitfalls include forgetting “without replacement,” which keeps denominators at 15 then 14, or double-counting ordered pairs; using combinations avoids that trap. Sanity check: different-color pairs should be much more likely than same-color pairs since there are three colors with uneven counts; 74105≈0.704\tfrac{74}{105}\approx 0.704 is reasonable.

Let integers be n,n+2,n+4n, n+2, n+4. Sum: n+(n+2)+(n+4)=3n+6=84n+(n+2)+(n+4)=3n+6=84. Solve: 3n=78⇒n=263n=78 \Rightarrow n=26. So integers are 26, 28, 30. Largest = 30. Choice C. Common pitfall: forgetting step size is 2, not 1. Another is misidentifying the “largest” vs “smallest.” On GRE arithmetic, write expressions systematically and solve step by step to avoid confusion.

Clues: “though experimental” contrasts with “engaging and clear.” The blank must capture readability. “Accessible” means easy to approach or understand, aligning perfectly. “Esoteric,” “obscure,” and “impenetrable” all signal difficulty, which contradicts the praise. GRE Verbal often places surprising contrasts: experimental form yet accessible execution. Inserting “accessible” makes the sentence consistent: praised as accessible despite experimentation.