GRE Section 2 Quantitative

GRE Section 2 Quantitative practice questions, page 12 of 17, with answer review and explanations.

Question 56

A. The quantity in Column A is greater; B. The quantity in Column B is greater; C. The quantities are equal; D. The relationship cannot be determined from the information given. Reveal Solution Hide Solution Discussion 241 Suggested Answer: A 🗳️ Both triangles are right triangles. The triangle described in Column A has legs 3 and 4 units long. The triangle described in Column B has legs 3 units long each. Hence, the hypotenuse and, in turn, the perimeter of the triangle described in Column A must be greater than those of the triangle described in Column B. Theres no need to calculate either hypotenuse or perimeter.

  1. The quantity in Column A is greater;
  2. The quantity in Column B is greater;
  3. The quantities are equal;
  4. The relationship cannot be determined from the information given.

Question 57

A. The quantity in Column A is greater; B. The quantity in Column B is greater; C. The quantities are equal; D. The relationship cannot be determined from the information given. Reveal Solution Hide Solution Discussion 241 Suggested Answer: B 🗳️ Quantity A (ad) is a negative fractional number greater than a and approaching zero (0). Similarly, Quantity B (bc) is a negative fractional number greater than b and approaching zero (0). But ad must be less than cd (that is, further to the left than cd on the number line). Why? If a and b were both multiplied by c (a positive number), the inequality between a and b (a <b) would remain unchanged: ac < bc. It makes sense that if a is ultiplied instead by a positive number D. that is greater than c, then the inequality between a and b not only remains the same but actually increases. In any event, ad < bc

  1. The quantity in Column A is greater;
  2. The quantity in Column B is greater;
  3. The quantities are equal;
  4. The relationship cannot be determined from the information given.

Question 58

A. The quantity in Column A is greater; B. The quantity in Column B is greater; C. The quantities are equal; D. The relationship cannot be determined from the information given. Reveal Solution Hide Solution Discussion 241 Suggested Answer: A 🗳️ The quickest route to the correct answer is to compare corresponding terms. For example, compare (in Column A) to (in Column B). Notice that . When you add the same number to a fractions numerator as its denominator, the fractions value increases, and so . You can analyze the other corresponding fraction pair in the same way. The value of the each fraction in Column A is greater than the value of the corresponding term in Column B. Thus, the sum of the fractions in Column A must be greater than the sum of the fractions in Column B.

  1. The quantity in Column A is greater;
  2. The quantity in Column B is greater;
  3. The quantities are equal;
  4. The relationship cannot be determined from the information given.

Question 59

A. The quantity in Column A is greater; B. The quantity in Column B is greater; C. The quantities are equal; D. The relationship cannot be determined from the information given. Reveal Solution Hide Solution Discussion 241 Suggested Answer: D 🗳️ The longest side may, but need not, pass through the center of the circle. Thus, its length could be either equal to or less than the circles diameter. NOTE: If the triangle were equilateral, the correct answer would have been choice (B); if it were a right triangle, the correct answer would have been choice (C).

  1. The quantity in Column A is greater;
  2. The quantity in Column B is greater;
  3. The quantities are equal;
  4. The relationship cannot be determined from the information given.

Question 60

A. The quantity in Column A is greater; B. The quantity in Column B is greater; C. The quantities are equal; D. The relationship cannot be determined from the information given. Reveal Solution Hide Solution Discussion 241 Suggested Answer: C 🗳️ The expression in Column A is a perfect cube, and the expression in Column B is a perfect square: As you can see, Quantity A equals Quantity B.

  1. The quantity in Column A is greater;
  2. The quantity in Column B is greater;
  3. The quantities are equal;
  4. The relationship cannot be determined from the information given.