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Extra resources for 501 Quantitative Comparison Questions: Master This Specialized Math Skill and Score Higher!
Subtracting 6x and −1 from both sides makes the equation 9x2 − 6x + 1 = 0. Factor this quadratic into two binomials; 9x2 − 6x + 1 = (3x − 1)(3x − 1). Now the equation is (3x − 1)(3x − 1) = 0. This will be true when 3x − 1 = 0; add one to both sides to give 3x = 1; divide both 1 sides by 3 and x = ᎏ3ᎏ. 145. d. The answer cannot be determined. The binomials in column A are the difference of two squares, so (x + 5)(x − 5) = x2 − 5x + 5x − 25 = x2 − 25. Since there is no indication as to whether x is positive or negative, the term 10x in column B could be either positive or negative and the answer cannot be determined.
The only prime divisible by 7 is 7. It is the same for 11—the only prime divisible by 11 is 11. If any other number was divisible by 7 or 11, it would not be prime. 121. a. 0989. 122. c. When multiplying by 105, move the decimal 5 places to the right to get 425,000. When dividing by 102, move the decimal 2 places to the left to get 425,000. The values in A and B are the same. 23 501 Quantitative Comparison Questions 123. c. The absolute value of opposites is the same number. For example, |5| = 5 and |−5| = 5; x − 8 is the opposite of 8 − x.
A. 04. 004. 004. 10. b. Compare ͙8 ෆ to ͙9 ෆ and ﬁnd that ͙9 ෆ is greater and comes from quantity B. Compare ͙13 ෆ to ͙19 ෆ and ﬁnd that ͙19 ෆ is greater and comes from quantity B. Since both parts of quantity B are greater than the parts of quantity A, quantity B is greater. 11. a. Compare 5 to 4 and ﬁnd that 5 is greater and comes from quantity A. Compare ͙32 ෆ to ͙23 ෆ and ﬁnd that ͙32 ෆ is greater and comes from quantity A. Since both parts of quantity A are greater than the parts of quantity B, quantity A is greater.