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1 Advanced GMAT Math Questions Version

2 Quantitative Fractions and Ratios 1. The current ratio of boys to girls at a certain school is to 5. If 1 additional boys were added to the school, the new ratio of boys to girls would be 4 to 9. How many boys currently attend the school? E

3 Quantitative Work 1. If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars? If 6 workers can build 4 cars in days, then how many days would it take 8 workers to build 6 cars? Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 4 hours to paint a house, then how many hours will it take Bea to paint a house alone? C. B. C

4 Quantitative Percent 1. What percent of 15 is 15 percent of 1? D 4

5 Quantitative Integer Properties 1. Marge has n candies, where n is an integer such that 0 < n < 50. If Marge divides the candies equally among 5 children, she will have candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children? If x is an integer, and k = (x 1)(x +) (x 1)(x ), then which of the following must be true? k is odd only when x is odd. k is odd only when x is even. k is even only when x is even. k is even only when x is odd. None of the above.. If k is an integer, and 5 1 k is an integer, then k could be each of the following, EXCEPT C. E. D 5

6 Quantitative Integer Properties 1. k is a positive integer and 5 and 16 are both divisors of k. If k = a b 5 c, where a, b and c are positive integers, what is the least possible value of a + b + c? What is the smallest positive integer k such that the product 1575 k is a perfect square? If j and k are positive integers, what is the remainder when 8 10 k + j is divided by 9? (1) k = 1 () j = 1 1. E. A. B 6

7 Quantitative - Powers 1. X X X + + = 9 X X +1 9 X X X. If n is an integer and 5 n > 4,000,000, what is the least possible value of n? w If = 9 10, then w k = k B. D. B 7

8 Quantitative Roots If x = 6, then x = Which of the following is the best approximation of.8 10? D. D 8

9 Quantitative Algebra Which of the following is equivalent to x + 1 for all values of x for which both expressions are defined? x 1 x x 1 x + 1 x + x ( ) x x + x 6. Which of the following is equivalent to for all values of x for which both expressions are defined? x + x x x + x + 1 x + 6 x 1 ( ). If x = y x, then what is the value of y in terms of x? x x 6 x x 6x 1. D. B. C 9

10 Quantitative Algebra ( ) 1. Which of the following is equivalent to xy + xy 1+ y y? xy ( y + 1) ( xy + 1)( xy 1) ( x + y) ( x + y) ( y) y x ( )( ) = What is the value of x? (1) (x 1) = y + x () (x +)(y +) = 0 4. Is x > y? (1) x + y > 0 () x y > 0 1. A. E. E 4. C 10

11 Quantitative Equation Solving x 1. If, then which of the following must be true? y = 5 I. II. III. y x y + x = + x y x = = I only I and II only I and III only II and III only I, II and III 1. D 11

12 Quantitative Word Problems 1. Which of the following could be the sum of three consecutive integers? A group of 10 people plan to contribute equally to pay for a friend s gift that costs G dollars. If n additional people want to contribute to pay for the gift, the required contribution per person will be reduced by how many dollars? Gn n 10 + n Gn 10G+ Gn n Gn + 10G Gn 10 10G n + 10n 1. C. A 1

13 Quantitative Systems of Equations 1. If x and y are integers and x y = 11, then 4x + y CANNOT be What is the value of x + y? (1) xy = 4 () x 8 y =. What is the value of x? (1) xy = 6 () x + y = 5 x + y + z = x + y z = 0 x + y z = 1 4. What is the value of y in the system above? D. E. E 4. A 1

14 Quantitative - Geometry 1. If the perimeter of a certain rectangle is 76 and its area is 60 then what is the length of its shortest side? If the volume of a cube is x cubic feet and the total surface area of the cube is x square feet, then what is the total length, in feet, of all the cube s edges? If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters? B. C. E 14

15 C Quantitative - Geometry B A E D 1. In the above circle AB = 4, BC = 6, AC = 5 and AD = 6. What is the length of DE? A B. In the above circle, the radius is 6 and chord AB = 6. What is the area of the shaded region? π 4π 4 4π 9 6π 6 6π 9 1. D. E 15

16 Quantitative - Geometry ( 6x 48) o m 4x o y o n m n 1. x + y = B C A D. What is the area of the trapezoid above if AB = BC = CD = 6, and AD = 1? C. E 16

17 Quantitative - Geometry x o A 50 o B 1. If the radius of the circle above is equal to the chord AB, then what is the value of x? If the circle above has a radius of 4, what is the perimeter of the inscribed equilateral triangle? B. D 17

18 Quantitative - Geometry B A 1. If the volume of the cube above is 64 cubic centimeters, what is the shortest distance, in centimeters, from point A to point B? A F B E I G D H C. If square ABCD has area x and line segment AE has length 4, and line segment AF has length, then what is the area of IGCH in terms of x? 4x + 1 7x 1 x 4 x x x + 1 7x B. E 18

19 Quantitative - Geometry A B 1. The two circles above have centers at A and B, and their circumferences are x and y respectively. If the two circles touch at one point, what is the distance between A and B? π x + π y x + y π π x + y π x + π y x + y π 1. B 19

20 Quantitative Strange Operators 1. For all numbers x, the operation is defined by If w =, then what is the value of w? x x = x D 0

21 Quantitative - Statistics 1. If the average (arithmetic mean) of, 6, 10, m and n is 9, then what is the average of m + 4 and n? If the average (arithmetic mean) of a and b is 45, and the average (arithmetic mean) of b and c is 5, then a c = What is the average (arithmetic mean) of x and 6y? (1) x + y = 18 () x +y = 1. C. C. B 1

22 Quantitative - Statistics 1. What is the value of (k w ) + (k x ) + (k y )? (1) w, x, and y are three consecutive odd numbers () The mean of w, x, and y is k. If d is the average (arithmetic mean) of a, b and c, then c = d a b d a+ b d a b d a+ b a+ b d 1. B. A

23 Quantitative - Counting 1. If there are 16 people to choose from, what is the ratio of the number of possible 7-person committees to the number of possible 8-person committees? 7:8 8:7 7:9 8:9 9:8. In how many ways can Ann, Bea, Cam, Don, Ella and Fey be seated if Ann and Bea cannot be seated next to each other? If p and q are prime numbers, how many divisors does the product pq have? How many positive integers less than 10,000 are there in which the sum of the digits equals 5? This is a 900-level question! 1. D. C. D 4. C

24 Quantitative Coordinate Geometry 1. In the xy - coordinate plane, the points (a, b ) and (a + k, b ) are on the line defined by y = x 5. What is the value of k? If points (0, -), (6, 0) and (k, 10) all lie on the same line, what is the value of k? C. E 4

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