# GRE 数学部分真题2007-2009

(2007,2009 GRE 数学 部份真题 ) USIV 整理 http://hi.baidu.com/usiv Thursday, December 13, 2007 1. If the sides of a right angled triangle are n, 2n-1, 2n+1 and 'n' being positive, then the value of 'n' is? b)8 c)12 d)15 e)17 Ans: B 2. x<1 Col A : x/y Col B : x+y Ans: D 3. A and B are independent events, p(A)=0.6 and p(B)=0.8. Col a : probobality of happening event A or B is Col b : 0.92 Ans: C 4. Col a: 1+1/2-1/4+1/8-1/16+1/32 Col b: 2(1-1/2+1/4-1/8+1/16-1/32) 5. 1cake +1pie=11.25 and 4cakes+5pie=50 Col a: cost of cake Col b: cost of pie Ans: A 6. What is the value of 'n' when 252^5 is divided by 6^n. Ans : 10 Monday, November 19, 2007 1. Col A : Least +ve integer with 3 different prime factors, each greater than 6 Col B : 1001 Ans: C 2. Twice the sum of 3 integers x ,y and z when divided by 7 gives remainder =1 wt is the remainder when x+y+z is divided by 7.? A. 0 B. 1 C. 2 D. 3 E. 4 Ans : E 3.The area of rectangular region R is equal to the area of rectangular region T.

The Ratio of the length to the width of R is 3 to 1. the length & width of T are 12 & W, respectively. Col A : w Col B : 4 Ans: C 4. Area of a square is 9 and that of a rectangle is 8. ColA ColB perimeter of square perimeter of rectangle Ans: D 5. Where will the point of intersection of the lines 3x - 5y = 7 and 2x + 10y = - 3 lie? A. On X-Axis B. On Y-Axis C. In Quadrant I D. In Quadrant III E. In Quadrant IV Ans : E 6. There are 37 employees in a company X. The month of july has more number of birthdays (of employees) than any other month in the year. Col A: Number of Birthdays in July Col B: 3 Ans: A 7. (1/2 + 1/3)+ (1/4 -1/3) + (1/2-1/4) Ans : 1 8. X^2-x-2 = 0. Number of possible value of X..? Ans: 2 9. F(x) = x^2 + x Col A : F(x+1) Col B : F(x) + F(1) Ans : A 10. Two Isosceles triangle was drawn, equal sides are 1, 1 in both triangle. Angle between equal side in one triangle is X, and in second is Y. and given X > Y. Col A: area of triangle with angle X Col B: area of triangle with angle Y Ans: A 11. Consider circle with centre O. AB is a chord of the circle. AOB is a right angle. C is a point on the circumference of the circle such that angle BOC = 60 degrees. Compare: Col A: Area of Triangle AOB Col B: Area of sector BOC

Ans: A Tuesday, November 20, 2007 1)Twice the sum of 3 integers x ,y and z when divided by 7 gives remainder 1 what is the remainder when x+y+z is divided by 7? Ans: 4 2) (1/2 + 1/3)+ (1/4 -1/3) + (1/2-1/4) = 1 3) 4 points A,B,C,D on a straight line such that AD:AB = 9:1 and AD:AC = 4:1 points A,B,C,D are:A. -20, -8, -10, 16 B. -20, -16, 11, 16 C. -20, -16, -11, 16 D. -20, -16, -11, 7 E. -20, -10, -11, 7 Ans: C 4) If probability of event M occuring is <1/4 Col a: prob of event M not occuring Col b: 3/4 5) A semicircle was given with area 2pie find the perimeter of the semicircle Ans: 2pie+4 6) x when divided by 7 leaves remainder 4.What is the remainder when 2x + 5 is divided by 7? Ans: 6 7) The probability of raining tomorrow night is 0.46 Col a Col b Probability of raining tomorrow night and at high heat temp of 85degress is 0.54 Ans: B Cool |x|<= 6, |y|<=4. Col a Col b The maximum value of |y/x| 1 Ans: D 9) The volume and height of a cylinder is given as 54pi and 6. Find the circumference of the base of cylinder? Ans: 6*pie 10) Given circle is x^2 + y^2 = 49 points on circle are A(3,a) and B(0,b) and given 'a' is positive and 'b' is negative. Col A : length of segment AB Col B : 12

Ans: A 11) Given a figure of triangle with sides t, t, n. If the average of two angles of the triangle is 65 then what is the value of n? Ans: 80 12) 0<1 Col a Col b x y^2 Ans: D 13) xy+x(y+2) when divided by 2 leaves a remainder Cola Colb Remainder 0 Ans: D Wednesday, November 21, 2007 1. x-y =5 & xy != 0 Col a: 1/x-1/y Col b: 5 2. Given f(n+3)=f(n) and f(-1)=6 f(0)= 5 f(1) = 4 then the value of f(Cool is Ans: 6 3. Given 0<1 Col A: X^50+X^51+x^52 ColB : 3(x^52) 4. A circle is inscribed in a square of side 2m. ColA: area of circle ColB: pie Ans: C 5. x^2+2x-8=0 Col A:The sum of the roots Col B: -2 Ans: C 6. An regular pentagon and an equilateral triangle were given. The perimeter of pentagon is twice that of triangle. Col A: Side of pentagon Col B: Side of triangle Ans: A

7. A telephone company has no.'s between 3000-3799. A Company called X uses the numbers from 3300-3499. Out of these managers of Division1 level use numbers ending with 0 or 1. What percent of the telephone company numbers are used by Managers of Division1 level of Comany X? Ans: 5% 8. x^2=1/5(x^2+(8/x^2)) find the value of x? Col A: x Col B: 2 9. A triangle ABC is given. A point D divides the side AB such that a trainge ADC is formed and AD/DB=1/3. If the area of the triangle ABC is r. Find the area of the triangle ADC in terms of r? Ans: r/4 10. If x = -1 then (1/x)+(1/x^2)+(1/x^3)+(1/x^4)=? Ans: 0 11. If x is a positive number which leaves a remainder 2 when divided by 8 and when divided by 5 it leaves a remainder 3. Find the least possible number? col A: x col B: 18 Ans: C 12. In a room there are more than 12 members which are divided into a 5 member group and a 8member group and a 12 member group. Find the least possible members in that room such that finally none were left? Col A the members in the room Col B: 120 Ans: C 13. |x-2|>4 then which of the following is true with the above realation A) -26 B) -4<4 C) -2<4 D) -6<6 Ans: A 14. A rectangular aquarium base has dimensions 10*8 and height 10. Aquarium is filled upto the height of 6, a solid bar is immersed into it... there by increasing the water level to 7. Col a: the bar dimensions Col b: 100 cubics Ans:B 15. Col A: 50 square + 51 Square + 52 square Col B: 3(square of 52) Ans: B

16. Mode of certain list is given as 45 Col A: find the mean Col B: 45 Ans: D Thursday, November 22, 2007 1. If d is the standard deviation of x,y and z then what is the standard of x+6,y+6 and z+6? A.d+6 B. 6d C.12d D.18d E.None Ans: E 2. Out of 45, 25 are married and 38 are houseowners. col A: least no.of houseowners who are married col b: 18 Ans: C 3. A two digit number is a multiple of 3 and thrice this number has 7 in its units place. col a: the number is col B: 69 Ans: D 4. (0.5)^-2 , (0.5)^-1 , (0.5)^0 , (0.5)^1 , (0.5)^2. Find the range of the above numbers Ans: 3.75 5. If n is an integer when divided by 17 leaves a reminder 4, what is the reminder when 5n is divided by 17 Ans : 3 6. In a set of 5 numbers, if 7 is the median, 4 is the mode & mean of the largest & second largest number is 20. Find average of 5 numbers. Ans: 11 7. Where will the point of intersection of the lines 3x + 5y = 7 and 2x - 10y = - 3 lie? A. On X-Axis B. On Y-Axis C. In Quadrant I D. In Quadrant III E. In Quadrant IV Ans: E 8.On a street, there are four houses which are to be painted. There is a choice of three colors, and one

house will be painted with a single color. In how many ways can the houses be painted? A. 4 B. 24 C. 64 D. 81 E. 128 Ans: D 9. A B + BA -----------CBC -----------Col A: B Col B: 2 Ans: C 10.There was a \$25 discount on every purchase of \$75 there was a 10% charge on shipping which was added before the discount and 20% sales tax after the discount was added. If john paid total \$300, what was the original amount of purchase if no sales tax was added per \$75 Ans : 240. 11. Consider circle with centre O. AB is a chord of the circle. AOB is a right triangle C is a point on the circumference of circle such that angle BOC = 60 degrees Compare. Col A : area of triangle AOB Col B : area of sector BOC. Ans : B 12. A company sold a product for x dollars in 1990. The price of product would increase by 2.5% every year. Which of the following expressions could be used to calculate the price of the product in the year 2000? Ans : x*(1.025)^10 13. Given ABCD is a square with perimeter k and M, N, O, P are the midpoints of the square. If with this midpoints another square MNOP is formed then Col A: perimeter of inner square is Col B: 1/2 k Ans: A 14. If x is an integer and (x-5)/2 is an integer. Then which of the following is an integer? A. (x+2)^2/9 B. (x+2)^2/4 .......

Ans: A 15. Col A: The number of real roots of 2x-3/7=0 Col B: The number of real roots of x^2+3=0 Ans: A Friday, November 23, 2007 1. If 0.8 is the probability that a person gets infected with the disease amongst a group, in which a person in a group is infected. Col A : the probablity that a person getting infected if none of the others among the group is infected. Col B : 0.4 Ans: D 2. Given Users of mixers are 14% and Users of AC's are 27%. Find the Range of users excluding the users of mixers and ACs. A) 41% to 59% B) 59% to 73% C)21% to 41% Ans: B 3. A price of product x is increased by p% to give new price y and then price of y is reduced by r% to give original price. Col A: p Col B: r Ans: D 4. Bryan and Kathleen live 150 miles apart. They each drive toward the other's house along a straight road connecting the two, Bryan at a constant rate of 30 miles per hour and Kathleen at a constant rate of 50 miles per hour. If Bryan and Kathleen leave their houses at the same time, how many miles are they from Bryan's house when they meet? A) 40 B) 51.5 C) 56.25 D) 75 E) 93.75 Ans: C 5.The area of rectangular region R is equal to the area of rectangular region T. The Ratio of the length to the width of R is 3 to 1. the length & width of T are 12 & W, respectively. Col A : w Col B : 4 Ans: D 6. (0.5)^-2 , (0.5)^-1 , (0.5)^0 , (0.5)^1 , (0.5)^2. Find the range of the above numbers Ans: 3.75 7.Two semicircles with thier diameters coincident...outer semicircle has diameter 12 feet and inner

semicircle has diameter 8 feet.The outer minus inner was painted with green paint at some cost per sq feet and the inner was painted with red at the same cost per sq feet. Col A: cost of green paint Col B: cost of red paint Ans: A 8. A label of vertical width w is stick on a cylinderical vessel with area A(some number) and height 10 cm. Col a: w Col b: 4.5 Ans: D Monday, November 26, 2007 1. In xy coordinate a square is drawn by connecting y, x, -y and -x coordinate. The area of the square is 36. Col A:Distance between the center of the coordinate and the point in –y coordinate Col B: 2.4 2. x is multiple of 3 and 3x has unit digit 7. Col A: x Col B: 69 Ans: D 3. In a company there are 54 members. If wednesday has more numbers of birthdays then what is the least number of birthdays on wednesday? A. 6 B. 7 C. 8 D. 9 E. 10 Ans: D 4. x and y are positive integers. Col A: remainder when xy+x(y+2) is devided by 2. Col B: 0 Ans: C 5. |J+2|<3 and (k-1)^2=16 Col A: jk Col B: 15 Ans: B 6. If x-x/2-x/4-x/8 = 16 find x? Ans: 128 7. A price of product x is increased by p% to give new price y and then price of y is reduced by r% to

give original price. Col A: p Col B: r Ans: A 8. A label of vertical width w is stick on a cylinderical vessel with area A(some number) and height 10 cm. Cola: w Colb: 4.5 Ans: D 9. A circle was given with radius 6, it contained a shaded area. The degree measure of the unshaded area was 260. Find the area of shaded region. Ans:10pie 10. There is a circular water fountain of Diameter 12m. The wall of the tank has a width of 2m. If the thickness of the fountain is 0.06m, what is the volume of the concrete used in constructing the tank? Ans: 1.68pi cu.m 11. 3^(4n+1) divided by 10 Col A: Remainder Col B: 0 12. x1, x2, x3, x4 & x5 are the events Rate of occurance of them are r1, r2, r3, r4 & r5 E = x1r1+x2r2+x3r3+x4r4+x5r5/(x1+x2+x3+x4+x5) x1=r1=1 x2=r2=2 x3=r3=3 x4=r4=4 x5=r5=5. Find E? Ans: 11/3 13. Given ax^2+bx+c=0, (2x+3)(2x-3)=0 Col a:a+b+c Col b: -5 Ans: C 14. Given average(arithmetic mean) of t,u,v is x. Col a:arithmetic mean of t,u,v and x Col b:x Ans: C 15. Col a: (-2)^-5 Col b: 1 Ans: B Tuesday, November 27, 2007

1. Three points in the coordinate system were given (4,5), (-2,-1) n (1,k) and all lie on the same line… Col A: k Col B: 2 Ans: C 2. A company sold a product for x dollars in 1990. The price of the product would increase by 2.5% every year. Which of the following expressions could be used to calculate the price of the product in the year 2000? A. x * (25)^10 B. x * (0.25)^10 C. x * (1.25) ^ 10 D. x * (1.025)^10 E. x * (0.125) ^ 10 Ans: D 3.There is a circular water fountain of Diameter 12m. The wall of the tank has a width of 2m. If the thickness of the fountain is 0.06m, what is the volume of the concrete used in constructing the tank? On a street, there are four houses which are to be painted. There is a choice of three colors, and one house will be painted with a single color. In how many ways can the houses be painted? A. 4 B. 24 C. 64 D. 81 E. 128 Ans: D 4. 3,1,4,2,3,1,4,2...... is a series in which 3,1,4,2 are repeated for every 4 terms then what is the product of the 67th,68th term? A. 2 B. 4 C. 6 D. 8 E. 3 Ans: C 5. n and k are positive numbers col a: (3^n/ 5^k)^2 colb: (n/k)^2 Ans: D 6. A+B=1 and M+T=2 A and M are positive and B and T are negative Cola :A^2 + B^2 Col b: M^2 + N^2 Ans: D 7.The number of numbers that can be formed by the digits 1,2,3,4,3,2,1. the odd digits are at odd places is given by

A) 430 B) 215 C) 93 D) 36 E) 18 Ans: E 8. The number of numbers that can be formed by the digits 1,2,3,4,3,2,1. the odd digits are at odd places is given by A) 430 B) 215 C) 93 D) 36 E) 18 Ans: E 9. Given a semicircle with radius 2 and its area is 2pie. Find the perimeter of the semicircle. Ans: 4+2pie 10. Two lines 3x-5y=10 and 2x-10y=-3 were given and the point of intersection of these lines lies in which quadrant? Ans: IVth quadrant 11. Given x ,10-x, 2x+3 are three numbers. If mean of these 3 numbers is 24. Find median. 12. If mode of a group of numbers is 78 then what is the range of the numbers. Ans: D 13. If x is not equal to 0. Col a : (x+y)^2 Col b : x^2 +y^2 Ans: D 14. Given a cylinder having volume V. There is one more cylinder that had radius and height both twice of that of the given cylinder, so what is the volume of 2nd cylinder in terms of V? Ans : 8V 15. (x^2+y^2)/2=xy then, col A: x col B: y Ans: D 16. There are 37 employees in a company X. The month of july has more number of birthdays (of employees) than any other month in the year. Col A: Number of Birthdays in July Col B: 3 Ans: A 17. {(0.401)*(0.211)*(0.197)} / {(0.some number)*(0.155)*(0.343)} = this type of question was given .

18. In a triangle the three angles are given as X,X,Y. and the avg of two angles is 65, then what is the possible value of Y in the below options? A. 60 B. 65 C. 70 D. 75 E. 80 Ans: E 19. x is an integer such that x > 3 Col a: number of even factors of 2x Col b: number of odd factors of 3x Ans: D 20. A set contains following no.'s a1,a2,a3.........a100 An= ((n+1)/n)+1) for n odd integer An= -An-1 for n even integer Find it's range... 21. lj+2l<3 and (k-1)^2=16 coll a:jk col b:15 Ans: B 22. A price of product x is increased by p% to give new price y and then price of y is reduced by r% to give original price. Col A: p Col B: r Ans: A 23. Three cuboids R, S and T were given… Sides of R x, y, z Sides of S x+10, y, z Sides of T x, y, z+10 Col A: volume of s minus volume of R Col B: volume of T minus volume of R Ans: D 24. John's salary for a particular month is given by the equation: 1520 + 0.15x where x is the amount obtained from the sales made by John. In July 2000, John got \$300 more than June 2000. By how much did John's sales increase in July 2000 as compared to June 2000? Ans : \$2000 25. A company has 54 employees. There are more birthdays on Wednesdays then on any other day of the week. Col A: minimum no. of birthdays on Wednesdays Col B: 8 Ans: A

Wednesday, November 28, 2007 1. A line 'l' passes through (3,-2) and cuts the coordinate axis. line 'm ' is perpendicular to line 'l' . Column A : Slope of line m Column B : 3/2 Ans:C 2. The distance travelled by a train is 'd' and the time taken is h hrs. Next day the train travels the same distance but reaches 15 min early. What is the average speed in terms of 'd' and 'h'? 3. 7 is the digit on tens place for X and 8 is the digit for tens place for Y. What is the Tens digit for (X+Y) Ans: 5 4. 0<1 col A : 1/x col B : 1/x^2 5. If n * sqrt(0.01) = 1 then What is the value of n? Ans: 10 6. (0.5)^-2 , (0.5)^-1 , (0.5)^0 , (0.5)^1 , (0.5)^2. Find the range of the above numbers Ans: 3.75 7. If a line passes through (-3,2) and cuts coordinate axis. Col A: x-intercept of line Col B: y-intercept of line Ans: B 8. Given f(x)=x^2+x Col a: f(x+1) Col b: f(x) + f(1) Ans: D 9. If a square is inside the circle with its side 's' then What is the area of the circle? Ans: pi * s^2/2 10. Tom brought 'n' shares for 't' dollars( n> 20).Then he sold 'n-20' shares at 't+1' per share and sold the remaining shares at 't+3' per share. Col A: total value of shares sold - total value of shares he bought Col B: t+40 Ans: C

Thursday, December 17, 2009

2. Find the total number of 4-digit odd integers greater than 1000 which have 6 in their hundredth place? 3. Given x((75+y) + (75-y)) = 900. Col A: xy Col B: 100 4. Which of the following cannot be expressed as the sum of three consecutive integers? A. 0 B. 1 C. 2 D. 3 E. 5 5. Given a < 0 < b < c Col A: ac/b Col B: ac 6. If 2^(2x+1) ? 2^2x = 2^1000, then what is the value of x? 7. Col A: (x^x)^x Col B: x^(x^x) 8. How many numbers among nine consecutive positive numbers are divisible by 9? 9. Given a set of numbers: {1/2, 1/8, 2, 8} Col A: Median of the set Col B: Mean of the set 10. There are 10 set of numbers. Each set contains numbers whose unit’s digit represent the set number. For example, if the set number is 1, the numbers in it are 21, 31, 51, and so on.. If the set number is 5 the numbers are 55, 75 and so on. So, if we take the cube of the numbers in set 7, then it represents which of the following set? A. 3 B. 4 C. 5 D. 6 E. 7 11. Given that two points (0, 2) and (2, 0) lie on the circle.

Col A: Radius of the circle Col B: 2 12. If x^2 + y^2 = 2xy, then Col A: x Col B: y 13. Given a set of three numbers {x, x^2, x^3}; -1 < x < 0. What is the ascending order of the set? 14. Given 7 < xy < 13, where x and y are positive integers. Find the total number of different possible values for XY? Wednesday, December 16, 2009 1. If (a)^(-3) + (b)^(-3) = 0 and ab is not equal to zero, then what is the value of (a/b)^2? 2. Col A: The number of ways of forming different groups of 2 kittens each from 8 kittens Col B: The number of ways of forming different groups of 6 kittens each from 8 kittens 3. Col A: sqrt (120) + sqrt (50) Col B: sqrt (90) + sqrt (80) 4. Given x is not equal to 0, y is not equal to 0 and xy is not equal to 0. Col A: 1/(x^3+y^3) Col B: 1/(x+y)^3 5. Given a line equation y = ax+b. If x-intercept is 5 and slope is 2, then Col A: y-intercept Col B: -10 6. Given a set of numbers: {10, 11, 12, 15, 15, 15, 17, 19, 20, 20}. If a number 15 is included in the series, then which of the following will change? A. Mean B. Median C. Mode D. Standard deviation E. None 7. Given total(t) = n * p. If 'p' is reduced by 20%, then by what percentage, 'n' should be increased to balance the total?

9. In a set of five consecutive numbers, if the greatest value is x + 5, then what is the least value? 10. Given two concentric circles. The inner circle is a garden of radius 6m and the outer circle which has a cement path around the garden has a radius 8m. If the width of cement is 0.06, what is the volume of the cement? (Similar to this) 11. Given statistics of bike sales in a company. In 1992, there is a loss of \$600 and in 1993 there is a profit of \$100. If in 1992, 3 million bikes were sold and in 1993, 4 million bikes were sold, then what is the net profit? 15th Dec Gre Quants Question 1. Let ‘S’ indicates sum of all even no's from 1 to 100 and ’N’ indicates sum of all odd no's from 1 to 100, then S-N equals to A. 0 B. 99 C. 100 D. 199 E. 200 (Similar to this) 2. If x > 1, then Col A: (x power x) power x Col B: x power (x to power x) 3. Col A: 2 power x (4 power x) Col B: 2 power 3x 4. Given sets f0, f1, f2, f3, .................. f9 which has numbers according to their unit digits for example f5 has numbers 5, 15, 25, ....... etc. Then, the cubes of the numbers of set f7 are present in which set? A. f2 B. f3 C. f5 D. f7 E. f9 (Similar to this) 5. Given f(x) = 4(x power 2) + 20x + 25; x as an integer. Col A: Minimum value of f(x)

Col B: 0 6. If a ball is dropped from a height of 6 miles, the ball will bounce back with 90% of its previous height. What is the height of the ball after 5th bounce? A. (6+0.9) power 5 B. (6+0.9) power 6 C. 6(0.9) power 4 D. 6(0.9) power5 E. 6(0.9) power 4 7. Given mod(2x-3) < 8; x is an integer. Find the number of possible values of ‘x’? A. 1 B. 2 C. 3 D. 4 E. 5 (Similar to this) 8. A circle is inscribed in a square of length ‘x’. Find the area of the circle inscribed in the square? A. (πx^2) / 2 B. (πx^2) / 4 C. (πx^2) & so on…… 9. Given that there are two parallel lines. P & Q are points on one parallel line and R & S are points on another parallel line. The distance between PQ is same as the distance between RS. If a point ‘T’ is the mid point of PQ, then Col A: Distance from T to R Col B: Distance from T to S

11. Two graphs were given with frequencies on y axis and numbers from 1 to 6 on x axis. The question was to check, which of the following were same for both graphs I. Mean II. Range III. Standard Deviation (Similar to this) 12. If the number of ways arranging a word is 180, then what is the word? In options, five words were given. (Something like this)

13. Col A: Number of positive factors of (2 power 3)(5 power 4)(7 power 5) Col B: Number of positive factors of (11 power 3)(13 power 4)(17 power 5) 14. If DC6 + 2D = D8C. What can be the value of D? A. 0 B. 1 C. 5 D. 8 E. 9 (Similar to this) 15. Given two concentric circles with radius 2 and 5, a tangent is drawn to smaller circle which intersects the larger one at points ‘P’ and ‘T’. Find the length of PT? (Similar to this) 16. Given (2)^(-6) < x < (2)^(-5) Col A: 4x Col B: 1/12

18. There are 20 colored pencils in a pencil stand. The probability of choosing a yellow pencil is 0.8. If there are 6 yellow pencils without an eraser, then what is the probability that a yellow pencil chosen is the one with eraser? A.1/4 B.1/2 C.1/8

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