(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
+ B A
------------
C B C
------------
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
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