GRE Numeric Entry SAMPLE QUESTIONS-8
GRE Numeric Entry Sample Questions
GRE Numeric Entry Sample Questions 1 | GRE Numeric Entry Sample Questions 2 | GRE Numeric Entry Sample Questions 3 | GRE Numeric Entry Sample Questions 4 | GRE Numeric Entry Sample Questions 5 | GRE Numeric Entry Sample Questions 6 | GRE Numeric Entry Sample Questions 7 | GRE Numeric Entry Sample Questions 8 | GRE Numeric Entry Sample Questions 9 | GRE Numeric Entry Sample Questions 10
1. Question :The height and radius of the base of a right circular cone are in the ratio 3:4. The ratio of the total surface area to the curved surface area is 9:5. The sum of the total surface area and the curved surface area of the cone is 224*pi sq.cm. Find the radius of the base.
Correct Answer: 8cm
Explanation:Let the height and radius of the base be 3x and 4x respectively.
Let the total surface area and curved surface area be 9y and 5y respectively.
9y+5y=224*pi
14y=224pi
y=224pi/12=16pi
Curved surface area = 5y = 5*16pi = 80pi ...(1)
Curved surface area =pi*r*l, where r is the radius of the base and l is the slant height
l=sqrt[(3x)^2+(4x)^2]
=sqrt(9x^2+16x^2)
=sqrt(25x) = 5x
Hence, curved surface area = pi*r*l = pi*4x*5x
=20pi*x^2
Equating with (1), we get
20pi*x^2=80pi
x^2=80/20=4
x=2
Radius = 2*4=8cm
[x^2=x*x]
2. Question :The distance between the points (x,-1) and (3,2) is 5. Find the value of x if the point lies in the fourth quadrant.
Correct Answer: 7
The distance between the points is given by
Sqrt[(x-3)^2+(-1-2)^2]=5
Squaring both sides, we get
(x-3)^2+(-3)^2=25
x^2-6x+9+9=25
x^2-6x-7=0
x^2-7x+x-7=0
x(x-7)+1(x-7)=0
x=7,-1
x=7 since (x,-1) lies in the fourth quadrant.
3. Question :The sum of the squares of two positive numbers is 340. The sum of the numbers is 22. Find the difference between the numbers.
Correct Answer: 14
Explanation:Let the numbers be x and y
x+y=22 ...(1)
x^2+y^2=340 ...(2)
Put x = 22-y from (1) in (2)
(22-y)^2+y^2=340
484-44y+y^2+y^2=340
2y^2-44y+484-340
y^2-22y+72=0
y^2-18y-4y+72=0
y(y-18)-4(y-18)=0
y=4, 18
When y = 4, x = 18
When y = 18, x = 4
Difference of the numbers = 18-4=14
[x^2=x*x]
GRE Numeric Entry Sample Questions
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