GRE Problem Solving Select Many SAMPLE QUESTIONS-9
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1. Question:Which of the following are the roots of the equation sqrt(7)x^2-6x-13*sqrt(7)=0? Indicate all correct choices.
A. - sqrt(7)
B. 13/sqrt(7)
C. 13*sqrt(7)/7
D. -13*sqrt(7)
E. 13-sqrt(7)
[x^2=x*x]
Correct Answer: A, B and C
Explanation:sqrt(7)x^2-6x-13*sqrt(7) = 0
sqrt(7)x^2 -13x+7x-13*sqrt(7)=0
x[sqrt(7)*x-13]+sqrt(7)[sqrt(7)*x-13]=0
[x+sqrt(7)][sqrt(7)*x-13]=0
x=-sqrt(7), 13/sqrt(7)
Also, 13/sqrt(7) = 13*sqrt(7)/7
Options A, B and C are true.
2. Question:Which of the following is true for the first 24 natural numbers? Indicate all correct options.
A. Their sum is given by 25*24/2
B. Half of them are even
C. Half of them are odd
D. There are 8 prime numbers
E. There are 5 co-prime numbers
Correct Answer: A, B and C
Explanation:There are 24 numbers
Sum of the first n natural numbers is given by n(n+1)/2
Sum of the first 24 natural numbers = 24(24+1)/2 = 24*25/2
Option A is true.
Since even and odd numbers alternate, half of the numbers are even and half are odd.
Options B and C are true.
Prime numbers less than 24 are 2, 3, 5, 7, 11, 13, 17, 19, 23
There are 9 prime numbers and hence option D is false.
There can be more than 5 pairs of co-prime numbers and hence option E is false.
3. Question:The arithmetic mean of two numbers is 5 and the geometric mean is 4. Which of the following are the numbers? Indicate all correct options.
A. 2
B. 4
C. 6
D. 8
E. 10
Correct Answer: A and D
Explanation:Let the two numbers be x and y
(x+y)/2 = 5 and sqrt(xy)=4
x+y = 5*2 and xy = 4^2=16
Put x = 10-y in xy=16
(10-y)y=16
10y-y^2=16
y^2-10y+16=0
y^2-8y-2y+16=0
y(y-8)-2(y-8)=0
(y-2)(y-8) = 0
The numbers are 2 and 8
Options A and D are true. All other options are wrong.
[4^2=4*4]
GRE Problem Solving Select Many Sample Questions
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