Problem Solving Select Many GRE Sample Questions 2
GRE Problem Solving Select Many Sample Questions
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1. Question:The distance between the points (4,p) and (1,0) is 5. Which of the following is the value of p? Indicate all such choices.
- A. 4
- B. -2
- C. 2
- D. 0
- E. -4
Explanation:
Distance between (4,p) and (1,0) = 5
Sqrt[(4-1)^2+(p-0)^2] = 5
Squaring both sides, we get
3^2+p^2= 5^2
9+p^2=25
p^2=25-9=16
p=sqrt(16) = 4, -4
Options A and E are true. All other options are false.
[p^2=p*p]
2. Question:
Which point is nearest to the origin? Indicate all correct options.
- A. (-1, -1)
- B. (1, 1)
- C. (2,0)
- D. (-2,2)
- E. (0,2)
Explanation:
The origin is the point (0,0)
The distance of the origin from the different points is
(-1,-1): Sqrt[(-1-0)^2+(-1-0)^2]= sqrt(1+1)= sqrt(2)
(1,1): Sqrt[(1-0)^2+(1-0)^2] = sqrt(1+1) = sqrt(2)
(2,0): Sqrt[(2-0)^2+(0-0)^2] = sqrt(4+0) = 2
(-2,2): Sqrt[(-2-0)^2+(2-0)^2] = sqrt(4+4) = sqrt(8)
(0,2): Sqrt[(0-0)^2+(2-0)^2] = sqrt(4) = 2
The points (-1,-1) and (1,1) are the closest.
Options A and B are true.
[4^2=4*4]
3. Question:
f(t) = 2t^2+2/t^2+5/t+5t. Which of the following is true? Indicate all correct choices.
- A. f(1/t) = -f(t)
- B. f(-t) = -f(t)
- C. f(1/t) = f(t)
- D. 1/f(t) = f(1/t)
- E. f(1) = 14
[t^2=t*t]
Correct Answer: C and EExplanation:
f(t)=2t^2+2/t^2+5/t+5t
-f(t) = -2t^2-2/t^2-5/t-5t
f(1/t) = 2(1/t)^2+2(1/1/t)^2+5/(1/t)+5(1/t)
= 2/t^2+2t^2+5t+5/t
f(-t)=2(-t)^2+2/(-t)^2+5/(-t)+5(-t)
= 2t^2+2/t^2-5/t-5t
1/f(t)=1/(2t^2+2/t^2+5/t+5t)
f(1/t) is not equal to -f(t). Option A is false.
f(-t) is not equal to -f(t). Option B is false.
f(1/t)=f(t). Option C is true.
1/f(t) is not equal to f(1/t). Option D is false.
f(1) = 2*1^2+2*1/1^2+5*1+5/1
= 2+2+5+5 = 14
Option E is true.
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