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
Correct Answer: A and E

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)
Correct Answer: A and B

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 E

Explanation:

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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