Problem Solving Select Many GRE Sample Questions 4
GRE Problem Solving Select Many Sample Questions
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1. Question:Which of the following is true for the equations 11/u-7/v=1 and 9/u-4/v=6? Indicate all correct statements.
- A. The equations have a unique solutions
- B. The equations represent parallel lines
- C. u<v
- D. v<u
- E. u+v=5/6
Explanation:
11/u-7/v=1 and 9/u-4/v=6
Put x = 1/u and y = 1/v
11x - 7y = 1 ...(1)
9x - 4y = 6 ...(2)
Multiply (1) by 4 and (2) by 7 and subtract one from the other
44x - 28y - 63x + 28y = 4 - 42
- 19x = -38
x = 38/19=2
Putting in (1), we get
11(2) - 7y = 1
7y = 22-1
y = 21/7 = 3
x = 2, y = 3
u = 1/x = 1/2 and v = 1/y = 1/3
The equations have a unique solution.
Option A is true and B is false.
v
u+v = 1/2+1/3 = (3+2)/6 = 5/6
Option E is true.
2. Question:
If x/a+y/b=2 and ax-by = a^2-b^2, then which of the following statements is true? Indicate all correct statements.
- A. ax+by=2
- B. bx-ay=0
- C. bx+ay = 2
- D. x/b+y/a = (a^2-b^2)
- E. x/b+y/a = (a^2+b^2)/ab
[a^2=a*a]
Correct Answer: B and EExplanation:
x/a+y/b=2 ...(1)
ax-by=a^2-b^2 ...(2)
Multiply (1) by a^2 and subtract (2) from it
ax+a^2y/b- ax + by = 2a^2 -a^2 + b^2
a^2y/b+by = a^2+b^2
(a^2+b^2)y/b = (a^2+b^2)
y = b
Put y = b in (1)
x/a+b/b=2
x/a = 2-1 = 1
x = a
x=a and y = b
bx-ay=ba-ab=0
x/b+y/a = a/b+ b/a
= (a^2+b^2)/ab
Options B and E are true and A, C and D are false.
3. Question:
The difference between two numbers is 5 and the difference between their squares is 65. Which of the following is true? Indicate all correct options.
- A. The sum of the numbers is 13
- B. The sum of their squares is 100
- C. The product of the numbers is 40
- D. The difference of their cubes is 665
- E. The product of their squares is 1296
Explanation:
Let the two numbers be x and y, x>y
x-y = 5 ...(1)
x^2-y^2=65 ...(2)
Put x = y+5 in (2)
(y+5)^2-y^2=65
y^2+25+10y-y^2=65
10y = 65 - 25 = 40
y = 4
x = y+5 = 4+5 = 9
The sum of the numbers = x+y = 9+4= 13
The sum of their squares = x^2+y^2
= 9^2+4^2 = 81+16 = 97
The product of the numbers = xy=9*4=36
The difference of their cubes = x^3-y^3
= 9^3-4^3 = 729 - 64 = 665
The product of their squares = x^2*y^2
= 9^2*4^2 = 81*16 = 1296
Options A, D and E are true.
GRE Problem Solving Select Many Sample Questions
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