A set of 10 questions similar to the GMAT problem solving, with detailed solutions are presented.

ABC is a triangle whose sides AB and BC have length of 3 and 5 respectively. Which of the following could be the length of side AC?
(I) 8
(II) 12
(III) 0.5
A) (I) only
B) (II) only
C) (III) only
D) (I) and (II) only
E) None

Given the following
If √ x = 3, then x^{4} =
A) 6561
B) 9
C) 81
D) 729
E) 3

If n is an odd integer, then which of the following is even?
(I) n^{2}
(II) n^{2} + 1
(III) 3n^{2}  1
A) (I) only
B) (II) only
C) (III) only
D) (I) and (II) only
E) (II) and (III) only

8×2^{100} + 4×2^{101} =
A) 2^{101}
B) 2^{102}
C) 2^{103}
D) 2^{104}
E) 2^{105}

If 3x + 5y = 5 and x + 3y = 20, then 2x + 4y =
A) 25
B) 25 / 2
C) 25 / 4
D) 15
E) 15 / 2

If n is positive and less than 1, then which of the following is true?
(I) n^{2}  n < 0
(II) n^{3} < n
(III) n + 1 < 1
A) (I) only
B) (II) only
C) (III) only
D) (I) and (II) only
E) (II) and (III) only

Which of the following has the greatest value?
A) 250%
B) 2 + 1/2
C) 5 × 0.5
D) 1 / 0.1
E) 4

(4x^{2}  4) / ( 3x + 3) =
A) ( 4/3)(x + 1)
B) x + 1
C) (4/3)(x + 1)
D) 4 (x  1)
E) (4/3)(x + 1)

For what values of b and c will the equation x^{2} + bx = c have the solutions 2 and 3?
A) b = 2 , c = 3
B) b = 1 , c = 3
C) b = 1 , c =  6
D) b = 1 , c = 6
E) b = 2 , c = 6

(√12  √3)(√12 + √3)
A) 9
B)  9
C) 15
D)  15
E) 18
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