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Q:

If ${(x + y)}^{2} = xy + 1$ and $x^{3} - y^{3} = 1$ , then what is the value of x – y?

A) 1	B) 0
C) -1	D) 2

Answer & Explanation Answer: A) 1

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

If (5x – y)/(5x + y) = 3/7, then what is the value of $(4 x^{2} + y^{2} - 4 xy) / (9 x^{2} + 16 y^{2} + 24 xy) ?$

A) 0	B) 3/7
C) 18/49	D) 1/6

Answer & Explanation Answer: A) 0

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Q:

If 2x + (9/x) = 9, then what is the minimum value of $x^{2} + \frac{1}{x^{2}} = ?$

A) 95/36	B) 97/36
C) 87/25	D) 623/27

Answer & Explanation Answer: B) 97/36

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Q:

If $\frac{11 - 13 x}{x} + \frac{11 - 13 y}{y} + \frac{11 - 13 z}{z} = 5$ then what is the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = ?$

A) 1	B) 13/11
C) 13/5	D) 4

Answer & Explanation Answer: D) 4

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Q:

$If (─) stands for division, (+) stands for multiplication, (\div) stands for subtraction and (\times) stands for addition, which one of the following equations is correct ?$

A) 100+5−10×250÷200 = 100	B) 200+10−20×200÷100 = 150
C) 50×5÷10+100−75 = 50	D) 300+5−20×200÷100 = 200

Answer & Explanation Answer: A) 100+5−10×250÷200 = 100

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Filed Under: Mathematical Operations
Exam Prep: Bank Exams

Q:

If a--b = 4 and ab = 45, find the value of $a^{3} - b^{3}$

A) 604	B) 370
C) 253	D) 199

Answer & Explanation Answer: A) 604

Explanation:

${(a - b)}^{2} = a^{2} + b^{2} - 2 ab \Rightarrow 16 = a^{2} + b^{2} - 90 \Rightarrow a^{2} + b^{2} = 106 a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + ab) \Rightarrow a^{3} - b^{3} = 4 X (106 + 45) \Rightarrow a^{3} - b^{3} = 4 X 151 \Rightarrow a^{3} - b^{3} = 604$