Question : If a : b = b : c, then what is the value of a6 : b6?
Option 1: a3 : b3
Option 2: b3 : ac
Option 3: a3 : c3
Option 4: a2 : b2
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Correct Answer: a3 : c3
Solution : a : b = b : c $⇒\frac{\text{a}}{\text{b}} = \frac{\text{b}}{\text{c}}$ $⇒ \text{b}^2 = \text{ac}$ Cubing on both sides, we get, $⇒ \text{b}^6 = \text{a}^3\text{c}^3$ $⇒ \frac{\text{a}^6}{\text{b}^6} = \frac{\text{a}^6}{\text{a}^3 \text{c}^3}$ $⇒ \frac{\text{a}^6}{\text{b}^6} = \frac{\text{a}^3}{\text{c}^3}$ Hence, the correct answer is $\text{a}^3: \text{c}^3$.
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Question : If A = 23 × 37, B = 27 × 35 and C = 28 × 34, then what is the least common multiple of A, B and C?
Option 1: 27× 37
Option 2: 26 × 37
Option 3: 28 × 37
Option 4: 29 × 37
Question : P = 25 × 38 and Q = 23 × 3K. If the highest common factor of P and Q is 23 × 33, then what is the value of K?
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 5
Question : If 2A = 3B = 7C, then what is the value of A : B : C?
Option 1: 3 : 2 : 1
Option 2: 21 : 14 : 6
Option 3: 21 : 7 : 6
Option 4: 14 : 18 : 5
Question : If a : b : c = 5 : 6 : 4, then what is the value of (a + b + c) : (3a + b – c)?
Option 1: 25 : 23
Option 2: 18 : 23
Option 3: 15 : 17
Option 4: 18 : 19
Question : If 'a' and 'b' are positive integers such that a2 – b2 = 19, then the value of 'a' is:
Option 1: 10
Option 2: 20
Option 3: 9
Option 4: 19
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