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
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Correct Answer: 3
Solution : Given: P = 25 × 38 and Q = 23 × 3K The HCF of P and Q = 23 × 33 ⇒ HCF(25 × 38, 23× 3K) = 23 × 33 By comparison, the value of K = 3. Hence, the correct answer is 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 : $A=2^K×3^5$ and $B=2^5×3^7$. If the least common multiple of A and B is $2^8×3^7$, then what is the value of K?
Option 1: 6
Option 2: 8
Option 3: 9
Option 4: 3
Question : If A + {5 × 8 ÷ 22} × 11 = 134, then what is the value of A?
Option 1: 24
Option 2: 4
Option 3: 14
Option 4: 34
Question : If P = 7 × 4 – 3, Q = 8 ÷ 4 + 2, and R = 14 ÷ 21 × 9, then what is the value of P × Q + R?
Option 1: 96
Option 2: 112
Option 3: 108
Option 4: 106
Question : If p : q : r = 2 : 5 : 3 and r : s = 6 : 5, then what is the value of p : q : r : s?
Option 1: 4 : 12 : 7 : 3
Option 2: 4 : 10 : 6 : 5
Option 3: 6 : 5 : 8 : 10
Option 4: 8 : 12 : 7 : 8
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