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
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Correct Answer: 8
Solution : Given: $A=2^K×3^5$ and $B=2^5×3^7$ ⇒ $A = 2^k × 3^5$ and $B = 2^5 × 3^7$ We have to take the highest power of the number from the above value The highest power of 3 = 7 Given: LCM of A and B = $2^8 × 3^7$ The highest power of 2 is 8 The power of 2 is $k$ and 8 From A and B, the highest power of 2 is 8 Hence, the correct answer is 8.
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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 : 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
Question : Find the value of $k$, if 5 : $k$ :: 30 : 42.
Option 1: 8
Option 2: 7
Option 3: 6
Option 4: 9
Question : What is the value of $\frac{17-8 \times 5+4 \times 3}{5 \times 3 \div 6+2 \times 4} ?$
Option 1: $\frac{-25}{21}$
Option 2: $\frac{-22}{21}$
Option 3: $\frac{-5}{6}$
Option 4: $\frac{-8}{7}$
Question : What is the value of [7 ÷ 14 × 8 + (5 ÷ 15 × 6 - 4 × 3)]?
Option 1: - 4
Option 2: - 2
Option 3: - 6
Option 4: - 5
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