Question : If $256, K, K, 81$ are in proportion, and $K$ is positive, then what is the value of $K$?
Option 1: 156
Option 2: 126
Option 3: 144
Option 4: 164
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Correct Answer: 144
Solution : Given: $256, K, K, 81$ are in proportion, and $K$ is positive. Use the formula, Mean proportional = $\sqrt{ab}$ where $a$, and $b$ are the numbers. According to the question, $K=\sqrt{81\times 256}$ $\therefore K=9\times 16=144$ Hence, the correct answer is 144.
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Question : If $\frac{J}{4}=\frac{K}{5}=\frac{L}{3}$, what is the value of $(L + J)^2:(J +K)^2:(K +L)^2$?
Option 1: 25 : 16 : 9
Option 2: 64 : 25 : 81
Option 3: 49 : 81 : 62
Option 4: 49 : 81 : 64
Question : If A is the mean proportion of 24 and 6. B is the mean proportion of 81 and 9. Find the value of 3A + B.
Option 1: 33
Option 2: 32
Option 3: 63
Option 4: 55
Question : Solve: [ (144 ÷ 12) + (43 × 3) ] + 45 – 20 × 3
Option 1: 127
Option 2: 111
Option 3: 126
Option 4: 156
Question : If $x$ percent of $x$ is 256, then what is the value of $x$?
Option 1: 180
Option 2: 200
Option 3: 150
Option 4: 160
Question : If the third proportion of 3 and $x$ is 27 and the third proportion of 2 and $y$ is 8, then find $x : y$.
Option 1: 7 : 9
Option 2: 4 : 5
Option 3: 3 : 7
Option 4: 9 : 4
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