Question : Find the third proportional to 23 and 31.
Option 1: $\frac{31}{23}$
Option 2: $\frac{961}{23}$
Option 3: $\frac{23}{31}$
Option 4: $\frac{23}{961}$
Correct Answer: $\frac{961}{23}$
Solution : Let the third proportional to 23 and 31 be $x$. $23 : 31:: 31: x$ ⇒ $\frac{23}{31}=\frac{31}{x}$ ⇒ $x=\frac{31\times 31}{23}$ ⇒ $x=\frac{961}{23}$ Hence, the correct answer is $\frac{961}{23}$.
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Question : Find the third proportional to 16 and 20.
Option 1: 25
Option 2: 23
Option 3: 24
Option 4: 26
Question : The ratio of the third proportional to 16 & 40 and the mean proportional between 10 & 40 is:
Option 1: 5 : 1
Option 2: 1 : 5
Option 3: 4 : 1
Option 4: 1 : 4
Question : Find the fourth proportional of 22, 66 and 11.
Option 1: 23
Option 2: 33
Option 3: 17
Option 4: 39
Question : Find the LCM of $\frac{3}{2}, \frac{81}{16}$ and $\frac{9}{8}$
Option 1: $\frac{91}{2}$
Option 2: $\frac{81}{2}$
Option 3: $\frac{111}{2}$
Option 4: $\frac{101}{2}$
Question : What is the simplified value of $\left(1-\frac{1}{4-\frac{2}{1+\frac{1}{\frac{1}{3}+2}}}\right) \times \frac{15}{16} \div \frac{2}{3}$ of $2 \frac{1}{4}-\frac{3+4}{3^3+4^3}$
Option 1: $\frac{5}{13}$
Option 2: $\frac{4}{13}$
Option 3: $\frac{8}{13}$
Option 4: $\frac{6}{13}$
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