Question : There are two regular polygons with numbers of sides equal to $(n-1)$ and $(n+2)$. Their exterior angles differ by 6°. The value of $n$ is:
Option 1: 14
Option 2: 12
Option 3: 13
Option 4: 11
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Correct Answer: 13
Solution : Given: There are two regular polygons with numbers of sides equal to ($n$–1) and ($n$+2). Their exterior angles differ by 6°. We know that exterior angle of a polygon = $\frac{360°}{\text{number of sides}}$ According to the question, $\frac{360°}{n-1}-\frac{360°}{n+2}=6°$ $⇒360°(\frac{1}{n-1}-\frac{1}{n+2})=6°$ $⇒60°[\frac{n+2-n+1}{(n-1)(n+2)}]=1$ $⇒n^2+n-2=180$ $⇒n^2+n-182=0$ $⇒(n+14)(n-13)=0$ $\therefore n=13$ (Since $n$ can't be negative) Hence, the correct answer is 13.
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Question : What is the value of $\frac{132}{11} \times \frac{13}{12} \div \frac{169}{14}-\frac{1}{13}?$
Option 1: 5
Option 2: 6
Option 3: 3
Option 4: 1
Question : If the mean of two numbers is 12, and the difference between the two numbers is 6, find the two numbers.
Option 1: 2 and 22
Option 2: 14 and 10
Option 3: 15 and 9
Option 4: 3 and 24
Question : Directions: Which two numbers should be interchanged to make the given equation correct? 11 × 2 + 15 ÷ 13 – 3 = 14
Option 1: 14 and 15
Option 2: 3 and 2
Option 3: 13 and 3
Option 4: 11 and 15
Question : What is the average of the first 13 odd numbers?
Option 2: 13.5
Option 3: 12
Option 4: 13
Question : What is the value of $\frac{13 \times 14+25 \times 14-38 \times 14}{14 \text { of } 2-7}?$
Option 1: 0
Option 2: 14
Option 3: 7
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