Tag: average

Quizzes (2) Questions (95)

Questions Related to average

Multiple choice maths average arithmetic mean of ap introduction to averages means

In a Maths test the average score of the $10$ girls in a class is $15$ and the average score of the $15$ boys is $10$. The average score of the class in the test is 

  1. $12$
  2. $12.5$
  3. $13$
  4. $12.75$`
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total score of 10 girls is 10 * 15 = 150. The total score of 15 boys is 15 * 10 = 150. The total class score is 300 for 25 students. The average is 300 / 25 = 12.

Multiple choice maths average arithmetic mean of ap introduction to averages means

The ratio of sum of n arithmetic means between two given numbers to that of single arithmetic mean between them id

  1. n : 1
  2. n$^2$ : 1

  3. 1 : 1
  4. $\sqrt{n}$ : 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of n arithmetic means between a and b is n * (a+b)/2. The single arithmetic mean is (a+b)/2. The ratio is therefore n : 1.

Multiple choice maths average arithmetic mean of ap introduction to averages means

If $\cfrac {a^n+b^n}{a^{n-1}+b^{n-1}}$ is the AM between a and b, then the value of n is 

  1. 0

  2. 1

  3. -1

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The A.M. of a and b is $\dfrac{a+b}{2}$.


Therefore, $\dfrac{a^{n+1}+b^{n+1}}{a^n+b^n}$ will be the A.M. of a and b, if 

$\dfrac{a^{n+1}+b^{n+1}}{a^n+b^n}=\dfrac{a+b}{2}$

$\Rightarrow 2(a^{n+1}+b^{n+1})=(a^n+b^n)(a+b)$

$\Rightarrow 2a^{n+1}+2b^{n+1}=a^{n+1}+a^nb+b^na+b^{n+1}$

$\Rightarrow a^{n+1}+b^{n+1}=a^nb+b^na$

$\Rightarrow a^n(a-b)=b^n(a-b)$

$\Rightarrow a^n=b^n$

$\Rightarrow \dfrac{a^n}{b^n}=1$

$\Rightarrow (\dfrac{a}{b})^n=1$

$\Rightarrow (\dfrac{a}{b})^n=(\dfrac{a}{b})^0$

$\Rightarrow n=0$

Multiple choice maths average arithmetic mean of ap introduction to averages means

A student bought $4$ books for $Rs.120$ from one book shop and $6$ books for $Rs.150$ from another. The average price (in  rupees), he paid per book was:

  1. $27$
  2. $27.50$
  3. $135$
  4. $138$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cost = 120 + 150 = 270. Total books = 4 + 6 = 10. Average price = 270 / 10 = 27.

Multiple choice maths average arithmetic mean of ap introduction to averages means

The average height of 25 boys is 1.4 m. When 5 boys leave the group, then the average height increases by 0.15 m. What is the average height of the 5 boys who leave?

  1. 0.8 m

  2. 0.9 m

  3. 0.95 m

  4. 1.05 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial total height = 25 * 1.4 = 35. New total height = 20 * 1.55 = 31. Total height of 5 boys = 35 - 31 = 4. Average = 4 / 5 = 0.8.