Question

If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30?

a) 0
b) 1
c) 2
d) 3

Answer 1

The average of four numbers being 30 implies that the sum of these numbers is 120. As having all numbers greater than 30 would exceed this sum, the correct answer is 0, indicating none of the numbers are greater than 30. So the correct option is (a) 0

Step-by-step explanation:

The given question states that the average of four different numbers is 30. Let's denote the four numbers as A, B, C, and D. The formula for the average is:

Average =
`(A + B + C + D)/(4)`

According to the question, the average is 30:

30 =
`(A + B + C + D)/(4)`

To find the total sum of the four numbers, you can multiply both sides of the equation by 4:

`\[ 4 * 30 = A + B + C + D \]`

120 = A + B + C + D

Now, let's consider the possibility of having all numbers greater than 30. If all numbers are greater than 30, their sum would be greater than 120, which contradicts the sum we calculated. Therefore, it's not possible for all four numbers to be greater than 30.

Hence, the correct answer is (a) 0, meaning none of the numbers are greater than 30. This is consistent with the fact that the average of the four numbers is 30, and it aligns with the logical reasoning applied in this explanation.So the correct option is (a) 0

Answer 2

The average (arithmetic mean) of four different numbers is 30 and the number greater than 30 is b) 1

Step-by-step explanation:

Let's consider that the four different numbers have an average of 30. If three numbers are less than 30, the fourth number would need to be significantly greater than 30 to balance the averag.

But since we're looking for distinct numbers and the average is 30, only one number can be greater than 30 for the average to remain unchanged. For the average of four numbers to be 30, the sum of these numbers must be 4 multiplied by 30, which is 120.

If one or more numbers were greater than 30, the others would need to be substantially lower than 30 to maintain the average. Thus, only one number can be greater than 30 to sustain an average of 30 for four distinct numbers.

Considering the arithmetic mean as a balancing point, the presence of more than one number above 30 would necessitate the existence of numbers considerably less than 30 to maintain the average, contradicting the given conditions of distinct numbers and an average of 30.

Hence, only b) 1 number can be greater than 30 among the four distinct numbers.