shrive555 wrote:

If the average of six numbers is 75, how many of the numbers are equal to 75

1) None of the six number is less than 75

2) None of the six numbers is greater than 75

Official explanation:

1) 5(75) + (75+x) = 6(75) + x, which is greater than (6)(75), contrary to the fact that sum is equal to 6*75.

2) 5(75) + (75-x) = 6(75) -x, which is less than 6*75, contrary to the fact that sum is equal to 6*75

I don't understand the Bold X... why its added in 1 and subtracted in 2 from the right side ?

X is the quantity by which

1. exceeds 75, hence 75 + x

2. less than 75,hence 75-x.

Consider this example, 3 numbers, average = 3. How many numbers are equal to 3.

sum of 3 numbers = average * 3 = 3*3 = 9

1. none of the 3 numbers are lesser than 3.

means - numbers can be 3,3,3 or 4,3,4 in the second case the sum 11 > 9.

X as mentioned in the

OG explanation is 4-3 = 1. (75+x here)

2. none of the 3 numbers are greater than 3.

means - numbers can be 3,3,3 or 2,3,2 in the second case the sum is 7 < 9.

X as mentioned in the

OG explanation is 3-2 = 1. (75-x here).