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The mean of twenty-five consecutive positive integers numbers is what [#permalink]

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28 Jul 2017, 09:54

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Bunuel wrote:

The mean of twenty-five consecutive positive integers numbers is what percent of the total?

(A) 4%

(B) 5%

(C) 20%

(D) 25%

(E) Cannot be determined by the information provided.

let the consecutive numbers be from 1 to 25 Sum = \(\frac{n}{2}*(first term + last term) =\) \(\frac{25}{2}*(1+25)\) or Sum = 25*13 Therefore Mean of 25 terms will be = \(\frac{25*13}{25}\) = 13 so Mean as % of Sum = \(\frac{13}{(25*13)}*100\) = 4% Option A

I assume when the question says "total" it means to say "sum". By definition, mean = sum/n, where n is the number of terms.

We have n = 25, so:

mean = sum / 25

so the mean is 1/25 of the sum, or 4% of the sum.

It's not important that the set consists of consecutive integers.
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I assume when the question says "total" it means to say "sum". By definition, mean = sum/n, where n is the number of terms.

We have n = 25, so:

mean = sum / 25

so the mean is 1/25 of the sum or 4% of the sum.

It's not important that the set consists of consecutive integers.

I guess this would be the best way to solve it. If we focus on the definition, we can indeed come to conclusion that the relation between Mean and Sum is -

Mean/Sum = 1/N, where N is the total number of terms.

With this inference in mind, it would hardly take any time to solve this question.

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

The mean of twenty-five consecutive positive integers numbers is what percent of the total?

(A) 4%

(B) 5%

(C) 20%

(D) 25%

(E) Cannot be determined by the information provided.

----------ASIDE---------------------- There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median." For example, in each of the following sets, the mean and median are equal: {7, 9, 11, 13, 15} {-1, 4, 9, 14} {3, 4, 5, 6} ------------------ For this question, let x = first value So, x+1 = second value x+2 = third value . . . x+24 = last value

This means x+12 is the median AND the mode

Since x+12 = the mean of the 25 numbers, we can conclude that (25)(x+12 ) = the SUM of the 25 numbers

The mean of twenty-five consecutive positive integers numbers is what percent of the total? We must convert (x+12)/(25)(x+12) to a PERCENT (x+12)/(25)(x+12) = 1/25 = 4/100 = 4% Answer: A