The average of five consecutive integers is 20. What is the average of

Question

The average of five consecutive integers is 20. What is the average of the first 3 of these integers?

(A) 15
(B) 17
(C) 18
(D) 19
(E) 21

harshtandel838 · Answer

For consecutive 5 integers the average will be the third term  (i.e 3rd integer is 20).

We are asked about the average of first 3 of these integers  here the middle term or average will be 2nd integer,   which is 19 for this set of consecutive integers

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Showmeyaa · Answer

Let the numbers be n, n + 1, n+2, n+3, n+4
Average of these numbers = 20
So, sum of(n, n + 1, n+2, n+3, n+4) = 20 * 5 = 100
5n + 10 = 100
5n = 90
n = 18
So, first three numbers are 18, 19 and 20. Average = 19, IMO(D)

AndreaBer · Answer

If you are struggling with the two previous demonstrations, here another one.

We know that the average of five consecutive numbers is 20. So (x1+x2+x3+x4+x5)/5=20. Moreover, we know that the sum of x1+x2+x3+x4+x5 must be 100 since 100/5=20.

Let's use the picking numbers method.
If the average of the first three numbers is 21 means you'll have 20 21 22   and then 23 24. However, in this case, the sum of all these numbers is 20+21+22+23+24= 110. too much.

let's try with 19. So 18,19,20,21,22= 100/5=20.Hence, 19 is the number we are looking for.

ajamar · Answer

Let the consecutive series be a-2 a-1 a a+1 a+2
Average of a consecutive number series when number of terms are odd is middle term 
here a= 20 
so a-2 a-1 a 18 19 20 
again the middle number will be the average of whole series 
so answer is 19

speedrevision37 · Answer

sum of 5 consecutive integers=x+x+1+x+2+x+3+x+4=5x+10
Avg=5x+10/5=x+2=20
x=18
avg of 3 consecutive integers=avg of 18,19,20=19

gauravpednekar · Answer

consecutive numbers must be in AP, so middle number is 20 that has to be average. so first three number must be 17 18 19, hence the average must be 18

bamfromtowerofgod · Answer

Why are we all assuming that that consecutive integers have to be x+1, x+2....and so on? A consecutive list can be separated by any multiple as long as its the same. Why did we choose spacing by 1?

Bunuel · Answer

When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1:  ... x-3, x-2, x-1, x, x+1, x+2, ...

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are  consecutive even integers .

3, 5, 7 ARE NOT consecutive integers, they are  consecutive odd integers .

2, 5, 8, 11 ARE NOT consecutive integers, they are  terms of arithmetic progression with common difference of 3 .

All sets of consecutive integers represent arithmetic progression but not vise-versa.

Hope it's clear.

Kinshook · Answer

Given: The average of five consecutive integers is 20. 
Asked: What is the average of the first 3 of these integers?

Let the five consecutive integers be x, x+1, x+2, x+3 & x+4
Average of the five consecutive integers = (x+ x+1+x+2+ x+3 + x+4)/5 = (5x + 10)/5 = x + 2 = 20 
x = 18

Average of the first 3 of these integers = (x + x+1 + x+2)/3 = (3x + 3)/3 = x + 1 = 19

IMO D

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The average of five consecutive integers is 20. What is the average of

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The average of five consecutive integers is 20. What is the average of

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