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Five positive consecutive integers starting with a have average b. Wha

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Five positive consecutive integers starting with a have average b. Wha  [#permalink]

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New post 08 Apr 2019, 01:05
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Five positive consecutive integers starting with a have average b. What is the average of 5 consecutive integers that start with b?

(A) a + 3

(B) a + 4

(C) a + 5

(D) a + 6

(E) a + 7

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Re: Five positive consecutive integers starting with a have average b. Wha  [#permalink]

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New post 08 Apr 2019, 03:25
1
This is an easy one.

Following are the 5 consecutive integers starting with a:
a, a+1, a+2, a+3, a+4

The average of these 5 consecutive integers will be a+2

Why?

If there are n consecutive integers, the average is
=> middle integer {when n is odd}
=> average of the middle 2 integers {when n is even}


Ok so we know:
The average of these 5 consecutive integers is b
And b = a+2

Now, the five consecutive integers starting with b are:
b, b+1, b+2, b+3, b+4

Again, the average of the above five integers is b+2

And we know that b = a + 2,
Therefore, the average is a + 2 + 2 = a + 4

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Five positive consecutive integers starting with a have average b. Wha  [#permalink]

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New post 08 Apr 2019, 05:03
Noshad wrote:
Five positive consecutive integers starting with a have average b. What is the average of 5 consecutive integers that start with b?

(A) a + 3

(B) a + 4

(C) a + 5

(D) a + 6

(E) a + 7


If first term is a then the terms are

a, a+1, a+2, a+3, a+4

CONCEPT: For terms in Arithmetic Progression, Mean = Median = (First+Last)/2


i.e. Mean of these terms = a+2 = b (given)

i.e. other 5 terms starting from b are

a+2, a+3, a+4, a+5, a+6

Median = Mean = a+4

Answer: Option B
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Re: Five positive consecutive integers starting with a have average b. Wha  [#permalink]

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New post 09 Apr 2019, 01:35
Noshad wrote:
Five positive consecutive integers starting with a have average b. What is the average of 5 consecutive integers that start with b?

(A) a + 3

(B) a + 4

(C) a + 5

(D) a + 6

(E) a + 7


Five positive consecutive integers starting with a have average b
5a+10/5 = b
and
the average of 5 consecutive integers that start with b
5b+10/5
substitute value of b
we get
5a+20/5 or say a+4
IMO B
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Re: Five positive consecutive integers starting with a have average b. Wha   [#permalink] 09 Apr 2019, 01:35
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