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# What is the average of all integers from 1 to 100 that end in 2?

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
What is the average of all integers from 1 to 100 that end in 2? [#permalink]

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01 Mar 2018, 00:52
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What is the average of all integers from 1 to 100 that end in 2?

(A) 46

(B) 47

(C) 48

(D) 50

(E) None of these
[Reveal] Spoiler: OA

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What is the average of all integers from 1 to 100 that end in 2? [#permalink]

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01 Mar 2018, 00:58
Bunuel wrote:
What is the average of all integers from 1 to 100 that end in 2?

(A) 46

(B) 47

(C) 48

(D) 50

(E) None of these

The integers which end in 2 from 1 to 100 are 2,12,22,32,42,52,62,72,82,92

The average of these numbers is the average of the middle 2 terms
,since the elements are in an AP and are even in number

Therefore, the average is $$\frac{42+52}{2} = \frac{94}{2} = 47$$(Option B)

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Re: What is the average of all integers from 1 to 100 that end in 2? [#permalink]

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01 Mar 2018, 00:58
Bunuel wrote:
What is the average of all integers from 1 to 100 that end in 2?

(A) 46

(B) 47

(C) 48

(D) 50

(E) None of these

Instead of exlplicitly calculating, we'll use the logic of arithmetic series.
This is a Logcial approach.

We're asked to find the average of 2,12,12,....82,92.
We can pair these off into 2 + 92, 12 + 82, ... 42 + 52, each of which sum to 94.
Since each pair has an average of 94/2 = 47, so does the total sum.

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Re: What is the average of all integers from 1 to 100 that end in 2? [#permalink]

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03 Mar 2018, 04:12
Bunuel wrote:
What is the average of all integers from 1 to 100 that end in 2?

(A) 46

(B) 47

(C) 48

(D) 50

(E) None of these

IMO B
number that lie between 1-100 and ends with 2 are 2,12,22.....so on
there are 10 number so total =n*(a+l)/2(n= number of terms, a=1st term, and l= last term)
10*(2+92)/2 =5*94
average = 5*94/10=47
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What is the average of all integers from 1 to 100 that end in 2? [#permalink]

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03 Mar 2018, 15:12
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Bunuel wrote:
What is the average of all integers from 1 to 100 that end in 2?

(A) 46

(B) 47

(C) 48

(D) 50

(E) None of these

Figure out only the lowest and highest terms: 2 and 92

In a set of evenly spaced integers, the average is
$$\frac{High + Low}{2}$$

$$\frac{92+2}{2}=\frac{94}{2}=47$$

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What is the average of all integers from 1 to 100 that end in 2?   [#permalink] 03 Mar 2018, 15:12
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