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If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30

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If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 20 Mar 2017, 03:43
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If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number of them?

A. 5
B. 10
C. 15
D. 20
E. 25
[Reveal] Spoiler: OA

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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 20 Mar 2017, 04:21
let the number be a , a+5, a+10, a+15, a+20
a +a +5 +a +10 +a+15+a+20 = 30*5
or 5a + 50 = 150
or a = 20

therefore the smallest number is 20

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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 22 Mar 2017, 02:49
==> If the average of 5 consecutive multiples of 5 is 30, from 20,25,30,35,40, the smallest multiple of 5 becomes 20.

Therefore, the answer is D.
Answer: D
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If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 22 Mar 2017, 05:56
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MathRevolution wrote:
If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number of them?

A. 5
B. 10
C. 15
D. 20
E. 25


Concept: For Arithmetic progression (or equally spaced series) arithmetic mean = median.



=> Median = 30 (3rd term of the series). Smallest number or 1st element will be 20. Answer D.

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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 22 Mar 2017, 07:08
let the number be
x,x+5,x+10,x+15,x+20
avg is 30


so
30*5=5x+50
5x=100
x=20
answer is D

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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 22 Mar 2017, 11:32
MathRevolution wrote:
If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number of them?

A. 5
B. 10
C. 15
D. 20
E. 25

\(5a + 5b + 5c + 5d + 5e = 150\)

Now, If the smallest number is 20 then we have....

\(20 + 25 + 30 + 35 + 40 = 150\)

Thus, answer must be (D) 20
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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 28 Mar 2017, 05:27
Since the 5 numbers are consecutive multiples of 5 and the mean is 30 ,the middle number must be 30
so 20,25,30,35,40
Answer : D

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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 28 Mar 2017, 05:53
Let the numbers be n,n+5,n+10,n+15,n+20 ( because numbers are consecutive multiple of 5)
Then (5n+50)/5=30 according to the question
Solving which we get n=20
Answer D


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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 08 Aug 2017, 02:46
For any A.P series => Mean = Median

Hence as number of terms = 5
Median => 3rd term.

Hence the series would be ==>

-
-
30
-
-


filling up the blanks => 20,25,30,35,40


Hence smallest => 20

Hence D.

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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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New post 10 Aug 2017, 10:52
MathRevolution wrote:
If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number of them?

A. 5
B. 10
C. 15
D. 20
E. 25


Let’s let x = the smallest multiple of 5. The next consecutive multiple of 5 is (x + 5); the one after that will be (x + 10), and so on.

We can create the following equation:

x + x + 5 + x + 10 + x + 15 + x + 20 = 150

5x = 100

x = 20

Answer: D
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Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30   [#permalink] 10 Aug 2017, 10:52
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