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

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

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20 Mar 2017, 03:43
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15% (low)

Question Stats:

74% (00:51) correct 26% (01:16) wrong based on 89 sessions

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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

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 05 Jan 2017 Posts: 427 Location: India Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink] ### Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5662 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 [#permalink]

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22 Mar 2017, 05:56
1
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.

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

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

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

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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

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

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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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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

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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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