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# The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.

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Joined: 02 Sep 2009
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The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.  [#permalink]

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12 May 2017, 05:08
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93% (01:08) correct 7% (01:46) wrong based on 117 sessions

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The average (arithmetic mean) of 3 consecutive prime numbers is 41/3. Which of the following is the largest of the three consecutive primes?

A. 5
B. 11
C. 13
D. 17
E. 19

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The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.  [#permalink]

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12 May 2017, 06:02
1
Bunuel wrote:
The average (arithmetic mean) of 3 consecutive prime numbers is 41/3. Which of the following is the largest of the three consecutive primes?

A. 5
B. 11
C. 13
D. 17
E. 19

The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.
So total of 3 consecutive numbers = 41

Try hit and trial (I got it in 1st guess though)... 11,13,17
[How to make exact guess?
To make the exact guess... divide the nearest multiple of 3 and mid number should be near to it.
So 41~42/3 = 14
So mid prime number should be near to 14
Take 13 and consecutive prime numbers become 11,13,17 . Sum = 41 ]

So the largest of the 3 consecutive prime numbers is 17 ..

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Re: The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.  [#permalink]

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12 May 2017, 12:57
The fastest way to do this is process elimination.
Only answer D works out to 41/3

PROOF: (11+ 13 + 17)/3 = 41/3

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Re: The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.  [#permalink]

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13 May 2017, 04:17
matthewsmith_89 wrote:
The fastest way to do this is process elimination.
Only answer D works out to 41/3

PROOF: (11+ 13 + 17)/3 = 41/3

Yes correct , the elimination method can help use to solve very fast....
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Re: The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.  [#permalink]

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13 May 2017, 12:36
Bunuel wrote:
The average (arithmetic mean) of 3 consecutive prime numbers is 41/3. Which of the following is the largest of the three consecutive primes?

A. 5
B. 11
C. 13
D. 17
E. 19

assume difference between smallest and middle is 2
assume difference between smallest and largest is 6
3x+8=41
x=11
x+2=13
x+6=17
17
D
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Re: The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.  [#permalink]

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14 May 2017, 15:10
average of 3 = 41/3
sum of 3 would be = 41/3*3 = 41

11 + 13 + 17

17
D

the options help in arriving at the sum 41 , so need not list primes and calculate sum
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Re: The average (arithmetic mean) of 3 consecutive prime numbers is 41/3.  [#permalink]

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18 May 2017, 20:08
1
Bunuel wrote:
The average (arithmetic mean) of 3 consecutive prime numbers is 41/3. Which of the following is the largest of the three consecutive primes?

A. 5
B. 11
C. 13
D. 17
E. 19

We are given that the average (arithmetic mean) of 3 consecutive prime numbers is 41/3 = 13 ⅔. Thus, within our set of consecutive prime numbers, we must find values that are less than 13 ⅔ and also greater. Thus, we see that neither 5, nor 11, nor 13 can be the greatest of the 3 consecutive prime numbers. Let’s start with answer choice D.

D. 17

Thus, our set would be 11, 13, 17. The average of those numbers is (11 + 13 + 17)/3 = 41/3.

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Re: The average (arithmetic mean) of 3 consecutive prime numbers is 41/3. &nbs [#permalink] 18 May 2017, 20:08
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