If the average of the five numbers n, 2n – 4, 4n + 3, 5n + 2

Question

If the average of the five numbers n, 2n – 4, 4n + 3, 5n + 2, and 6n + 5 is 52, what is the value of n ?

A. 2 5/9
B. 10
C. 12
D. 14 1/9
E. 15

Bunuel · Answer

The average of the five numbers is 52 means that  n+(2n-4)+(4n+3)+(5n+2)+(6n+5)=5*52  -->  n=\frac{127}{9}=14\frac{1}{9} .

Answer: D.

EMPOWERgmatRichC · Answer

Hi All,

While most Test Takers would solve this with an Algebraic approach (which is fine), it can also be solved by TESTing THE ANSWERS...

We're told that the average of the five numbers N, (2N – 4), (4N + 3), (5N + 2), and (6N + 5) is 52. We're asked for the value of N.

Let's start with Answer B: 10

IF...N = 10, then the 5 numbers are...
10, 16, 43, 52 and 65.

The average of this group of numbers is 186/5 = 37.2, which is TOO LOW (it's supposed to be 52). Eliminate A and B. To raise the average almost 15, we need each of the 5 values to be considerably higher, so I'm going to jump to Answer E.

Answer E: 15

IF...N = 15, then the 5 numbers are...

15, 26, 63, 77 and 95

The average of this group of numbers is 276/5 = 55.2, which is TOO HIGH. Since it's relatively close to 52, the correct answer will be closer to 15 than it is to 10. Of the two remaining answers, there's only one that makes sense...

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

Arro44 · Answer

I can follow the apporach up to the point at which we divide by 9. 
Can someone help me understand?

Best regards,
Chris

abhimahna · Answer

Hey Arro44 , Welcome to GMATClub

Are you asking why did we divide by 9 OR how did we convert n=\frac{127}{9}=14\frac{1}{9} ? Please clarify!

Arro44 · Answer

Hi abhimahna,

thanks for reaching out so quicky.

I was uncertain how we obtained the 9 and therefore couldnt follow why we would divide by it.

Best regards,
Chris

abhimahna · Answer

Hey  Arro44  ,

Let's solve this equation:

n+(2n-4)+(4n+3)+(5n+2)+(6n+5)=5*52

==>  18n + 6 = 5*52

==>  9n + 3 = 5*26  (I removed the common 2 from both the sides.)

==>  9n = 130 - 3

==>  9n = 127

==>  n=\frac{127}{9}=14\frac{1}{9}

Does that make sense?

Arro44 · Answer

Yes. now it is fully clear to me how we come up with the right solution.

Thank you so much!!

If the average of the five numbers n, 2n – 4, 4n + 3, 5n + 2

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If the average of the five numbers n, 2n – 4, 4n + 3, 5n + 2

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