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The average of four consecutive odd numbers is 24. Find the largest nu

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The average of four consecutive odd numbers is 24. Find the largest nu  [#permalink]

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New post 21 Feb 2019, 00:59
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A
B
C
D
E

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  5% (low)

Question Stats:

94% (01:00) correct 6% (00:46) wrong based on 33 sessions

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Re: The average of four consecutive odd numbers is 24. Find the largest nu  [#permalink]

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New post 21 Feb 2019, 01:07
Bunuel wrote:
The average of four consecutive odd numbers is 24. Find the largest number.

A. 20
B. 27
C. 36
D. 45
E. 46



\(\frac{x + x + 2 + x + 4 + x + 6}{4}\) = 24

4x + 12 = 96

4x = 84

x = 21.

largest integer = x + 6 = 21 + 6 = 27.

B is our answer.
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Re: The average of four consecutive odd numbers is 24. Find the largest nu  [#permalink]

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New post 21 Feb 2019, 10:45
Bunuel wrote:
The average of four consecutive odd numbers is 24. Find the largest number.

A. 20
B. 27
C. 36
D. 45
E. 46



x+x+2+x+4+x+6 = 96
4x+12=96
x= 21
x+6 ; 27
IMO B
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Re: The average of four consecutive odd numbers is 24. Find the largest nu  [#permalink]

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New post 21 Feb 2019, 16:36
The solutions posted above are correct.

A slightly alternative way to tackle the problem is posted below. This way has less computation.

Let the 4 consecutive odd numbers be x-3, x-1, x+1, x+3

Given that (x-3 + x-1 + x+1 + x+ 3)/4 = 24

4x/4=24

x=24

Our greatest number in the above assumed series is x+3.
Hence, x+3 = 27.

Hence the answer is B
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Re: The average of four consecutive odd numbers is 24. Find the largest nu  [#permalink]

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New post 21 Feb 2019, 16:51
For easy calculation we can take consecutive numbers as -

x-2,x,x+2,x+4

Avg of them is 24

SUm of numbers = 4x+4
Avg of number = x+1

This equals to 24 .

So x+1 = 24
x= 23

largest number =x+4 = 27
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The average of four consecutive odd numbers is 24. Find the largest nu  [#permalink]

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New post 21 Feb 2019, 21:55
Bunuel wrote:
The average of four consecutive odd numbers is 24. Find the largest number.

A. 20
B. 27
C. 36
D. 45
E. 46


because the numbers are a consecutive odd sequence,
24 will be their median also, between 23 and 25
27
B
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Re: The average of four consecutive odd numbers is 24. Find the largest nu  [#permalink]

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New post 24 Feb 2019, 06:50
Bunuel wrote:
The average of four consecutive odd numbers is 24. Find the largest number.

A. 20
B. 27
C. 36
D. 45
E. 46


Let x = the smallest (odd) integer. The next consecutive odd integer is x + 2, and the two consecutive odd integers after that are x + 4 and x + 6. We can create the equation:

(x + x + 2 + x + 4 + x + 6)/4 = 24

4x + 12 = 96

4x = 84

x = 21, so the largest integer is 27.

Alternate Solution:

By looking at the answer choices, we can reject choices A, C and E since they are not odd. We can also reject choice D since, if the largest number is 45, the average could never be 24. So the only correct answer is choice B (27) and it’s reasonable since 27 is close to the average (24).

Answer: B
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Re: The average of four consecutive odd numbers is 24. Find the largest nu   [#permalink] 24 Feb 2019, 06:50
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