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If the sum of four consecutive integers is 66, what is the greatest of

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Bunuel
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If the sum of four consecutive integers is 66, what is the greatest of [#permalink] New post  22 May 2020, 06:20
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If the sum of four consecutive integers is 66, what is the greatest of these integers?

A. 14
B. 15
C. 16
D. 17
E. 18


PS21196
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If the sum of four consecutive integers is 66, what is the greatest of [#permalink] New post  22 May 2020, 06:31
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Important rules for consecutive integers:
1. Sum of sequence = Mean * Total numbers
2. Mean=Median, since \(n=4=even \) median= \(\frac{n2+n3}{2}\)

\(66=4x\)
\(x=16,5\) --> \(\frac{16+17}{2 }\)

\(n2= 16\),\(n3=17\) --> \( n4= 18\)

Answer E
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BrentGMATPrepNow
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Re: If the sum of four consecutive integers is 66, what is the greatest of [#permalink] New post  22 May 2020, 06:42
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Bunuel wrote:
If the sum of four consecutive integers is 66, what is the greatest of these integers?

A. 14
B. 15
C. 16
D. 17
E. 18

PS21196


Let x = the smallest integer
So, x + 1 = the next integer
And x + 2 = the next integer
And x + 3 = the GREATEST integer

The sum of four consecutive integers is 66
We can write: (x) + (x + 1) + (x + 2) + (x + 3) = 66
Simplify: 4x + 6 = 66
Subtract 6 from both sides to get: 4x = 60
Divide both sides by 4 to get: x = 15

Since x + 3 = the GREATEST integer, we know that the greatest integer = 15 + 3 = 18

Answer: E

Cheers,
Brent
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If the sum of four consecutive integers is 66, what is the greatest of [#permalink] New post  22 May 2020, 07:17
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Bunuel wrote:
If the sum of four consecutive integers is 66, what is the greatest of these integers?

A. 14
B. 15
C. 16
D. 17
E. 18


PS21196


In case of consecutive Integers, FIrst + FOrth = Second + third term

i.e. Second + third = 66/2 = 33

Two consecutive integers sum = 33 i.e. second = 16 and third = 17

ie. Forth = 18

ANswer: Option E
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Re: If the sum of four consecutive integers is 66, what is the greatest of [#permalink] New post  22 May 2020, 07:58
Bunuel wrote:
If the sum of four consecutive integers is 66, what is the greatest of these integers?

A. 14
B. 15
C. 16
D. 17
E. 18


PS21196

\(( a - 1 ) + a + ( a + 1 ) + ( a + 2 ) = 66\)

Or, \(4a + 2 = 66\)

Or, \(4a = 64\)

So, a = 16 Thus, the greatest number must be 16 + 2 = 18 , Answer must be (D)
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Re: If the sum of four consecutive integers is 66, what is the greatest of [#permalink] New post  22 May 2020, 08:17
Bunuel wrote:
If the sum of four consecutive integers is 66, what is the greatest of these integers?

A. 14
B. 15
C. 16
D. 17
E. 18


PS21196


4 consective terms
x,x+1, x+2 , x+3 ;
sum = 4x+6 = 66
x= 15 so greatest term ; 15+3 ; 18
OPTION E
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Re: If the sum of four consecutive integers is 66, what is the greatest of [#permalink]
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