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# In a series of six consecutive integers, the sum of the first three

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Joined: 02 Sep 2009
Posts: 58320
In a series of six consecutive integers, the sum of the first three  [#permalink]

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23 Jan 2019, 02:16
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80% (00:58) correct 20% (01:07) wrong based on 46 sessions

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In a series of six consecutive integers, the sum of the first three integers is 93. What is the sum of the last three integers?

A 96
B 99
C 102
D 105
E 108

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Joined: 15 Feb 2018
Posts: 365
Re: In a series of six consecutive integers, the sum of the first three  [#permalink]

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23 Jan 2019, 06:08
six consecutive integers
x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)

the sum of the first three integers is 93
x+(x+1)+(x+2)=33
3x+3=93

x=30

What is the sum of the last three integers?
(x+3)+(x+4)+(x+5)=?
(33)+(34)+(35)=102

C
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Re: In a series of six consecutive integers, the sum of the first three  [#permalink]

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23 Jan 2019, 07:40
Bunuel wrote:
In a series of six consecutive integers, the sum of the first three integers is 93. What is the sum of the last three integers?

A 96
B 99
C 102
D 105
E 108

x x+1 x+2 x+3 x+4 x+5
x+ x+1+x+2 = 93
x= 30

so
3x+12 ; 90+12 ; 102 IMO C
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Re: In a series of six consecutive integers, the sum of the first three  [#permalink]

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27 Jan 2019, 19:55
Bunuel wrote:
In a series of six consecutive integers, the sum of the first three integers is 93. What is the sum of the last three integers?

A 96
B 99
C 102
D 105
E 108

Letting x = the first integer, we can create the equation:

x + (x + 1) + (x + 2) = 93

3x + 3 = 93

3x = 90

x = 30

The first integer is 30, and so the 4th integer is (30 + 3), the 5th integer is (30 + 4), and the 6th integer is (30 + 5). So the sum of the last 3 integers is:

(30 + 3) + (30 + 4) + (30 + 5) = 102

Alternate solution:

The 4th, 5th and 6th integers are 3 more than the 1st, 2nd and 3rd integers, respectively. Thus the sum of the last 3 integers is 3 x 3 = 9 more than the sum of the first 3 integers. Since the sum of the first 3 integers is 93, the sum of the last 3 integers is 93 + 9 = 102.

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In a series of six consecutive integers, the sum of the first three  [#permalink]

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27 Jan 2019, 20:50
Bunuel wrote:
In a series of six consecutive integers, the sum of the first three integers is 93. What is the sum of the last three integers?

A 96
B 99
C 102
D 105
E 108

second integer is 93/3=31, mean of first three integers
fifth integer is 31+3=34, mean of last three integers
3*34=102, sum of last three integers
C
In a series of six consecutive integers, the sum of the first three   [#permalink] 27 Jan 2019, 20:50
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