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# Two sets of 4 consecutive positive integers have exactly one integer

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Math Expert
Joined: 02 Sep 2009
Posts: 62496
Two sets of 4 consecutive positive integers have exactly one integer  [#permalink]

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22 May 2016, 12:49
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25% (medium)

Question Stats:

85% (01:38) correct 15% (01:03) wrong based on 84 sessions

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Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

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Re: Two sets of 4 consecutive positive integers have exactly one integer  [#permalink]

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23 May 2016, 03:51
Let 2 sets of 4 consecutive positive integers be
{1,2,3,4} and {4,5,6,7}
and 4 is the common integer in the 2 sets .
Difference in sum of integers = (5-3)+(6-2)+(7-1)
=2+4+6
=12
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Joined: 02 Aug 2009
Posts: 8302
Re: Two sets of 4 consecutive positive integers have exactly one integer  [#permalink]

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23 May 2016, 05:51
Bunuel wrote:
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

Many ways to do it...

1) If say the sets are big and adding is difficult-
since the largest of one and smallest of other are same...
The numbers are actually seven consecutive number with fourth common..
so for the smaller set, we need to add first three, which will be 3*2nd number...
For the bigger set, we need to add 5th to 7th number, which will be 3* 6th number..

Difference = 3*6th number-3*2nd number = 3*(6th-2nd) = 3*4 =12.................... 6th -2nd = 4 as the number are consecutive..

2) If set has few elements..
take any set of numbers 1,2,3,4 and 4,6,7,8...
so 4+6+7+8-(1+2+3+4)=12...

3) numbers are consecutive so the fourth number of smaller set is the 1st number of bigger set..
so difference in the FIRST number of each = 4-1 =3..
the difference will be same for 2nd number of each or 3rd of each and 4th of each..so Total difference = 3+3+3+3 =12
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Re: Two sets of 4 consecutive positive integers have exactly one integer  [#permalink]

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23 May 2016, 08:08
A=(1,2,3,4), sum of this=10
B=(4,5,6,7), sum of this=22,

The differenct between 22-10=12

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Re: Two sets of 4 consecutive positive integers have exactly one integer  [#permalink]

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23 May 2016, 10:17
Bunuel wrote:
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

A = { ( a ) , ( a + 1 ) , ( a + 2 ) , ( a + 3 )}

B = { ( a + 3 ) , ( a + 4 ) , ( a + 5 ) , ( a + 6 )}

Sum of A = 4a + 6

Sum of A = 4a + 18

Difference = (4a + 18) - (4a + 6) => 12

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Joined: 07 Dec 2014
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Two sets of 4 consecutive positive integers have exactly one integer  [#permalink]

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23 May 2016, 19:06
1
with x as common integer,
define overlapping sets as:
x+3
x+2
x+1
x
x-1
x-2
x-3
sum of higher set=4x+6
sum of lower set=4x-6
(4x+6)-(4x-6)=12
Two sets of 4 consecutive positive integers have exactly one integer   [#permalink] 23 May 2016, 19:06
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