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# m17 #27

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Intern
Joined: 29 Sep 2009
Posts: 13

Kudos [?]: 25 [0], given: 18

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26 Mar 2011, 15:34

Is the product of four consecutive even integers positive?

(1)The sum of these integers is positive but smaller than 20
(2)The product of the middle two of these integers is positive
(C) 2008 GMAT Club - m17#27

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Can me please somebody explain, why A is correct? I thought that following two sequences of even integers are possible in the case 1: -2,0,2,4 => sum is positive and product is zero, 2,4,6,8 => sum is positive and product is positive as well.

Kudos [?]: 25 [0], given: 18

Intern
Joined: 29 Sep 2009
Posts: 13

Kudos [?]: 25 [0], given: 18

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26 Mar 2011, 15:35
sorry,

now I see smaller than 20. It is clear.

Kudos [?]: 25 [0], given: 18

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1965

Kudos [?]: 2099 [0], given: 376

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27 Mar 2011, 03:04
Knesl wrote:

Is the product of four consecutive even integers positive?

(1)The sum of these integers is positive but smaller than 20
(2)The product of the middle two of these integers is positive
(C) 2008 GMAT Club - m17#27

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Can me please somebody explain, why A is correct? I thought that following two sequences of even integers are possible in the case 1: -2,0,2,4 => sum is positive and product is zero, 2,4,6,8 => sum is positive and product is positive as well.

Let the consecutive even integers be
x-2,x,x+2,x+4

1.
0 < x-2+x+x+2+x+4 < 20
0 < 4x + 4 < 20
0 < x+1 < 5
-1 < x < 4
x=0
x=2
The possible sets are:
-2,0,2,4. Product=0
0,2,4,6. Product=0
Both cases; Product=0
Product is not +ve.
Sufficient.

2.
x-2,x,x+2,x+4
x(x+2) > 0
x<-2 or x>0
Possible sets:
x=10; 8,10,12,14. product=+ve
x=-4; -6,-4,-2,0. product=0
Not Sufficient.

Ans: "A"
_________________

Kudos [?]: 2099 [0], given: 376

Re: m17 #27   [#permalink] 27 Mar 2011, 03:04
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# m17 #27

Moderator: Bunuel

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