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by avada » Tue Aug 28, 2012 9:12 pm
Having trouble with this one:

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 smallest two of these integers is positive

the answer may be incorrect on the app
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Aug 28, 2012 9:46 pm
consider option 1 (The sum of these integers is positive but smaller than 20)
when we take 2,4,6,8 (4 consecutive positive integers) the sum is 20. but we need sum to be less than 20 and positive. so the numbers we are left are (0,2,4,6) , (-2,0,2,4).
if we take (-4,-2,0,2) the sum is not positive.
with these two sets the product is 0, which means it is not positive.
hence it can be answered with option 1 alone.

consider option 2 (The product of the smallest two of these integers is positive)
take (2,4,6,8) and (-4,-2,0,2). the product of smallest two of these sets is positive.
but the option (2,4,6,8) product is positive. where as (-4,-2,0,2) product is 0 (not positive).
so we are not able to answer with option 2.

Hence, it is A
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by neelgandham » Tue Aug 28, 2012 9:50 pm
Is the product of four consecutive even integers positive?
Let the four consecutive even integers be 2n-2, 2n , 2n+2, 2n+4, where n is an integer.
1. The sum of these integers is positive but smaller than 20
Sun of these integers = 2n- 2 + 2n + 2n+2 + 2n+4 = 8n+4.
0<8n+4<20
-4<8n<16.
-1/2<n<2. Since, n is an integer, it can be 0 or 1.
If n = 0, the integer set is -2,0,2,4. The product of the members of the set is 0.
If n = 1, the integer set is 0,2,4,6. The product of the members of the set is 0.
For both the cases, product of four consecutive even integers is NOT positive. So, Statement I is sufficient to answer the question.
2. The product of the smallest two of these integers is positive
Case 1: If the set is -4,-2,0,2, then the product of these integers is 0.
Case 2: If the set is 2,4,6,8, then the product of these integers is greater than 0.
Since we don't have a definite answer, Statement II is Insufficient to answer the question.

IMO A
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by neelgandham » Tue Aug 28, 2012 9:58 pm
Do you also know that the product of four consecutive integers is either zero or positive.

Case 1: 1,2,3,4 - The product is Positive.
Case 2: 0,1,2,3 - The product is 0.
Case 3: -3,-2,-1,0 - The product is 0.
Case 3: -4,-3,-2,-1 - The product is Positive.

Do you also know that the product of four consecutive even integers is either zero or positive.

Case 1: 2,4,6,8 - The product is Positive.
Case 2: 0,2,4,6 - The product is 0.
Case 3: -6,-4,-2,0 - The product is 0.
Case 3: -8,-6,-4,-2 - The product is Positive.
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