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Number properties Q10

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Intern
Joined: 07 Oct 2009
Posts: 32

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02 Jan 2010, 06:27
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

• 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

I marked 'B' but OA is 'A'.Can someone help me understand this.Thanks!

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Math Expert
Joined: 02 Sep 2009
Posts: 42248

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02 Jan 2010, 09:34
rajkar001 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

I marked 'B' but OA is 'A'.Can someone help me understand this.Thanks!

First of all: the product of four consecutive even integers can be either 0 or positive:
If all terms are positive, product will be positive;
If one of the terms is zero, product will be zero;
If all terms are negative, product will be positive.
Note: no other option is possible for 4 consecutive integers.

(1) The sum of these integers is positive but smaller than 20:

If the greatest term is >=8, eg {2,4,6,8}, then the sum will be equal or more than 20.
If the smallest term <-2, eg {-4,-2,0,2}, then the sum won't be positive.

Hence this statement gives only TWO possible sets {0,2,4,6} and {-2,0,2,4} --> sum<20 and product =0, which is not positive hence sufficient to answer the question. Sufficient.

(2) The product of the middle two of these integers is positive.

It's possible to have {0,2,4,6} --> product zero OR {2,4,6,8} --> product positive OR {-8,-6,-4,-2}--> product positive.

_________________

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Intern
Joined: 07 Oct 2009
Posts: 32

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02 Jan 2010, 10:46
Thanks GMAT Quant Forum Moderator!

actually i missed the word 'positive' in stmt1.

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Re: Number properties Q10   [#permalink] 02 Jan 2010, 10:46
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Number properties Q10

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