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Number Properties

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Number Properties [#permalink] New post 21 Jan 2010, 13:03
Hi,
Could anyone have a look in the following question:

Q: 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

The OA is A. With the explanation that the sum of four consecutive integers whose sum is positive and less than 20 are 0,2,4,6....which concludes that product would be zero and hence not positive. but nowhere it has been mentioned that these integers are positive. They can be individually negative with total sum positive and less than 20.
e.g. -2,2,6,10 Total sum=16<20 and positive.
I could be wrong in assuming consecutive even integers to be even and with a fixed even difference like 4 in my example.
Please clarify.

Thanks in anticipation.
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Re: Number Properties [#permalink] New post 21 Jan 2010, 13:26
Expert's post
amitanand wrote:
...I could be wrong in assuming consecutive even integers to be even and with a fixed even difference like 4 in my example.


Yeah, you are wrong in your assumption. "Consecutive even integers" means step 2, not 4 or any other. In other words, 2,4,6,8 are consecutive even integers, but 2,6,10,12 are not consecutive even integers.
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Re: Number Properties [#permalink] New post 21 Jan 2010, 13:39
Hi Walker,

Really appreciate your response.

Thanks
-Amit
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Re: Number Properties [#permalink] New post 22 Jan 2010, 01:18
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Proper logic:

take 4 numbers n-3 , n-1 , n+1 ,n+3
where n is odd number.

now sum of these = n-3 + n-1 + n+1 + n+3= 4n < 20
=> n<5

i.e. n =1 or n=3

in either case one of the number will be 0
Thus A

2. n^2-1 >0 product of middle is +ve
thus we cannot conclude the value of n to justify sign the product of 4 number
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Re: Number Properties [#permalink] New post 22 Jan 2010, 08:26
+1 for that.

Thanks Gurpreet for your explanation.
Re: Number Properties   [#permalink] 22 Jan 2010, 08:26
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