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which of the following CANNOT be zero? I The sum of 7

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which of the following CANNOT be zero? I The sum of 7 [#permalink] New post 19 Jun 2006, 09:35
which of the following CANNOT be zero?
I The sum of 7 cosecutive integers?
II The sum of the 10 consecutive integers
III The product of 13 cosecutive integers

A)II only
B)I and II only
C)I and III only
D)II and III only
E) I,II and III
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 [#permalink] New post 19 Jun 2006, 09:48
A) II is the only sequence with the even number of integers.
I and III have odd number of elements, therefore if the middle one is zero, the others will eliminate each other when being added up.
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 [#permalink] New post 19 Jun 2006, 10:59
A)II only

Straddle zero with the rest even/odd pairs to add up to zero.

Even number of consecutive integers cannot straddle zero, so that the pairs addup to zero.

For III product can be a zero if any one of the numbers is a zero

Therefore only II cannot add up to zero.
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 [#permalink] New post 19 Jun 2006, 11:00
Note that III is product of 13 consecutive integers

So logic for addition of consecutive doesn't apply... trick option... doesn't harm though!

helg wrote:
A) II is the only sequence with the even number of integers.
I and III have odd number of elements, therefore if the middle one is zero, the others will eliminate each other when being added up.
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 [#permalink] New post 19 Jun 2006, 21:20
haas_mba07 wrote:
Note that III is product of 13 consecutive integers

So logic for addition of consecutive doesn't apply... trick option... doesn't harm though!

helg wrote:
A) II is the only sequence with the even number of integers.
I and III have odd number of elements, therefore if the middle one is zero, the others will eliminate each other when being added up.


Thanks! I have overlooked this, indeed... Might not be so lucky at the actual exam
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 [#permalink] New post 19 Jun 2006, 21:24
haas_mba07 wrote:
A)II only

Straddle zero with the rest even/odd pairs to add up to zero.

Even number of consecutive integers cannot straddle zero, so that the pairs addup to zero.

For III product can be a zero if any one of the numbers is a zero

Therefore only II cannot add up to zero.


Hmmm... Doesn't that mean that III CAN be zero (if a zero is included). Isn't D the correct answer then?
  [#permalink] 19 Jun 2006, 21:24
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which of the following CANNOT be zero? I The sum of 7

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