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# Is the product of three consecutive integers negative?

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Re: Is the product of three consecutive integers negative? [#permalink]
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Statement 1:
can be satisfied with (1,2,3) sum =6, product = 6
can be satisfied with (-1,-2,-3) sum = -6, product = -6

Insufficient

Statement 2: clearly insufficient

1 and 2:
can be satisfied with (-1,-2,-3)
can be satisfied with (-1,0,1) product is not negative

E
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Re: Is the product of three consecutive integers negative? [#permalink]
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great example of why you can't blindly reduce equations [e.g. (x-1)x(x+1)=3x --> (x-1)(x+1)=3]
thanks Bunuel.
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Re: Is the product of three consecutive integers negative? [#permalink]
Hi Bunuel , great question - but can you please explain why we cannot blindly cancel upon the "x's" on both sides of the equation you used ( i.e. (x−1)x(x+1)(x−1)+x+(x+1)=(x−1)x(x+1) --> 3x )

I have noticed you not cancelling out such scenarios in multiple questions (including not drawing direct conclusions in ratio based questions as well) - any reason why? and any guidance on when not to cancel out such cases??

TIA!
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Re: Is the product of three consecutive integers negative? [#permalink]
NidSha wrote:
Hi Bunuel , great question - but can you please explain why we cannot blindly cancel upon the "x's" on both sides of the equation you used ( i.e. (x−1)x(x+1)(x−1)+x+(x+1)=(x−1)x(x+1) --> 3x )

I have noticed you not cancelling out such scenarios in multiple questions (including not drawing direct conclusions in ratio based questions as well) - any reason why? and any guidance on when not to cancel out such cases??

TIA!

Because that cancels out one result. You will notice that if you cut that x out, you will not get X=0 and thus believe that there is only one answer.

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Re: Is the product of three consecutive integers negative? [#permalink]
Antreev - so should i generalize that each time we are trying to find solutions for an unknown variable, such cases should not be cancelled ?

Though this confuses me - don't we usually arrive to such equations to find possible solutions for an unknown variable?
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Re: Is the product of three consecutive integers negative? [#permalink]
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NidSha wrote:
Antreev - so should i generalize that each time we are trying to find solutions for an unknown variable, such cases should not be cancelled ?

Though this confuses me - don't we usually arrive to such equations to find possible solutions for an unknown variable?

Hello Nidsha

If you could take particular example then it would be better to discuss question by question
It varies from question to question. Eg, if we have:
3x(x-1) = x(x+1)

then we cannot cancel x from both sides, because x could be '0' also, and cancellation by '0' (division by 0) is not permissible.

But in the above equation if we know that x is a non-zero number, then we can cancel x from both sides.

I would request you to take example of that particular question that you are talking about so we could discuss it in detail.
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Re: Is the product of three consecutive integers negative? [#permalink]
amanvermagmat - thank you so much for this explanation - i think i was hugely missing the '0' based fact/' exception while looking at such equations - explains it all now - thank you so much again!
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Re: Is the product of three consecutive integers negative? [#permalink]
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Re: Is the product of three consecutive integers negative? [#permalink]
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