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# Is the largest of three consecutive integers odd?

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Re: Is the largest of three consecutive integers odd? [#permalink]
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(1) The product of the three integers is 0.
Case 1: 0*1*2 --> Largest = Even
Case 2: -1*0*1 --> Largest = Odd
--> Insufficient

(2) The sum of the three integers is 0.
Only 1 case is possible: -1 + 0 + 1 = 0 --> Largest = 1 (Odd) --> Sufficient

Option B
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Is the largest of three consecutive integers odd? [#permalink]
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Bunuel wrote:
Is the largest of three consecutive integers odd?

(1) The product of the three integers is 0.
(2) The sum of the three integers is 0.

Given : Three consecutive INTEGERS x, (x+1) and (x+2)
To Find : Is (x+2)=Odd?
or is x=Odd? ( because Odd-2= Odd-Even=Odd)

St1: (x)(x+1)(x+2)=0
we could have the following possibility {0,1,2} , {-1,0,1}, {-2,-1,0} where x=0(Even) or -1(Odd) or -2 (Even)
Not Sufficient

St 2: x + x+1 + x+ 2=0
3x +3 =0
x=-1 -->Odd
Sufficient

Ans: (B
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Re: Is the largest of three consecutive integers odd? [#permalink]
Hi Bunuel! I wonder whether by today's standard this question should be framed more precisely as to mention excluding 'consecutive even' and 'consecutive odd' sequence
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Re: Is the largest of three consecutive integers odd? [#permalink]
cburanawit wrote:
Hi Bunuel! I wonder whether by today's standard this question should be framed more precisely as to mention excluding 'consecutive even' and 'consecutive odd' sequence

No, the question is perfectly OK. We are given three consecutive integers and are asked whether the largest of them is odd. The sequence can be {odd, even, odd} or {even, odd, even}, so the question asks whether we have the first case.
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Is the largest of three consecutive integers odd? [#permalink]
Bunuel wrote:
cburanawit wrote:
Hi Bunuel! I wonder whether by today's standard this question should be framed more precisely as to mention excluding 'consecutive even' and 'consecutive odd' sequence

No, the question is perfectly OK. We are given three consecutive integers and are asked whether the largest of them is odd. The sequence can be {odd, even, odd} or {even, odd, even}, so the question asks whether we have the first case.

Bunuel
But in consecutive odd integers, for example: x, x+2, x+4 or 3,5,7, this is also called a consecutive sequence right? Most times when I encounter questions dealing with consecutive numbers I always thought they meant 'a series of evenly spaced numbers which includes both all even, all odd, or a mixture of both'. Any tips on the language cue? Thank you for your clarification!
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Re: Is the largest of three consecutive integers odd? [#permalink]
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cburanawit wrote:
Bunuel wrote:
cburanawit wrote:
Hi Bunuel! I wonder whether by today's standard this question should be framed more precisely as to mention excluding 'consecutive even' and 'consecutive odd' sequence

No, the question is perfectly OK. We are given three consecutive integers and are asked whether the largest of them is odd. The sequence can be {odd, even, odd} or {even, odd, even}, so the question asks whether we have the first case.

Bunuel
But in consecutive odd integers, for example: x, x+2, x+4 or 3,5,7, this is also called a consecutive sequence right? Most times when I encounter questions dealing with consecutive numbers I always thought they meant 'a series of evenly spaced numbers which includes both all even, all odd, or a mixture of both'. Any tips on the language cue? Thank you for your clarification!

"Consecutive integers" ALWAYS mean integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....

For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

1, 3, 5 ARE NOT consecutive integers, they are consecutive odd integers.
Re: Is the largest of three consecutive integers odd? [#permalink]
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