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Is the largest of three consecutive integers odd?

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Bunuel
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Is the largest of three consecutive integers odd? [#permalink] New post  28 Feb 2020, 02:26
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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.
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Re: Is the largest of three consecutive integers odd? [#permalink] New post  28 Feb 2020, 02:54
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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.


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


Solution


Step 1: Analyse Question Stem


We need to see whether the largest of three consecutive integers is odd or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: The product of three integers is 0.
    • It means one of the integers is 0, then only the product will be 0.
      o If integers are -1, 0, and 1, then the largest integer will be Odd.
      o If integers are 0, 1, and 2, then the largest integer will be Even.
Hence, statement 1 is not sufficient, we can eliminate answer options A and D
Statement 2: The sum of three integers is 0.
    • It means at least one of the integers is negative and the other is positive.
    • It is only possible when integers are -1, 0, and 1.
      o The largest integer is an odd integer.
Hence, statement 2 is sufficient, the correct answer is Option B.
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Re: Is the largest of three consecutive integers odd? [#permalink] New post  28 Feb 2020, 03:44
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Is the largest of three consecutive integers odd?

Statement 1: The product of the three integers is 0.
If the product is 0 then the 3 integers can be
{-2, -1, 0} or {-1, 0, 1} or {0, 1, 2}
but we cannot determine which one is the largest integer.
Not Sufficient

Statement 2: The sum of the three integers is 0.
If the sum of 3 consecutive integers is 0 then 3 integers can be:
{-1, 0, 1} - No any other combination will suffice the condition.
Largest integer is 1 which is odd.
Sufficient

So, the answer is (B)
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Re: Is the largest of three consecutive integers odd? [#permalink] New post  29 Feb 2020, 01:05
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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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Re: Is the largest of three consecutive integers odd? [#permalink] New post  29 Feb 2020, 02:08
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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.


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


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] New post  10 Jun 2023, 09:37
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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Bunuel
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Re: Is the largest of three consecutive integers odd? [#permalink] New post  10 Jun 2023, 09:43
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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] New post  11 Jun 2023, 21:45
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] New post  11 Jun 2023, 23:40
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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.
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Re: Is the largest of three consecutive integers odd? [#permalink]
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