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Is the sum of three consecutive even integers zero?

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Is the sum of three consecutive even integers zero? [#permalink] New post   19 Mar 2021, 09:03
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67% (01:08) correct 33% (01:20) wrong based on 51 sessions
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Is the sum of three consecutive even integers zero?
1) The product of the three consecutive even integers is zero
2) The sum of the least and the greatest integer is zero
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B
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MarmikUpadhyay
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Is the sum of three consecutive even integers zero? [#permalink] New post   19 Mar 2021, 09:29
Expert Reply
Is the sum of three consecutive integers = 0?
Let three consecutive integers = n, n + 2 and n + 4.
Is n + n + 2 + n + 4 = 3n + 6 = 0?

Statement 1:
n * (n + 2) * (n + 4) = 0
In this case, any one of the three numbers can be 0.
Case 1: n = 0, then, n + 2 = 2, and n + 4 = 4.
Sum = 3n + 6 = 3 * 0 + 6 = 6 \(\neq\) 0
Case 2: n + 2 = 0 => n = -2, and n + 4 = 2
Sum = 3n + 6 = 3 * (-2) + 6 = 0
Case 3: n + 4 = 0 (not needed as we got two different answers for above two cases, still can check this case)
Statement 1 is Not Sufficient.

Statement 2:
n + (n + 4) = 0
=> 2n + 4 = 0
=> n = -2
Sum = 3n + 6 = 3 * (-2) + 6 = 0
Statement 2 is Sufficient.

So, correct answer is option B.
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Re: Is the sum of three consecutive even integers zero? [#permalink] New post   25 Mar 2021, 15:19
Am I missing something?

St1 -
x = 0, y = 1, z = 2 ---> 1 + 2 + 0 = 3
x = -1, y = 1, z = 0 ---> -1 + 1 + 0 = 0
Insufficient

St2 -
x = -1, y = 0, z = 1 ---> -1 + 1 + 0 = 0 YES
x = -2, y = 1, z = 2 ---> -2 + 1 + 2 = 1 NO

Shouldn't St2 be insufficient?
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Re: Is the sum of three consecutive even integers zero? [#permalink] New post   25 Mar 2021, 16:16
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CEdward wrote:
Am I missing something?

St1 -
x = 0, y = 1, z = 2 ---> 1 + 2 + 0 = 3
x = -1, y = 1, z = 0 ---> -1 + 1 + 0 = 0
Insufficient

St2 -
x = -1, y = 0, z = 1 ---> -1 + 1 + 0 = 0 YES
x = -2, y = 1, z = 2 ---> -2 + 1 + 2 = 1 NO

Shouldn't St2 be insufficient?


-2, 1 and 2 are not three consecutive even integers

On another note, you cannot take the example of -1,0,1 as well because those are not three consecutive even integers too.

-2,0,2 is the only set that can be true for st.2

Posted from my mobile device
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Re: Is the sum of three consecutive even integers zero? [#permalink] New post   25 Mar 2021, 18:40
firas92 wrote:
CEdward wrote:
Am I missing something?

St1 -
x = 0, y = 1, z = 2 ---> 1 + 2 + 0 = 3
x = -1, y = 1, z = 0 ---> -1 + 1 + 0 = 0
Insufficient

St2 -
x = -1, y = 0, z = 1 ---> -1 + 1 + 0 = 0 YES
x = -2, y = 1, z = 2 ---> -2 + 1 + 2 = 1 NO

Shouldn't St2 be insufficient?


-2, 1 and 2 are not three consecutive even integers

On another note, you cannot take the example of -1,0,1 as well because those are not three consecutive even integers too.

-2,0,2 is the only set that can be true for st.2

Posted from my mobile device


Silly mistakes be damned...
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Re: Is the sum of three consecutive even integers zero? [#permalink]
25 Mar 2021, 18:40
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