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Is the product of three consecutive integers negative?
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28 Feb 2014, 04:14
28 Feb 2014, 04:14
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Difficulty:
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Question Stats:
46% (01:53) correct
54%
(01:48)
wrong
based on 284
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Is the product of three consecutive integers negative?
(1) The sum of the integers is equal to the product of the integers.
(2) At least one of the integers is negative.
(1) The sum of the integers is equal to the product of the integers.
(2) At least one of the integers is negative.
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Re: Is the product of three consecutive integers negative?
[#permalink]
28 Feb 2014, 04:14
28 Feb 2014, 04:14
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Expert Reply
Official Solution:
Is the product of three consecutive integers negative?
(1) The sum of the integers is equal to the product of the integers.
Let the three consecutive integers be \((x-1)\), \(x\), and \((x+1)\). Hence, the above statement implies that \((x-1)+x+(x+1) = (x-1)x(x+1)\):
\(3x=x(x^2-1)\)
\(x(x^2-4)=0\)
Thus, \(x=-2\), \(x=0\), or \(x=2\).
The possible sets are: {-3, -2, -1}, {-1, 0, 1}, or {1, 2, 3}. Not sufficient.
(2) At least one of the integers is negative.
Considering this, we can have three scenarios:
(i) All three integers are negative. In this case, their product is negative.
(ii) Two of the integers are negative: {-2, -1, 0}. In this case the product will be zero.
(iii) Only one of the integers is negative: {-1, 0, 1}. In this case the product will be zero.
Not sufficient.
(1)+(2) We still can have 2 sets: {-3, -2, -1} and {-1, 0, 1}. So, the product can be negative as well as zero. Not sufficient.
Answer: E.
Is the product of three consecutive integers negative?
(1) The sum of the integers is equal to the product of the integers.
Let the three consecutive integers be \((x-1)\), \(x\), and \((x+1)\). Hence, the above statement implies that \((x-1)+x+(x+1) = (x-1)x(x+1)\):
\(3x=x(x^2-1)\)
\(x(x^2-4)=0\)
Thus, \(x=-2\), \(x=0\), or \(x=2\).
The possible sets are: {-3, -2, -1}, {-1, 0, 1}, or {1, 2, 3}. Not sufficient.
(2) At least one of the integers is negative.
Considering this, we can have three scenarios:
(i) All three integers are negative. In this case, their product is negative.
(ii) Two of the integers are negative: {-2, -1, 0}. In this case the product will be zero.
(iii) Only one of the integers is negative: {-1, 0, 1}. In this case the product will be zero.
Not sufficient.
(1)+(2) We still can have 2 sets: {-3, -2, -1} and {-1, 0, 1}. So, the product can be negative as well as zero. Not sufficient.
Answer: E.
General Discussion
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Joined: 24 Sep 2011
Posts: 14
Given Kudos: 46
Location: India
Schools: IIM
GMAT 1: 650 Q50 V26
GPA: 4
Re: Is the product of three consecutive integers negative?
[#permalink]
28 Feb 2014, 06:38
28 Feb 2014, 06:38
1
Kudos
Consider consecutive integers as
a-1, a, a+1
1. According to statement 1 ,
Sum = product
so 3a= a ( a^2 -1) solving we get a=0, a=-2 , +2
three values of a so ,
integers are -1, 0, 1 -3,-2,-1, and 1, 2 , 3
as we cannot answer the target question with certainty ..Statement is insufficient
2. Second statement : clearly insufficient , as when 1 is negative = product is -ve
2 are -ve = product is +ve
So 2nd statement is also insufficient
Combining both we get consecutive integers as : -1, 0 , 1 ===product is zero
-3, -2, -1 ===product is -ve
E is the answer
a-1, a, a+1
1. According to statement 1 ,
Sum = product
so 3a= a ( a^2 -1) solving we get a=0, a=-2 , +2
three values of a so ,
integers are -1, 0, 1 -3,-2,-1, and 1, 2 , 3
as we cannot answer the target question with certainty ..Statement is insufficient
2. Second statement : clearly insufficient , as when 1 is negative = product is -ve
2 are -ve = product is +ve
So 2nd statement is also insufficient
Combining both we get consecutive integers as : -1, 0 , 1 ===product is zero
-3, -2, -1 ===product is -ve
E is the answer
