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Is the product of three consecutive integers negative? [#permalink]
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28 Feb 2014, 03:14
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Re: Is the product of three consecutive integers negative? [#permalink]
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28 Feb 2014, 03:14
SOLUTIONIs 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 \((x1)\), \(x\), and \(x+1\), so we are given that \((x1)+x+(x+1)=(x1)x(x+1)\) > \(3x=x(x^21)\) > \(x(x^24)=0\) > \(x=2\), \(x=0\), or \(x=2\). The set can be: {3, 2, 1}, {1, 0, 1}, or {1, 2, 3}. Not sufficient. (2) At least one of the integers is negative. We can have three cases: (i) All three integers are negative. In this case the product will obviously be 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.
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Re: Is the product of three consecutive integers negative? [#permalink]
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28 Feb 2014, 05:38
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Consider consecutive integers as a1, 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



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Re: Is the product of three consecutive integers negative? [#permalink]
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28 Feb 2014, 06:09
My Answer is "C"
Statement 1 is insufficient for example 1,2,3 have product and sum and product of 6 While 1,2,3 have a sum and product of 6 so there are two possibilities.
Statement 2 is insufficient because at least one negative means that there could be 1,2 or 3 numbers negative and each will have a different outcome and in the case of 1,0,1 the product is 0.
However, statement 1 and 2 taken together mean that the three numbers have to be negative and have a sum and product that is equal . So yes "C" means the product is negative !!
What is OA !!



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Re: Is the product of three consecutive integers negative? [#permalink]
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28 Feb 2014, 14:07
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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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03 Mar 2014, 11:22
SOLUTIONIs 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 \((x1)\), \(x\), and \(x+1\), so we are given that \((x1)+x+(x+1)=(x1)x(x+1)\) > \(3x=x(x^21)\) > \(x(x^24)=0\) > \(x=2\), \(x=0\), or \(x=2\). The set can be: {3, 2, 1}, {1, 0, 1}, or {1, 2, 3}. Not sufficient. (2) At least one of the integers is negative. We can have three cases: (i) All three integers are negative. In this case the product will obviously be 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.
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Re: Is the product of three consecutive integers negative? [#permalink]
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03 Mar 2014, 19:54
great example of why you can't blindly reduce equations [e.g. (x1)x(x+1)=3x > (x1)(x+1)=3] thanks Bunuel.
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Re: Is the product of three consecutive integers negative? [#permalink]
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07 Sep 2015, 08:47
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Is the product of three consecutive integers negative? [#permalink]
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08 Sep 2015, 06:24
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution. 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. In the original condition we have three consecutive integers thus we just need to know the first term, thus we have 1 variable. Since we need 1 equation, D is likely the answer. In case of 1), for (3,2,1) the answer is yes, for (1,0,1) the answer is no, and same for (1,2,3). The answer is not unique, therefore it is not sufficient. In case of 2), for (1,0,1) the answer is no, and for (3,2,1) the answer is yes. Thus the condition is not sufficient. Using both 1) & 2) together, for (1,0,1) the answer is no, for (3,2,1) the answer is yes. therefore the conditions are not sufficient. The answer is E.
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Re: Is the product of three consecutive integers negative? [#permalink]
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21 Feb 2017, 13:50
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Is the product of three consecutive integers negative?
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