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If P is the product of n distinct integers, is P<0?
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Updated on: 04 Aug 2019, 11:56
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If P is the product of n distinct integers, is P<0? 1. n distinct integers are consecutive numbers and their median is 4.5 2. Out of n distinct integers 5 are negative
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Originally posted by raghavrf on 04 Aug 2019, 04:01.
Last edited by Bunuel on 04 Aug 2019, 11:56, edited 1 time in total.
Edited the OA.



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Re: If P is the product of n distinct integers, is P<0?
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04 Aug 2019, 06:41
raghavrf wrote: If P is the product of n distinct integers, is P<0? 1. n distinct integers are consecutive numbers and their median is 4.5 2. Out of n distinct integers 5 are negative If the OA is B, there's something wrong with the question. If Statement 1 is true, then either the set contains a small number of consecutive integers, and every value is positive, so their product is positive, or the set is larger and the lower values in the set extend to zero or past zero into negative values. But if it's a set of consecutive integers, then the set would then contain zero, so the product of the values in the set would be zero. The product could never be negative, so Statement 1 is sufficient to give a "no" answer to the question. Statement 2 is not sufficient, because if we have five negative values, and the rest of the values are positive, the product is negative, but if we have five negative values and we have zero in the set, the product is zero. So we can't be sure if the product is negative.
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Re: If P is the product of n distinct integers, is P<0?
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04 Aug 2019, 07:01
Statement 1: the median is 4.5 hence middle terms are 4 and 5 and there is even number of terms in the set. terms can be 1,2,3,4,5,6,7,8  product>0 terms can be 5,4,3,2,1,0,1,2,3,4,5 product=0 see that product will never be <0 if median is 4.5 because 0 crossover will always be there Sufficient Statement 2: there are 5 negative terms out of n consecutive terms 5,4,3,2,1  product is <0 5,4,3,2,1,0  product=0 Not Sufficient Answer A Bunuel please correct the answer



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Re: If P is the product of n distinct integers, is P<0?
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04 Aug 2019, 12:05
vinayakvaish wrote: Statement 1: the median is 4.5 hence middle terms are 4 and 5 and there is even number of terms in the set. terms can be 1,2,3,4,5,6,7,8  product>0 terms can be 5,4,3,2,1,0,1,2,3,4,5 product=0 see that product will never be <0 if median is 4.5 because 0 crossover will always be there Sufficient Statement 2: there are 5 negative terms out of n consecutive terms 5,4,3,2,1  product is <0 5,4,3,2,1,0  product=0 Not Sufficient Answer A Bunuel please correct the answer _____________________ Edited the OA. Thank you.
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Re: If P is the product of n distinct integers, is P<0?
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04 Aug 2019, 19:30
We know that numbers are consecutive integers. For statement 2, If 5 values out of n are negative than, the remaining values will be equal to or more than 0. Therefore, if the value of n is 5 then P will be negative; otherwise, P will be 0 in all other cases. For ex. 5, 4, 3, 2, 1 then P IS NEGATIVE. 5, 4, 3, 2, 1, 0 then P is 0. 5. 4, 3, 2, 1, 0, 1 Then P is O. The main problem is that we are not told whether n is 5. quote="IanStewart"] raghavrf wrote: If P is the product of n distinct integers, is P<0? 1. n distinct integers are consecutive numbers and their median is 4.5 2. Out of n distinct integers 5 are negative If the OA is B, there's something wrong with the question. If Statement 1 is true, then either the set contains a small number of consecutive integers, and every value is positive, so their product is positive, or the set is larger and the lower values in the set extend to zero or past zero into negative values. But if it's a set of consecutive integers, then the set would then contain zero, so the product of the values in the set would be zero. The product could never be negative, so Statement 1 is sufficient to give a "no" answer to the question. Statement 2 is not sufficient, because if we have five negative values, and the rest of the values are positive, the product is negative, but if we have five negative values and we have zero in the set, the product is zero. So we can't be sure if the product is negative.[/quote]



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Re: If P is the product of n distinct integers, is P<0?
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04 Aug 2019, 19:36
According to your explanation, terms can be 5,4,3,2,1,0,1,2,3,4,5 product=0But in your sequence, the median is not 4.5. We can understand this as below. Seq.1= 2, 3, 4, 5, 6 7 >>>>P= POSITIVE Seq.2= 1, 2, 3, 4, 5, 6, 7, 8>>>>>p= zero Seq.3 = 1,0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 =>>>>P=ZER0. so P will never be negative. vinayakvaish wrote: Statement 1: the median is 4.5 hence middle terms are 4 and 5 and there is even number of terms in the set. terms can be 1,2,3,4,5,6,7,8  product>0 terms can be 5,4,3,2,1,0,1,2,3,4,5 product=0 see that product will never be <0 if median is 4.5 because 0 crossover will always be there Sufficient Statement 2: there are 5 negative terms out of n consecutive terms 5,4,3,2,1  product is <0 5,4,3,2,1,0  product=0 Not Sufficient Answer A Bunuel please correct the answer




Re: If P is the product of n distinct integers, is P<0?
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04 Aug 2019, 19:36






