If P is the product of n distinct integers, is P

Question

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

vinayakvaish · Accepted Answer

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 cross-over 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

IanStewart · Answer

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.

Bunuel · Answer

_____________________
Edited the OA. Thank you.

gvij2017 · Answer

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"]

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.

gvij2017 · Answer

According to your explanation,
 terms can be -5,-4,-3,-2,-1,0,1,2,3,4,5- product=0

But 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.

SatvikVedala · Answer

Considering Option 1, Given

n distinct  integers  are  consecutive numbers  and their  median is 4.5

considering x(as one integer) & y(as another integer)

(x+y)/2 =4.5 ==> (x+y) = 9 ==> (x+x+1) = 9 ==> x = 4

Therefore one integer is 4 & one integer is 5

the sequences are beyond 0 i.e. -4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,13 - Product is 0

the sequences are after 0 i.e. 1,2,3,4,5,6,7,8- Product > 0

No chance for P to be less than 0

From Option 2

if 5 integers are negative, as per the example above P can be -ve or 0

So we can opt option A

QuantMadeEasy · Answer

I have used a strategy to solve the question. The detailed solution is provided in the video below. I hope this helps.

https://www.youtube.com/watch?v=rUg4o70H_LQ

If P is the product of n distinct integers, is P<0?

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GMAT Data Sufficiency (DS) Questions

If P is the product of n distinct integers, is P<0?

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