A certain list consists of several different integers

[Ladan]

I also don't seem to understand how the following DS problem can be solved with the given information.



Thanks for you all you guys and gals do at ManhattanGMAT - you've all been so helpful!

[GMAT 2007]

Ladan,

From statement (1), we know the product of the highest and the lowest integer is + ve, it means either both of them are +ve or -ve

For ex: -2,-1,1,2 in this list the product of -2&2 is -4. It proves both the highest and the lowest terms have to be of same sign.

(+ve or -ve) the other factor that needs to be considered is the no. of terms in the list,

If the no. of terms is odd and all the integers are -ve, the product of all the integers will be -ve this information is given by statement (2)

no. of terms in the list are even, hence the product of all the integers in the list will always be +ve.

So if you combine (1) & (2), they are sufficient.

GMAT 2007

[guest]

What does "ve" mean?

[GMAT 2007]

+ve = positive
-ve = negative

GMAT 2007

[PositiveNegative]

Here is how I tried it but I still get choice E.

I eliminated choice A,B, and D.

Now I am using both statements together. In this case I have 4 different integers, ordered from least to smallest, which satisfies statement 2.
={+,-,-,+} ==> Positive Product
={-,-,-,-} ===> Positive Product
={+,-,+,+} ===> Negative product

we have two conflicting results, enough for us to choose C

[Positive Neg]

Can someone from MGMAT staff pleas provide assistance? thanks.

[kevincan]

(1) The n integers are all positive, in which case their product is positive, or all negative, in which case the product is negative if n is odd or positive if n is even.
(2) There may be an even or odd number of negative numbers, so not sufficient
(T) Even if the integers are all negative, the product is positive, as n is even

Kevin Armstrong
Madrid, Spain

[Guest]

Here is how I tried it but I still get choice E.

I eliminated choice A,B, and D.

Now I am using both statements together. In this case I have 4 different integers, ordered from least to smallest, which satisfies statement 2.
={+,-,-,+} ==> Positive Product
={-,-,-,-} ===> Positive Product
={+,-,+,+} ===> Negative product

we have two conflicting results, enough for us to choose C

I meant we have two conflicting results, enough for us to choose E

[Captain]

={+,-,-,+} ==> Positive Product
={-,-,-,-} ===> Positive Product
={+,-,+,+} ===> Negative product

You have to multiply the smallest and the largest to satisfy case I. For exmple {+,-,-,+} does not satisfy case I. You have taken both negative numbers in the middle. But the smallest number will be one of the negative numbers and the largest one of the positive ones, giving a negative product of as opposed to positive. Same holds for the third example you have used.

[Guest]

I get it now, thanks Captain.

[RonPurewal]

={+,-,-,+} ==> Positive Product
={-,-,-,-} ===> Positive Product
={+,-,+,+} ===> Negative product

You have to multiply the smallest and the largest to satisfy case I. For exmple {+,-,-,+} does not satisfy case I. You have taken both negative numbers in the middle. But the smallest number will be one of the negative numbers and the largest one of the positive ones, giving a negative product of as opposed to positive. Same holds for the third example you have used.

yep - if you have numbers arranged from least to greatest, then any '-' numbers must show up to the left of all '+' numbers. otherwise, you've created an impossible situation in which a negative number is somehow bigger than a positive number.

the rest of the explanations on this thread are fantastic, so there's really not much that we official types can add here.

[anky666]

Why dont we consider 0 here? 0 is also an integer.

[anky666]

I got it.. 0 cannot be in the list.

Thanks anyways..

[Andrew]

HEY~Don't u think the setence"Is the product of all integers in this list positive? "is ambiguous
ex. (-2,-1,1,2) imo, it means -2*-1*1*2 not mean -2*2 to satisfy I
moreover " There is an even number of integers"
means the number of intrgers is even number,but i always misunderstand to be "exist an even number"
i'm a chinese , so feel difficult to identify the little difference lol

[RR]

I got it.. 0 cannot be in the list.

Thanks anyways..

anky666, I don't know why you said that zero cannot be on the list. I feel that zero can be on the list. But the good part is, the answer does not change if zero is there. If zero is there, the product of all numbers in the list will be zero and hence positive. And you still need choices 1 & 2 if the list consists of only non-zero numbers.