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GMAT Prep Integer Question

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GMAT Prep Integer Question

by Baldini » Tue Mar 10, 2009 1:13 am
A certain list consists of several different integers. is the product of all the integers in the list positive?

(1) the product of the greatest and the smallest integer in the list is positive
(2) there is an even number of integers in the list

I get OA E but official OA is C. Can someone please explain how to get the answer?
thanks in advance[/spoiler]
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by cubicle_bound_misfit » Tue Mar 10, 2009 2:47 am
The answer is obviously C.

te trick lies in the sentence product of greatest and smallest integer is positive--> so, they have to have same 'sign' and what comes in between should have same sign also.

if the list contains even numbers of integers the product has to be positive.
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by Vemuri » Wed Mar 11, 2009 1:58 am
cubicle_bound_misfit wrote:The answer is obviously C.

te trick lies in the sentence product of greatest and smallest integer is positive--> so, they have to have same 'sign' and what comes in between should have same sign also.

if the list contains even numbers of integers the product has to be positive.
I don't think I understand your explanation. The question does not say that the signs of the integers change alternatively or if they are consecutive integers. It simply says different numbers. So, the signs of the integers can be anything.

Statement I: Does not help because we know nothing about the integers in between the greatest & smallest integers.

Statement II: Does not help because even we know nothing about the pattern of signs for the integers. Even or odd number of integers will not help us determine if the product of all the numbers is positive or not.

Both the statements put together will also not help. If there are even number of integers (lets assume 6), and the product of the smallest & largest integers is positive, we still don't know anything about the numbers in between.
ex: -1, -2, 3, 4, 5, -6 (satisfies both the statement conditions), but gives a product value that is negative.
ex: -1, -2, -3, -4, -5, -6 (satisfies both the statement conditions), but gives a product value that is positive.

Hence the answer should be E. Can anybody explain what I am doing wrong?
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by DanaJ » Wed Mar 11, 2009 5:11 am
I posted an explanation on another occasion:

Here's how I see it:
1. tells us that (smallest)*(greatest) is positive means that:
a. both are positive and since they are the "ends" of the series, that makes all the numbers positive. In this case, the product will be positive
b. both are negative, making all of the numbers negative. However, in this case we cannot tell if the product is positive, since we don't know if we have an even or an odd "number" of numbers. Take for example: -5, -4, -3. While it's true that (-5)*(-3) is positive, that cannot be said about the product of the three.

2 doesn't help much. All numbers could be positive, or you could have smth like: -5, 3, 4, 5.

Put the two together and you "eliminate" that weak spot in case b from stmt 1: even if all numbers are negative, they "cancel" each other's minuses. So the OA is ok.
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by cramya » Wed Mar 11, 2009 5:16 am
ex: -1, -2, 3, 4, 5, -6 (satisfies both the statement conditions), but gives a product value that is negative.

Vemuri,
With the above example stmt II's condition is satisfied but not statement I's.

lowest : -6 highest: 5

The product turns out negative but it should be positive from stm I

This may have been the missing piece.

Hope this helps.

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Re: GMAT Prep Integer Question

by marcusking » Wed Mar 11, 2009 6:09 am
Baldini wrote:A certain list consists of several different integers. is the product of all the integers in the list positive?

(1) the product of the greatest and the smallest integer in the list is positive
(2) there is an even number of integers in the list

I get OA E but official OA is C. Can someone please explain how to get the answer?
thanks in advance[/spoiler]
I always approach these problems by trying to prove them insufficient so for statement 1 I will try to make it negative and positive.

1) lets take the set [-5,-3,-1] the product of -5 & -1 is positive but the product of all the numbers in the set is -15 If I add one number in the set i get [-5,-3,-2,-1] greatest and smallest (-5 & -1) has a positive integer but all numbers multiplied together is +30. There is ambiguity in the answers so immediately it's not sufficient.

2) lets try to prove this one insufficient also. lets try [-2,1] product of these numbers is -2. lets also try [2,1] this product is +2. Once again we have ambiguity so this is insufficient.

We are now down to choices E or C.

Lets try them both together
In order for both the smallest and greatest number to be positive when multiplied together both must have the same sign (+ or -) and all numbers in between must thus have the same sign.

[1,2,3,4] product of these is 24
[-1,-2,-3,-4] product of these is also 24

No matter what numbers you plug in or however many are in the set, as long as they are even and are all of the same sign the product must be positive.

C.
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