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Integer properties

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Integer properties

by daflower » Mon Jul 19, 2010 8:31 pm
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 smallest number is positive
(2) There is an even number of integers on the list

A) Statement 1 alone is sufficient
B) Statement 2 alone is sufficient
A) Both statements together are sufficient, but neither ALONE is sufficient
A) Each statement alone is sufficient
A) Statement 1 and 2 are not sufficient
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by Rahul@gurome » Mon Jul 19, 2010 9:55 pm
daflower 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 smallest number is positive
(2) There is an even number of integers on the list

A) Statement 1 alone is sufficient
B) Statement 2 alone is sufficient
C) Both statements together are sufficient, but neither ALONE is sufficient
D) Each statement alone is sufficient
E) Statement 1 and 2 are not sufficient
(1) 1st statement implies that either both of them are positive or both of them negative. It means all the integers between largest and positive integers should also have the same sign. So, either every integer in the list is positive, or every integer in the list is negative.
So, (1) is NOT SUFFICIENT.

(2) 2nd statement implies that product of integers is either positive or negative.
So, (2) is NOT SUFFICIENT.

Combining (1) & (2), the set of integers are either all positive and even or negative and even, which implies that the product will always be positive.

The correct answer is[spoiler] (C)[/spoiler].
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by Patrick_GMATFix » Tue Jul 20, 2010 12:02 pm
Rahul explained this well. For the product of all integers to be positive, there must be an even number of negative values (so that the negatives will cancel each other out).

(1) tells us that all values have the same sign
(2) tells us that there are an even number of values

Merging the statements guarantees that we have an even number of negatives (either 0 which is even, or some other even number of values all negative)

The answer is C. A more complete discussion and take-away lesson as well as step-by-step video solution can be found at GMATPrep Question 1106. To practice similar questions, set topic='Number Properties' and difficulty='600-700' in the Drill Generator

Good luck,
-Patrick
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