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# M02-18

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Intern
Joined: 29 Sep 2017
Posts: 5

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10 Jul 2018, 09:45
how can you say on the basis of 2nd statement that the set consists of only negative or only positive numbers? The smallest and largest numbers will have the same sign. Excluding the smallest and largest numbers, other numbers can be mix of positive and negative.
Intern
Joined: 16 Jun 2018
Posts: 10

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13 Aug 2018, 00:35
(1) The product of any three integers in the set is negative. If the set consists of only 3 terms, then the set could be either {negative, negative, negative} or {negative, positive, positive}. If the set consists of more than 3 terms, then the set can only have negative numbers. Not sufficient.

(2) The product of the smallest and largest integers in the set is a prime number. Since only positive numbers can be primes, then the smallest and largest integers in the set must be of the same sign. Thus the set consists of only negative or only positive integers. Not sufficient.

(1)+(2) Since the second statement rules out {negative, positive, positive} case which we had from (1), then we have that the set must have only negative integers. Sufficient.

Bunuel

If the set consists of more than 3 terms, then the set can only have negative numbers.--?

Bunuel what if we have the set as -1 -1 1 1 in that case we do have a case of any 3 numbers turning up a negative result for -1 1 and 1.
How can all the numbers be negative if more than 3 terms exist?

Pls explain.
Math Expert
Joined: 02 Sep 2009
Posts: 50712

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13 Aug 2018, 00:57
psych77 wrote:
(1) The product of any three integers in the set is negative. If the set consists of only 3 terms, then the set could be either {negative, negative, negative} or {negative, positive, positive}. If the set consists of more than 3 terms, then the set can only have negative numbers. Not sufficient.

(2) The product of the smallest and largest integers in the set is a prime number. Since only positive numbers can be primes, then the smallest and largest integers in the set must be of the same sign. Thus the set consists of only negative or only positive integers. Not sufficient.

(1)+(2) Since the second statement rules out {negative, positive, positive} case which we had from (1), then we have that the set must have only negative integers. Sufficient.

Bunuel

If the set consists of more than 3 terms, then the set can only have negative numbers.--?

Bunuel what if we have the set as -1 -1 1 1 in that case we do have a case of any 3 numbers turning up a negative result for -1 1 and 1.
How can all the numbers be negative if more than 3 terms exist?

Pls explain.[/quote]

{-1, -1, 1, 1} does not satisfy the condition that the product of ANY three integers in the set is negative: -1*(-1)*1 = 1 = positive.

As explained in the solution, this could be true if:
a. the set consists of only 3 terms, then the set could be either {negative, negative, negative} or {negative, positive, positive}.
b. the set consists of more than 3 terms, then the set can only have negative numbers.
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Joined: 20 May 2018
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17 Sep 2018, 02:21
definitely a high quality question!
Re: M02-18 &nbs [#permalink] 17 Sep 2018, 02:21

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# M02-18

Moderators: chetan2u, Bunuel

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