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M02-18

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Re M02-18 [#permalink]

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New post 10 Sep 2016, 04:35
I think this is a high-quality question.

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New post 10 Sep 2016, 04:36
I think this is a high-quality question and I agree with explanation.

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New post 25 Nov 2016, 19:12
I think this is a high-quality question and I agree with explanation.

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Re: M02-18 [#permalink]

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New post 18 Dec 2016, 20:24
Please elaborate how did you choose option C ? From option B you have concluded that the possibility is only {negative,positive,positive} as prime numbers can only be positive and from option C you have eliminated the same case and choose all numbers to be negative.

Kindly help where I am missing !

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Re: M02-18 [#permalink]

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New post 18 Dec 2016, 22:23
GouthamNandu wrote:
Please elaborate how did you choose option C ? From option B you have concluded that the possibility is only {negative,positive,positive} as prime numbers can only be positive and from option C you have eliminated the same case and choose all numbers to be negative.

Kindly help where I am missing !


From (1): the set could be either {negative, negative, negative} or {negative, positive, positive}.
From (2): the set consists of only negative or only positive integers.

(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.
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Re: M02-18 [#permalink]

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New post 17 Mar 2017, 22:20
one of the finest question. How the statemen 2 incorporated in question
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Re: M02-18 [#permalink]

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New post 18 May 2017, 03:16
Bunuel wrote:
Official Solution:


(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.


Answer: C


I think there is an error in the explanation to statement 1. I agree if there are 3 terms, there can be either 1 negative or all 3 negative. However in any set with a higher no of elements all the terms need to be negative. eg.According to your explanation, if there are 5 terms with 1 positive integer then lets say, {3, -3, -4, -5, -6} are the terms. As per statement 1, we have to select 3 terms, so if I select (-3, -4, 3) it makes the product positive. But the statement says that any 3 nos. selected at random will have negative product which can only be possible if all the terms are negative (when the total elements are more than 3).

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Re: M02-18 [#permalink]

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New post 18 May 2017, 03:21
Ashy Boy wrote:
Bunuel wrote:
Official Solution:


(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.


Answer: C


I think there is an error in the explanation to statement 1. I agree if there are 3 terms, there can be either 1 negative or all 3 negative. However in any set with a higher no of elements all the terms need to be negative. eg.According to your explanation, if there are 5 terms with 1 positive integer then lets say, {3, -3, -4, -5, -6} are the terms. As per statement 1, we have to select 3 terms, so if I select (-3, -4, 3) it makes the product positive. But the statement says that any 3 nos. selected at random will have negative product which can only be possible if all the terms are negative (when the total elements are more than 3).


Where is an error? The solution clearly says: If the set consists of more than 3 terms, then the set can only have negative numbers.
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Re: M02-18 [#permalink]

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New post 29 Jun 2017, 21:51
What a brilliant question!!
I got it wrong during the test but while I was analyzing the test, I solved it correctly.

For A ; Its easy to overlook the set with only 3 numbers - { -1,2,5} or { -1,-2,-5} which will tell that it is NOT SUFFICIENT
For B; knowing that only positive nos are prime is the key.
since product of smallest & largest nos is always > 0; hence either all ae positive nos or all are negative nos- NOT SUFFICIENT

Combining A & B -> from A, we got only one set with 3 nos which was not sufficient, now we know that first and last numbers are of same sign (to be >0)
Hence { negative, positive, positive} set is not possible as product will be < 0.
So, all the numbers in set have to be negative!
C wins!

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Re: M02-18 [#permalink]

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New post 07 Nov 2017, 03:46
Bunuel wrote:
Set S consists of more than two integers. Are all the integers in set S negative?

(1) The product of any three integers in the set is negative.

(2) The product of the smallest and largest integers in the set is a prime number.



Statement 1: This does not imply that all integers in the set will be negative. If there are 3 integers and any one of these is negative, then the product will be negative.

Statement 2: A prime number is always positive. So, the smallest and largest integer of the set will be 1 and a prime number or -1 and -prime. Insufficient.

Together: From 1 we know the product of any 3 is negative. The first combination obtained through statement 2 is not possible as an integer lying between 1 and 5 will be positive and would not render any negative product. Thus, the second combination where all integers are negative will hold and this gives us a definite Yes as an answer. C.

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Re M02-18 [#permalink]

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New post 26 Nov 2017, 11:14
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. (2) The product of the smallest and largest integers in the set is a prime number.

I don´t see how can this actually happen. The set consist of more than two integers, and the only prime number that can be the product of two integers is 2. Therefore, it could be:
- 1 * - 2 = 2 or (-1 being the largest integer and -2 being the smallest)
1 * 2 = 2 (1 being the smallest and 2 being the largest)

However, it says that the set consists of more than two integers.... Please advise

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Re: M02-18 [#permalink]

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New post 26 Nov 2017, 11:22
rperaalv wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. (2) The product of the smallest and largest integers in the set is a prime number.

I don´t see how can this actually happen. The set consist of more than two integers, and the only prime number that can be the product of two integers is 2. Therefore, it could be:
- 1 * - 2 = 2 or (-1 being the largest integer and -2 being the smallest)
1 * 2 = 2 (1 being the smallest and 2 being the largest)

However, it says that the set consists of more than two integers.... Please advise


This could happen VERY easily. Foe example:

{-3, -2, -1} --> The product of the smallest and largest integers in the set = (-3)*(-1) = 3 = prime number.
{-7, -6, -4, -1} --> The product of the smallest and largest integers in the set = (-7)*(-1) = 7 = prime number.
{1, 2, 3, 4, 5, 17} --> The product of the smallest and largest integers in the set = 1*17 = 17 = prime number.
...

Hope now is clear/.
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Re: M02-18   [#permalink] 26 Nov 2017, 11:22

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