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M02-18

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New post 18 Dec 2016, 21:24
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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New post 18 Dec 2016, 23:23
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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New post 17 Mar 2017, 23:20
one of the finest question. How the statemen 2 incorporated in question
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New post 18 May 2017, 04:16
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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New post 18 May 2017, 04:21
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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New post 29 Jun 2017, 22:51
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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New post 07 Nov 2017, 04:46
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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New post 26 Nov 2017, 12:14
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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New post 26 Nov 2017, 12:22
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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New post 13 Feb 2018, 04:03
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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New post 13 Feb 2018, 05:25
karn99 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.


I'd suggest to read the whole discussion once again and ask specific question.

P.S. The question is 100% correct and up to highest GMAT standards. It's not that easy though for novices.
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New post 13 Feb 2018, 05:55
Bunuel wrote:
karn99 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.


I'd suggest to read the whole discussion once again and ask specific question.

P.S. The question is 100% correct and up to highest GMAT standards. It's not that easy though for novices.


According to statement (2) the set S can contain {-1,2,-3} and isn't it sufficient to answer that all the elements of set S are NOT negative?
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New post 13 Feb 2018, 05:58
karn99 wrote:
Bunuel wrote:
karn99 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.


I'd suggest to read the whole discussion once again and ask specific question.

P.S. The question is 100% correct and up to highest GMAT standards. It's not that easy though for novices.


According to statement (2) the set S can contain {-1,2,-3} and isn't it sufficient to answer that all the elements of set S are NOT negative?


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

In set {-1,2,-3} the smallest number is -3 and the largest number is 2, their product is -6, which is not a prime number.
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New post 13 Feb 2018, 09:34
As the questions says that the product of any three numbers is negative.

Lets say if one number is positive,
+1, -1, -3, -9

As it says any three integers, we can take +1, -1, -3
prod = +3

The only way the product of "ANY" three integers are negative is only if all the numbers in the set are -ve.

The answer should be A.
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New post 13 Feb 2018, 09:45
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dileeprk wrote:
As the questions says that the product of any three numbers is negative.

Lets say if one number is positive,
+1, -1, -3, -9

As it says any three integers, we can take +1, -1, -3
prod = +3

The only way the product of "ANY" three integers are negative is only if all the numbers in the set are -ve.

The answer should be A.


The answer should be and is C, not A.

The product of any three integers in the set is negative means that no matter which three integers you pick from the set their product will turn out to be negative. Or in other words ALL sets of three integers you could pick will give negative product. The solution shows a set which gives a negative product while not having all negative terms: {negative, positive, positive}. The solution also mentions the following: If the set consists of more than 3 terms, then the set can only have negative numbers.
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New post 08 Jun 2018, 20:45
I think this the explanation isn't clear enough, please elaborate. In the second statement it is given the product of smallest and largest no is prime, thus only these two should be of same sign. How is it assumed that all three numbers will be of same sign.
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New post 08 Jun 2018, 22:24
Anishajha wrote:
I think this the explanation isn't clear enough, please elaborate. In the second statement it is given the product of smallest and largest no is prime, thus only these two should be of same sign. How is it assumed that all three numbers will be of same sign.


This is explained several times in this thread. Please read it. Hope it helps.
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M02-18  [#permalink]

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New post 07 Jul 2018, 04:33
Hi Bunuel!

This question was in my Quant CAT today. I chose A. At the back of my mind, I was confused between A and C. But could not find a good an example. In the question it says that set S has more than 2 integers and according to statement 1, product of any 3 integers is negative. The explanation gives an example where S has 3 integers. Consider the following set
{2,3,-5,-2,-4}
In this set, the product of any 3 integers will be negative if we take odd number of negative integers i.e 1 and 3. However, in a case where we choose {2,-5,-4} or similar 3 integers from set S, where there are even number of negative integers, the product is positive.
Please can you help me identify my mistake.

Thanks,
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New post 07 Jul 2018, 08:19
vaibhav1221 wrote:
Hi Bunuel!

This question was in my Quant CAT today. I chose A. At the back of my mind, I was confused between A and C. But could not find a good an example. In the question it says that set S has more than 2 integers and according to statement 1, product of any 3 integers is negative. The explanation gives an example where S has 3 integers. Consider the following set
{2,3,-5,-2,-4}
In this set, the product of any 3 integers will be negative if we take odd number of negative integers i.e 1 and 3. However, in a case where we choose {2,-5,-4} or similar 3 integers from set S, where there are even number of negative integers, the product is positive.
Please can you help me identify my mistake.

Thanks,
V


{2,3,-5,-2,-4} does not satisfy the condition that the product of ANY three integers in the set is negative: 2*(-5)*(-2) = 20 = 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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Re: M02-18  [#permalink]

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New post 10 Jul 2018, 10:37
how can you say on the basis of 2nd statement that the set consists of only positive or only negative numbers?
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