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Bunuel
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M28-53 11 Apr 2020, 05:22
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ritikapatni
Hi Bunuel

For statement 1, why are you assuming that the set can have only 3 numbers, what if the set has many more numbers. Then how will you combine the statements?

Please advise.

Thanks!
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There are two cases considered:

(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.
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M28-53 01 Jun 2020, 11:00
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Since primes can only be positive, How can they be negative.
Statement b alone is sufficient and hence answer will be B
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Bunuel
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M28-53 01 Jun 2020, 11:12
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AashishGautam
Since primes can only be positive, How can they be negative.
Statement b alone is sufficient and hence answer will be B
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Primes cannot be negative and the solutions explicitly says that:

(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.

Check the examples below to see that (2) is not sufficient.
{-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.
...
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M28-53 07 Apr 2023, 12:35
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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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How it rules out (positive, positive) case? I Don’t understand. See suppose second case gives us (-1, -2 ) then it will fit and in the other case it is giving (1, 1), then it will not fit. And from S1 we are getting (1,2, -3) or any other combination and (-1, -2, -3). Taking s2 in consideration sill (1,2, -3 ) case can occur. Why is it wrong. Please justfy.

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M28-53 07 Apr 2023, 13:09
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innochandan
Bunuel
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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.


How it rules out (positive, positive) case? I Don’t understand. See suppose second case gives us (-1, -2 ) then it will fit and in the other case it is giving (1, 1), then it will not fit. And from S1 we are getting (1,2, -3) or any other combination and (-1, -2, -3). Taking s2 in consideration sill (1,2, -3 ) case can occur. Why is it wrong. Please justfy.

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{1, 2, -3} case is not possible because it does not satisfy the second statement, which says that "The product of the smallest and largest integers in the set is a prime number". The product of the smallest and largest integers of {1, 2, -3} is -3*2 = -6, which is not a prime.

Again, from (2) ("The product of the smallest and largest integers in the set is a prime number") we can conclude that since only positive numbers can be primes, the smallest and largest integers in the set must be of the same sign. Thus, the set consists of either only negative or only positive integers.

Hope it helps.
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M28-53 16 Apr 2023, 11:56
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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M28-53 24 May 2023, 06:54
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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. (1) says the product of ANY three integers in the set is negative. That means if the set has any positive integer, the product of three could be positive because the positive integer could be drawn into the set of three. I think A is the correct choice or the wording needs to be changed.
(-)(-)(-) = (-)
(-)(+)(+) = (-)
(-)(-)(+) = (+)
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M28-53 24 May 2023, 07:20
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hotchillipepper
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. (1) says the product of ANY three integers in the set is negative. That means if the set has any positive integer, the product of three could be positive because the positive integer could be drawn into the set of three. I think A is the correct choice or the wording needs to be changed.
(-)(-)(-) = (-)
(-)(+)(+) = (-)
(-)(-)(+) = (+)
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The problem is entirely correct, and the solution is exact. However, I think you're not grasping the meaning of "The product of ANY three integers in the set is negative." It indicates that, irrespective of the three integers you choose from the set, the product is guaranteed to be negative. This can occur in the following scenario ONLY:

1. If the set consists of only three terms, then it could be {negative, negative, negative}, giving an YES answer to the question, or {negative, positive, positive}, giving an NO answer to the question.

2. However, if the set consists of more than three terms, then it can only have negative numbers, also giving an YES answer to the question. Not sufficient.

P.S. I'd also recommend, before posting, reading the entire discussion. It's likely that your questions have already been answered there.
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M28-53 05 Jul 2023, 01:47
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Thankyou for the solution. Clears it out for me!
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M28-53 12 Aug 2023, 11:42
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I think this is a high-quality question and I agree with explanation.
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M28-53 15 Aug 2023, 08:58
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rip2020
Hi Bunuel

For statement 1, why are you assuming that the set can have only 3 numbers, what if the set has many more numbers. Then how will you combine the statements?

Please advise.

Thanks!
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Hi rip2020,

I am not sure if this is still helpful but the question says that "ANY 3 Nos" multiplied with each other should give a negative number. Take for example - (2,2,-2,-2,-2). This set has more than 3 nos - while statement A can be true for sub set (-2,2,2) it cannot be true for (-2,-2,2). As you can see this set "could" be true as per the question but it not ""ALWAYS TRUE". Since the statements should be "ALWAYS TRUE" the condition stated in the question can only be satisfied with 3 nos such that 2 are positives and 1 is negative or where all the values in the set are negative.
Please note that ANY 3 nos picked must be negative and hence, it is essential we create a set that will always be true. U can probably pick some nos yourself and check that the higher the no of positives u have in a set the lesser the chances of satisfying the first statement.

I agree with the explanation provided by Bunuel
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