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# M38-03

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RucksackTales wrote:
How is A the correct answer, the question doesn't mention that the integers are in a series. now the set can have any number as the greatest number, viz. 1000000000 OR could be 4 where all other integers are -Ve Even number, their number being 99 (odd), so the product is still -ve.??

My dear friend, when posing a question, it is crucial to be as clear and precise as possible. That is, if your goal is to get accurate responses and enhance your GMAT skills.

Please take a moment to carefully reread the question and the solution. If you still find it unclear, make sure to rephrase your question in a way that is easy to understand, without the need for a team of decipherers. Thank you!
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Bunuel for option A, any reason the set cannot be {-2, 10, 20, 30, 40 .........500} and the range is > 200; In this sample set product of all the numbers in the set is negative as well
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1219bob1219 wrote:
Bunuel for option A, any reason the set cannot be {-2, 10, 20, 30, 40 .........500} and the range is > 200; In this sample set product of all the numbers in the set is negative as well

Your set satisfies the first statement, making it a possible scenario. However, it is important to note your set as well as all other possible sets will also have a range greater than or equal to 200, resulting in a definitive answer of NO to the question.
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Bunuel wrote:
1219bob1219 wrote:
Bunuel for option A, any reason the set cannot be {-2, 10, 20, 30, 40 .........500} and the range is > 200; In this sample set product of all the numbers in the set is negative as well

Your set satisfies the first statement, making it a possible scenario. However, it is important to note your set as well as all other possible sets will also have a range greater than or equal to 200, resulting in a definitive answer of NO to the question.

For the set {-2, 10, 20, 30, 40 .........500} Range > 200
And for a similar set { -52, -50, -48, -46 ............2, 4, .......... 46, 48, 50, 52, 54, 56} (no zero is included in the set) and the range is < 200; Probably I'm missing something that makes this answer as A
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1219bob1219 wrote:
Bunuel wrote:
1219bob1219 wrote:
Bunuel for option A, any reason the set cannot be {-2, 10, 20, 30, 40 .........500} and the range is > 200; In this sample set product of all the numbers in the set is negative as well

Your set satisfies the first statement, making it a possible scenario. However, it is important to note your set as well as all other possible sets will also have a range greater than or equal to 200, resulting in a definitive answer of NO to the question.

For the set {-2, 10, 20, 30, 40 .........500} Range > 200
And for a similar set { -52, -50, -48, -46 ............2, 4, .......... 46, 48, 50, 52, 54, 56} (no zero is included in the set) and the range is < 200; Probably I'm missing something that makes this answer as A

Hey, your second example doesn't include 100 terms mate

Posted from my mobile device
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1219bob1219 wrote:
Bunuel wrote:
1219bob1219 wrote:
Bunuel for option A, any reason the set cannot be {-2, 10, 20, 30, 40 .........500} and the range is > 200; In this sample set product of all the numbers in the set is negative as well

Your set satisfies the first statement, making it a possible scenario. However, it is important to note your set as well as all other possible sets will also have a range greater than or equal to 200, resulting in a definitive answer of NO to the question.

For the set {-2, 10, 20, 30, 40 .........500} Range > 200
And for a similar set { -52, -50, -48, -46 ............2, 4, .......... 46, 48, 50, 52, 54, 56} (no zero is included in the set) and the range is < 200; Probably I'm missing something that makes this answer as A

What's happening here is that because you have an even number of numbers and the product is negative, they have to be on both sides of zero but they can't be zero.
Now the only case where the 100 DISTINCT even integers would have a range of less than 200 is if they are consecutive integers (as a simple example, from 2 to 200 you have 100 numbers and 198 as the range). But to satisfy option A, you need to have at least one 'gap' in the form of zero. Hence, the range will never be less than 200.

I'll admit it was a stupidly tricky question. I fell for it too.
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ashutoshbirla wrote:
What's happening here is that because you have an even number of numbers and the product is negative, they have to be on both sides of zero but they can't be zero.
Now the only case where the 100 DISTINCT even integers would have a range of less than 200 is if they are consecutive integers (as a simple example, from 2 to 200 you have 100 numbers and 198 as the range). But to satisfy option A, you need to have at least one 'gap' in the form of zero. Hence, the range will never be less than 200.

I'll admit it was a stupidly tricky question. I fell for it too.

Your analysis is spot on! This GMAT Club question is a real challenge, requiring a combination of advanced skills: it's hard, tricky, and educational all at once.
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Thanks ashutoshbirla and Bunuel

to make life easier for others I drew up a sample set and the reason i failed was for 200 different even integers vs 100 even integers

{-102,-100,-98,-96,-94,-92,-90,-88,-86,-84,-82,-80,-78,-76,-74,-72,-70,-68,-66,-64,-62,-60,-58,-56,-54,-52,-50,-48,-46,-44,-42,-40,-38,-36,-34,-32,-30,-28,-26,-24,-22,-20,-18,-16,-14,-12,-10,-8,-6,-4,-2,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98}

=== === === === === === === ===
Life isn't easy, but lets try to make it easier
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How do we know that the range of all even numbers from 0 to 200 is 202 and not 200? Shouldn't the range equal largest - smallest (which in this case would be 200-0=200)?
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hydr01 wrote:
How do we know that the range of all even numbers from 0 to 200 is 202 and not 200? Shouldn't the range equal largest - smallest (which in this case would be 200-0=200)?

The range of all even integers, from 0 to 200, inclusive is indeed 200 - 0 = 200. Notice though that the set of all even integers from 0 to 200 inclusive has 101 elements, not 100. From here I don't really understand your point. Can yuo please elaborate what you mean? Thank you!
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Bunuel wrote:
hydr01 wrote:
How do we know that the range of all even numbers from 0 to 200 is 202 and not 200? Shouldn't the range equal largest - smallest (which in this case would be 200-0=200)?

The range of all even integers, from 0 to 200, inclusive is indeed 200 - 0 = 200. Notice though that the set of all even integers from 0 to 200 inclusive has 101 elements, not 100. From here I don't really understand your point. Can yuo please elaborate what you mean? Thank you!

No worries, I understand the original question of the day better from your response, thanks!
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