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I've seen several problems where knowing that half of a consecutive integers set is even, and the other odd is integral to the solution.
I'm wondering what's required for that to be true?
Let's take a even range. e.g. 10
Start with odd number: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Half the set is even.
Start with an even number: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Half the set is even.
Let's try an odd range. e.g. 11
Start with odd number: 1,2,3,4,5,6,7,8, 9, 10, 11. We have 5 even and 6 odd numbers.
Start with even number: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. We have 6 even and odd numbers.
If we have an even range we can deduce that even and odd numbers are equal.
If the range is odd the distribution depends on the starting number. If we start with an even number, we're going to end with en even number so the number of even is equal to the number of odd numbers + 1
To the more experienced GMAT test takers out there, I've seen a few problems where the clever solution involved taking the subset of the given set. Any popular takeaways regarding that?
Note: This post started as a question, but I answered my own question. (Assuming no mistakes above) Regardless I thought I'd post in the hopes this is useful information to someone out there.
I'm wondering what's required for that to be true?
Let's take a even range. e.g. 10
Start with odd number: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Half the set is even.
Start with an even number: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Half the set is even.
Let's try an odd range. e.g. 11
Start with odd number: 1,2,3,4,5,6,7,8, 9, 10, 11. We have 5 even and 6 odd numbers.
Start with even number: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. We have 6 even and odd numbers.
If we have an even range we can deduce that even and odd numbers are equal.
If the range is odd the distribution depends on the starting number. If we start with an even number, we're going to end with en even number so the number of even is equal to the number of odd numbers + 1
To the more experienced GMAT test takers out there, I've seen a few problems where the clever solution involved taking the subset of the given set. Any popular takeaways regarding that?
Note: This post started as a question, but I answered my own question. (Assuming no mistakes above) Regardless I thought I'd post in the hopes this is useful information to someone out there.
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