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K is a set of integers such that if the integer r is in K

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by VJesus12 » Sun Apr 28, 2019 9:41 am

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K is a set of integers such that if the integer r is in K, then r + 1 is also in K. Is 100 in K?

(1) 50 is in K.
(2) 150 is in K.

[spoiler]OA=A[/spoiler]

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Source: — Data Sufficiency |

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by Ian Stewart » Mon Apr 29, 2019 3:28 am
If we know r is in K, then we know r+1 is in K. So if 50 is in K, we know that 51 is in K, but then we know 52 is in K, and 53 is in K, and so on, so 100 will be in K. So Statement 1 is sufficient.

From Statement 2, we know 150 is in K, so we know 151, 152, 153 etc are also in K. But we don't know anything about values smaller than 150. It's possible the set is just this infinite set:

150, 151, 152, 153, 154, ...

but it could also be, say, the set of all positive integers. So Statement 2 is not sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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