Please help with the below problem:
K is a set of numbers such that
i) if x is in K, then (x) is in K and,
ii) if each of x and y is in K, then xy is in K
Is 12 in K?
1) 2 is in K
2) 3 is in K
Thank you,
Prerna
DS problem
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Target question: Is 12 in K?prernamalhotra wrote:
K is a set of numbers such that
i) if x is in K, then (x) is in K and,
ii) if each of x and y is in K, then xy is in K
Is 12 in K?
1) 2 is in K
2) 3 is in K
Statement 1: 2 is in K
By rule i, 2 is also in set K
By rule ii, if 2 and 2 are in set K, then 4 is in set K
By rule i, 4 is also in set K
By rule ii, if 2 and 4 are in set K, then 8 is in set K
By rule ii, if 2 and 4 are in set K, then 8 is in set K
etc..
So, all we can say is that the following numbers MUST be in K: ...16, 8, 4, 2, 2, 4, 8, 16...
Since we don't know what other numbers might be in K, 12 might be K or 12 might NOT be in K.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3 is in K
By rule i, 3 is also in set K
By rule ii, if 3 and 3 are in set K, then 9 is in set K
By rule i, 9 is also in set K
By rule ii, if 3 and 9 are in set K, then 27 is in set K
By rule ii, if 3 and 9 are in set K, then 27 is in set K
etc..
So, all we can say is that the following numbers MUST be in K: ...27, 9, 3, 3, 9, 27,...
Since we don't know what other numbers might be in K, 12 might be K or 12 might NOT be in K.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that 4 must be in set K
Statement 2 tells us that 3 must be in set K
By rule ii, if 4 and 3 are in set K, then 12 is in set K
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent

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Hi Brent[email protected] wrote:Target question: Is 12 in K?prernamalhotra wrote:
K is a set of numbers such that
i) if x is in K, then (x) is in K and,
ii) if each of x and y is in K, then xy is in K
Is 12 in K?
1) 2 is in K
2) 3 is in K
Statement 1: 2 is in K
By rule i, 2 is also in set K
By rule ii, if 2 and 2 are in set K, then 4 is in set K
By rule i, 4 is also in set K
By rule ii, if 2 and 4 are in set K, then 8 is in set K
By rule ii, if 2 and 4 are in set K, then 8 is in set K
etc..
So, all we can say is that the following numbers MUST be in K: ...16, 8, 4, 2, 2, 4, 8, 16...
Since we don't know what other numbers might be in K, 12 might be K or 12 might NOT be in K.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3 is in K
By rule i, 3 is also in set K
By rule ii, if 3 and 3 are in set K, then 9 is in set K
By rule i, 9 is also in set K
By rule ii, if 3 and 9 are in set K, then 27 is in set K
By rule ii, if 3 and 9 are in set K, then 27 is in set K
etc..
So, all we can say is that the following numbers MUST be in K: ...27, 9, 3, 3, 9, 27,...
Since we don't know what other numbers might be in K, 12 might be K or 12 might NOT be in K.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that 4 must be in set K
Statement 2 tells us that 3 must be in set K
By rule ii, if 4 and 3 are in set K, then 12 is in set K
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
I did not understand that how can 4 be in K and not other multiples of 2 like 6 etc? Why only exponential powers of 2 and 3 are in K?
Regards
Sukriti
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Rules i and ii ensure that only POWERS of 2 are in K (from statement 1)sukriti2hats wrote:
Hi Brent
I did not understand that how can 4 be in K and not other multiples of 2 like 6 etc? Why only exponential powers of 2 and 3 are in K?
Regards
Sukriti
As you can see from the progression that I demonstrated, there's no way for other multiples of 2 to sneak into K.
Once we know that 2 and 2 are in set K, we've exhausted the limitations of rule i.
From this point, rule ii tells us that 4 is in set K.
And then rule i ensures that 4 is in set K.
At this point, we know that 2, 2, 4 and 4 are in set K.
Notice that neither rule i nor rule ii will allows to take these four values and somehow ensure that 6 is in set K
Cheers,
Brent