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# For every integer a>1, a* is defined as the least prime factor of a.

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Re: For every integer a>1, a* is defined as the least prime factor of a. [#permalink]
sainaren wrote:
For every integer a>1, a* is defined as the least prime factor of a. Is b*<c*?

1. b is an odd integer greater than 1
2. c is an even integer

When they define a weird function like this one, it's not a bad idea to jot down a couple of examples before you start, just to make sure you understand what they're telling you.

For instance, here, we'd quickly calculate x* for a couple of different values of x.

If x is prime, then x* is just equal to x itself, since it doesn't have any smaller prime factors.

If x = 10, then x* = 2.

If x = 15, then x* = 3.

You might notice, at this point, that whenever x is even, x* should equal 2, because 2 is a prime factor of every even number and 2 is the smallest prime number. The words even and odd in the statements also give a clue that you should be thinking about how even and odd numbers behave differently from each other.

Statement 1: b is an odd integer greater than 1. We already tried the example of 15; if b = 15, then b* = 3. c* could be smaller than this (for example, if c = 2, then c* = 2, which is less than 3.) Or, c* could be bigger than this (for example, if c = 7, then c* = 7, which is more than 3.) Therefore, this statement is insufficient.

Statement 2: As discussed above, this one tells you that c* = 2.

The question asks whether b* is less than c*. Since 2 is the smallest prime number, 2 is the smallest value that b* could possibly have. b* definitely can't be less than 2. (Remember that 1 isn't prime.)

Therefore, the answer to the question is 'no' - since c* = 2, b* definitely is NOT less than c*. This statement is sufficient.

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Re: For every integer a>1, a* is defined as the least prime factor of a. [#permalink]
ccooley wrote:
sainaren wrote:
For every integer a>1, a* is defined as the least prime factor of a. Is b*<c*?

1. b is an odd integer greater than 1
2. c is an even integer

When they define a weird function like this one, it's not a bad idea to jot down a couple of examples before you start, just to make sure you understand what they're telling you.

For instance, here, we'd quickly calculate x* for a couple of different values of x.

If x is prime, then x* is just equal to x itself, since it doesn't have any smaller prime factors.

If x = 10, then x* = 2.

If x = 15, then x* = 3.

You might notice, at this point, that whenever x is even, x* should equal 2, because 2 is a prime factor of every even number and 2 is the smallest prime number. The words even and odd in the statements also give a clue that you should be thinking about how even and odd numbers behave differently from each other.

Statement 1: b is an odd integer greater than 1. We already tried the example of 15; if b = 15, then b* = 3. c* could be smaller than this (for example, if c = 2, then c* = 2, which is less than 3.) Or, c* could be bigger than this (for example, if c = 7, then c* = 7, which is more than 3.) Therefore, this statement is insufficient.

Statement 2: As discussed above, this one tells you that c* = 2.

The question asks whether b* is less than c*. Since 2 is the smallest prime number, 2 is the smallest value that b* could possibly have. b* definitely can't be less than 2. (Remember that 1 isn't prime.)

Therefore, the answer to the question is 'no' - since c* = 2, b* definitely is NOT less than c*. This statement is sufficient.

In the case of this question, should we not consider the possibility that b can be EQUAL to c OR GREATER than c? In which case, the option is insufficient as we will have 2 answer options at hand..?
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Re: For every integer a>1, a* is defined as the least prime factor of a. [#permalink]
As the OA is currently diverging from the opinion of several posters it would be most helpful if a moderator could settle the matter once and for all.

Please: chetan2u Bunuel help us, you are our only hope!
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For every integer a>1, a* is defined as the least prime factor of a. [#permalink]
1
Kudos
NerdatroN wrote:
As the OA is currently diverging from the opinion of several posters it would be most helpful if a moderator could settle the matter once and for all.

Please: chetan2u Bunuel help us, you are our only hope!

Hi
1) b is odd so least possible value of b* is 3 and b could be anything greater than 2, and also c can be anything and so c* could be 2,3,5,7 etc..insuff
2) c is even so c* is surely 2. Now whatever be the value of b, answer will always be NO
For example say b is also even so b* is 2, we are then looking for is b*<c* or 2<2... answer is NO
Say b is 3, then 3*<2*.. again NO
Suff

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Re: For every integer a>1, a* is defined as the least prime factor of a. [#permalink]
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Re: For every integer a>1, a* is defined as the least prime factor of a. [#permalink]
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