For every integer a1, a* is defined as the least prime factor of a.

Question

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

LevanKhukhunashvili · Answer

1 stm --> b is odd and we dont know anything about c;  insuff 
2 stm --> c is even, so the least prime factor of c is 2. 2 cant be greater than any prime;  suff

P.S Honestly I dont like the wording of the question

IMO
Ans:  B

fireflyejd1 · Answer

Statement 1: B is odd
 Even if B is an odd number, C can be an odd number of a higher or smaller maginitude containing a superior on inferior prime number. Or it can be another even n umber. We do n ot know. Insufficient.

Statement 2: C is even

Ok, since C is even, B can either be even or odd. The only possible outcome is for b is to be either equal to or greater than c. In no possible way can it ever be smaller than c. Solved.

ANSWER: B

ccooley · Answer

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.

The answer is B.

fireflyejd1 · Answer

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..?

NerdatroN · Answer

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!

chetan2u · Answer

Hi Answer is B

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*

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia