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Sara is an avid lottery player. In the certain game...

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Sara is an avid lottery player. In the certain game...

by BTGmoderatorLU » Sun Jan 07, 2018 7:03 am
Sara is an avid lottery player. In the certain game she plays, she must pick one number between 30 and 39, inclusive, one number between 40 and 49, inclusive, and one number between 50 and 59, inclusive. She believes that she will have the best chance of winning if her three numbers, as a set, has the greatest number of distinct prime factors possible. According to Sara's theory, which of the following sets of three numbers should she use?

A. 32 - 48 - 52
B. 33 - 42 - 56
C. 39 - 40 - 54
D. 38 - 49 - 51
E. 36 - 42 - 56

The OA is D.

I'm really confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.
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by EconomistGMATTutor » Sun Jan 07, 2018 8:54 am
Hello LUANDATO.

Let's take a look at your question.

We have to find all the prime factors of each option.

Option A: $$32=2^5\ \ \ -\ \ \ 48=2^4\cdot3\ \ \ -\ \ \ 52=2^2\cdot13.$$ Option B: $$33=3\cdot11\ \ \ -\ \ \ 42=2\cdot3\cdot7\ \ \ -\ \ \ 56=2^3\cdot7.$$ Option C: $$39=3\cdot13\ \ \ -\ \ \ 40=2^3\cdot5\ \ \ -\ \ \ 54=2\cdot3^3.$$ Option D: $$38=2\cdot19\ \ \ -\ \ \ 49=7^2\ \ \ -\ \ \ 51=3\cdot17.$$ Option E: $$36=2^2\cdot3^2\ \ \ -\ \ \ 42=2\cdot3\cdot7\ \ \ -\ \ \ 56=2^3\cdot7.$$ If we take a look of all distinct prime factors on each set, we can conclude that the option D has 5 distinct prime factors and the rest has 4 distinct prime factors or less.

Hence, the correct answer is the option D. I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.
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