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At a certain high school, a student's popularity is...

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by BTGmoderatorLU » Sat Feb 10, 2018 7:30 am
At a certain high school, student's popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and Dyson get lockers with the numbers 300, 400, 150, and 420, respectively. Who is the most popular student?

A. Johanna
B. Jamal
C. Brianna
D. Dyson
E. They have equal popularity

The OA is D.

Experts, to solve this PS question, I just need to find the distinct prime factors for each number, right?

Distinct prime factors for 300
Distinct prime factors for 400
Distinct prime factors for 150
Distinct prime factors for 420

Experts, any suggestion? Thanks in advance.
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by regor60 » Sat Feb 10, 2018 8:13 am
LUANDATO wrote:At a certain high school, student's popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and Dyson get lockers with the numbers 300, 400, 150, and 420, respectively. Who is the most popular student?

A. Johanna
B. Jamal
C. Brianna
D. Dyson
E. They have equal popularity

The OA is D.

Experts, to solve this PS question, I just need to find the distinct prime factors for each number, right?

Distinct prime factors for 300
Distinct prime factors for 400
Distinct prime factors for 150
Distinct prime factors for 420

Experts, any suggestion? Thanks in advance.

yes that is the correct approach
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answer

by [email protected] » Sat Feb 10, 2018 11:08 am
Hi LUANDATO,

Yes - prime factoring the 4 values would get you to the correct answer. There IS a shortcut that you can take advantage though - and avoid some of that work. Since 300 is a multiple of 150, ALL of the prime factors of 150 are ALSO in 300. The number 300 is '2 times' 150 - and since both those numbers are already EVEN, the 'extra 2' won't matter (since we're only concerned with the DISTINCT prime factors of each number). This means that 150 and 300 have the SAME number of prime factors - and since we're looking for the number with the MOST distinct prime factors, neither A or C could be the correct answer. You really just have to prime factor 400 and 420. Based on how the answer choices are written, if one of them has more factors than the other, then that would have to be the correct answer; if they have the same number of prime factors, then all 4 numbers have the same number of prime factors.

Final Answer: D

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