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A lecture course consists of 595 students. The students are

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by alanforde800Maximus » Wed Oct 19, 2016 5:03 am
A lecture course consists of 595 students. The students are to be divided into discussion sections, each with an equal number of students. Which of the following cannot be the number of students in a discussion section.

a) 17
b) 35
c) 45
d) 85
e) 119

Please assist with above problem.
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by DavidG@VeritasPrep » Wed Oct 19, 2016 5:29 am
alanforde800Maximus wrote:A lecture course consists of 595 students. The students are to be divided into discussion sections, each with an equal number of students. Which of the following cannot be the number of students in a discussion section.

a) 17
b) 35
c) 45
d) 85
e) 119

Please assist with above problem.
We're basically looking for which of those numbers is NOT a factor of 595. So let's break it down.

595 = 5*119; 119 is a factor, so E is out
119 = 7 * 17; 17 is a factor, so A is out

Now we've got the prime factorization of 595: 5 * 7 * 17
5*7 = 35; 35 is a factor, so B is out.
5*17 = 85; 85 is a factor, so D is out.

That leaves us with C
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by DavidG@VeritasPrep » Wed Oct 19, 2016 5:31 am
alanforde800Maximus wrote:A lecture course consists of 595 students. The students are to be divided into discussion sections, each with an equal number of students. Which of the following cannot be the number of students in a discussion section.

a) 17
b) 35
c) 45
d) 85
e) 119

Please assist with above problem.
A shortcut: 5 + 9 + 5 = 19. Because 19 is not a multiple of 3, 595 is not a multiple of 3. Any number that had 45 as a factor would HAVE to be a multiple of 3, so we know that 45 is not a factor of 595. Answer is C
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by [email protected] » Wed Oct 19, 2016 10:11 am
Hi alanforde800Maximus,

Prime Factorization works nicely on this question (as David has shown). If you're comfortable doing math by hand though, you might be able to 'brute force' this question in 30 seconds. Based on the description, we're looking for a number that is NOT divisible into 595. Once you find it, you're done. So, starting at Answer A, how long would it take you to divide in those numbers before you found the answer?

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