• e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

A machine manufactures notebooks in a series of...

This topic has 1 expert reply and 1 member reply

A machine manufactures notebooks in a series of...

Post Wed Nov 08, 2017 6:46 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A machine manufactures notebooks in a series of five colors: red, blue, black, white and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day?

    A. 27
    B. 34
    C. 50
    D. 61
    E. 78

    The OA is E.

    I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

    Top Member

    Post Thu Nov 09, 2017 6:39 am
    LUANDATO wrote:
    A machine manufactures notebooks in a series of five colors: red, blue, black, white and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day?

    A. 27
    B. 34
    C. 50
    D. 61
    E. 78

    The OA is E.

    I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
    The first book in the series is red and the last is yellow, comprising 5 books. The next black book to be printed is 3 books into the next series.

    So, in the first series of printing the first black book is the 3rd printed. However, 3 is not among the answer choices.

    The next black book is 5 books away, so a total of 8 books. 8 is also not among the answer choice, but you can see that the correct answer should be a multiple of 5 if you subtract 3 from it.

    The only answer choice that fits that description is E, 78-3=75> a multiple of 5

    Thanked by: LUANDATO
    Post Thu Nov 09, 2017 7:00 am
    Quote:
    A machine manufactures notebooks in a series of five colors: red, blue, black, white and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day?

    A. 27
    B. 34
    C. 50
    D. 61
    E. 78

    The OA is E.

    I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
    Hi LUANDATO,
    Let's take a look at your question.

    The question states:
    A machine manufactures notebooks in a series of five colors: red, blue, black, white and yellow.
    If the machine starts its production from a red notebook and ends at a black note book, then the sequence must be like:

    RED, BLUE, BLACK, WHITE, YELLOW, RED, BLUE, BLACK, WHITE, YELLOW, RED, BLUE, BLACK, WHITE, ..., BLACK
    The sequence will be like this and we need to find how many notebooks were printed during the day.
    If we look at the sequence, we can see that,
    The minimum number of books that can be printed will be 3 from RED to BLACK. (RED, BLUE, BLACK)
    or the number of books could be 8. (RED, BLUE, BLACK, WHITE, YELLOW, RED, BLUE, BLACK)
    or 13 if one more cycle is completed. (RED, BLUE, BLACK, WHITE, YELLOW, RED, BLUE, BLACK, WHITE, YELLOW, RED, BLUE, BLACK)

    So the sequence of the number of books that can possibly be printed during the day is:
    3, 8, 13, ...
    This is an arithmetic sequence with:
    $$a_1=3$$
    $$d=5$$

    The maximum number of books that can be manufactured will be from one of the choices given. So we will check each option to check which could be the nth term of this sequence using the formula of arithmetic sequence:
    $$a_n=a_1+\left(n-1\right)d$$
    $$a_n=3+\left(n-1\right)5$$
    $$a_n=3+5n-5$$
    $$a_n=5n-2$$

    Let's check Option A.
    $$a_n=27$$
    Plugin the value in the formula:
    $$a_n=5n-2$$
    $$27=5n-2$$
    $$29=5n$$
    $$n=\frac{29}{5}$$
    It results into a decimal number, which is not a valid value for the number of terms. n should be a whole number.
    So we will discard this.

    Let's now check Option B.
    $$a_n=34$$
    Plugin the value in the formula:
    $$a_n=5n-2$$
    $$34=5n-2$$
    $$36=5n$$
    $$n=\frac{36}{5}$$
    It results into a decimal number, which is not a valid value for the number of terms. n should be a whole number.
    So we will discard this.

    Let's now check Option C.
    $$a_n=50$$
    Plugin the value in the formula:
    $$a_n=5n-2$$
    $$50=5n-2$$
    $$52=5n$$
    $$n=\frac{52}{5}$$
    It results into a decimal number, which is not a valid value for the number of terms. n should be a whole number.
    So we will discard this too.

    Let's now check Option D.
    $$a_n=61$$
    Plugin the value in the formula:
    $$a_n=5n-2$$
    $$61=5n-2$$
    $$63=5n$$
    $$n=\frac{63}{5}$$
    It results into a decimal number, which is not a valid value for the number of terms. n should be a whole number.
    So we will discard this as well.

    Let's now check Option E.
    $$a_n=78$$
    Plugin the value in the formula:
    $$a_n=5n-2$$
    $$78=5n-2$$
    $$80=5n$$
    $$n=\frac{80}{5}$$
    $$n=16$$
    n is a whole number now. Which shows that the number of books manufactured during the day is 78.

    Therefore, Option E is correct.

    Hope it helps.
    I am available if you'd like any follow up.

    _________________
    GMAT Prep From The Economist
    We offer 70+ point score improvement money back guarantee.
    Our average student improves 98 points.

    Thanked by: LUANDATO
    Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

    Best Conversation Starters

    1 LUANDATO 160 topics
    2 lheiannie07 87 topics
    3 Roland2rule 75 topics
    4 ardz24 60 topics
    5 AAPL 55 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description EconomistGMATTutor

    The Economist GMAT Tutor

    168 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    130 posts
    3 image description Jay@ManhattanReview

    Manhattan Review

    128 posts
    4 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    117 posts
    5 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    103 posts
    See More Top Beat The GMAT Experts