Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

saifoo.khan

  • 2 years ago

The sum of "z" consecutive integers is 90. Which of the following cannot be the value of "z". 3, 4, 5, 6, 9.

  • This Question is Closed
  1. mathslover
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it seems that the answer given by saurav is very correct

  2. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i still don't get it. lol.

  3. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    maybe first put it like this: \[n+(n+1)+(n+2)+...+(n+(z-1))=90\] and find it from here

  4. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How? Why? @myko

  5. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    guys lets work it step by step \[n+1+n+2+...+n+z=90\]\[nz+\frac{z(z+1)}{2}=90\]\[z^2+(2n+1)z=180\]\[z(z+2n+1)=180\] we can find all integers \(z\) that satisfies the last equality...but here we have options and we can plug them into equation and see what happens...

  6. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the expretion would be equal to: n*z+ sum of first (z-1) integers = 90

  7. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mukushla your sum is of z+1 consecutive integers

  8. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    no its z n+1 n+2 ... n+z

  9. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    should be nz+z(z-1)/2=90

  10. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So..?

  11. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2nz+z^2-z=180 z^2+(2n-1)z-180=0 and I think just check for possible natural solutions of this

  12. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    now u have \[n=\frac{90}{z}-\frac{z+1}{2}\] now plug the values of \(z\) and if the value of \(n\) becomes an integer then that \(z\) is your answer

  13. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mukushla : Your's and @myko 's methods are same right?

  14. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes they are

  15. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    for example \(z=3\) gives \[n=\frac{90}{3}-\frac{3+1}{2}=30-2=28\]

  16. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    yes they are same

  17. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    only difference is that i start fomr n and @mukushla from n+1

  18. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So answer is 3?

  19. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it asks: Which of the following cannot be the value of "z". and 3 aparently , is.

  20. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    But it's incorrect. :S

  21. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    let me complete the solution \[z=3 ---------> n=\frac{90}{3}-\frac{3+1}{2}=28\] \[z=4 ---------> n=\frac{90}{4}-\frac{4+1}{2}=20\] \[z=5 ---------> n=\frac{90}{5}-\frac{5+1}{2}=15\] \[z=6 ---------> n=\frac{90}{6}-\frac{6+1}{2}=11.5\] \[z=9 ---------> n=\frac{90}{9}-\frac{9+1}{2}=5\] so the answer is only z=6

  22. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4and 6 would be the answer

  23. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i think

  24. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Myko's thinking is going the correct way!

  25. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i got it by mine first formula using n like a start integer.

  26. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but aparently there should be no difference in starting from n+1 or n+2 or n+whatever

  27. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm

  28. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    for \(z=4\) \[21+22+23+24=90\]

  29. rsadhvika
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4 90/4 - 4+1/2 90/4 - 10/4 80/4 is an integer

  30. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4 is incorrect too!

  31. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    its impossible ... see my last reply

  32. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The answer is 6. :S

  33. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm going to type the solution.. just a sec.

  34. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    @saifoo.khan thats right answer is 6...

  35. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How? Why? :D

  36. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    man... we already solved it...

  37. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    But you were getting 11.5 when we inserted 6.

  38. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    well that means there is not 6 consecutive integers such that their sum is 90

  39. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (behind the book) Solution: Plug in numbers! This may take some time, but we will eventually find the answer. Three numbers 20+30+31=90,eliminate A, four numbers 21+22+23+24=90,eliminate b,five numbers 16+17+18+19+20=90,elimnate c.nine numbers 6+7+8+9+10+11+12+13+14=90 elimate e.no six consecutive numbers add up to 90

  40. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mukushla , got it right!

  41. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I totally get it. Thanks a ton! @mukushla & @myko

  42. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 6

    yw :)

  43. myko
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

  44. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.