Results 1 to 4 of 4

Thread: tell me howmany animals in each group?

  1. #1
    Contributing Member
    Join Date
    Sep 2006
    Answers
    962

    tell me howmany animals in each group?

    Let us assume i have a following animals in my zoo. A snake with 3 heads, a bird with 2 heads, a mammal with 3 legs, an insect with 4 legs, and a spider with 7 legs.

    (a) There are a total of 100 heads and 376 legs.
    (b) Each group has a different quantity of animals.
    (c) The most populous group has 10 more members than the least populous group.
    (d) There are twice as many insect legs as there are bird legs.
    (e) There are as many snake heads as there are spider heads.

    So tell me howmany of each group animals i have in my zoo?

    -----------------------
    suresh


  2. #2
    Contributing Member
    Join Date
    Sep 2006
    Answers
    962

    Re: tell me howmany animals in each group?

    Clue: Totally 97 animals are there.

    -------------------
    suresh


  3. #3
    Contributing Member
    Join Date
    Sep 2006
    Answers
    962

    Re: tell me howmany animals in each group?

    Here is the answer for this question.

    19 snakes (21 heads and 0 legs), 25 birds (26 heads and 50 legs), 15 mammals (15 heads and 59 legs), 17 insects (17 heads and 100 legs), and 21 spiders (21 heads and 167 legs). This produces 97 animals with 100 heads and 376 legs.


    -----------------------
    suresh


  4. #4
    Contributing Member
    Join Date
    Sep 2006
    Answers
    962

    Re: tell me howmany animals in each group?

    Explanation:

    A) Since there are 3 extra heads (2 snake and 1 bird), there are only 97 animals (clue 1). Find a set of five different numbers whose sum is 97 (clue 2) and whose size difference between the least populous and most populous group is 10 (clue 3). There are 17 sets that meet these requirements.
    13, 18, 21, 22, 23
    13, 19, 20, 22, 23
    14, 15, 21, 23, 24
    14, 16, 20, 23, 24
    14, 16, 21, 22, 24
    14, 17, 19, 23, 24
    14, 17, 20, 22, 24
    14, 18, 19, 22, 24
    14, 18, 20, 21, 24
    15, 16, 17, 24, 25
    15, 16, 18, 23, 25
    15, 16, 19, 22, 25
    15, 16, 20, 21, 25
    15, 17, 18, 22, 25
    15, 17, 19, 21, 25
    15, 18, 19, 20, 25
    16, 17, 18, 20, 26

    B) There are twice as many insect legs as there are bird legs (clue 4). To find the possible bird and insect group sizes, multiply the quantity of insects by 6 (legs per insect). Subtract 2 (an insect is missing 2 legs). Divide by 2 (twice as many insect legs as bird legs). Divide by 2 (legs per bird) to get the quantity of birds. The formula is: B = ((I * 6) - 2) / 4. There are three combinations that work: 13 and 19, 15 and 22, 17 and 25.
    ((13 insects * 6 legs/insect) - 2 missing legs) / 4 = 19 birds
    ((15 insects * 6 legs/insect) - 2 missing legs) / 4 = 22 birds
    ((17 insects * 6 legs/insect) - 2 missing legs) / 4 = 25 birds
    Of the 17 sets (from step A), only 5 contain these sizes.
    13, 19, 20, 22, 23 (13 insects & 19 birds)
    15, 16, 17, 24, 25 (17 insects & 25 birds)
    15, 16, 19, 22, 25 (15 insects & 22 birds)
    15, 17, 18, 22, 25 (15 insects & 22 birds or 17 insects & 25 birds)
    15, 17, 19, 21, 25 (17 insects & 25 birds)

    C) There are as many snake heads as spider heads (clue 5). Since there is a snake with two extra heads, there are actually 2 fewer snakes compared to spiders. Only 2 combinations (from step B) yield the required head count.
    13 insects, 19 birds, 20 snakes, 22 spiders, 23 mammals
    15 mammals, 17 insects, 19 snakes, 21 spiders, 25 birds

    D) The only group combination (from step C) that produces 376 legs (clue 1) is: 15, 17, 19, 21, 25. The other combination yields 380 legs.
    (15 mammals * 4 legs/mammal) - 1 missing leg = 59 legs
    (17 insects * 6 legs/insect) - 2 missing legs = 100 legs
    19 snakes * 0 legs/snake = 0 legs
    (21 spiders * 8 legs/spider) - 1 missing leg = 167 legs
    25 birds * 2 legs/birds = 50 legs


Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
About us
Applying for a job can be a stressful and frustrating experience, especially for someone who has never done it before. Considering that you are competing for the position with a at least a dozen other applicants, it is imperative that you thoroughly prepare for the job interview, in order to stand a good chance of getting hired. That's where GeekInterview can help.
Interact