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Homework Help: Annoying Logic Problems!

  1. Aug 16, 2008 #1

    Gib Z

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    Ok well I got a set of 15 logic-ish problems, never really been very good at this stuff. I got about 7 of them fine, but I'll put them up just to check.

    999. 998. 997. 996
    729. 648. 567. 486
    126. 192. 210. 192
    12. 18. ? 18

    Which Of the following is the missing number? 0, 18, 36, 52, 256, 412 or 666.

    No Idea for that one, can't see any simple pattern through the rows. =[
    Q2 involves some pictures and my scanners broken at the moment :(
    Q3. Two people starting at the same place walk in opposite directions for 4 meters, turn left and walk another 3 meters. Which of these answers is closest to the distance between them in meters?

    2, 2.5, 6, 9, 9.5, 10, 10.5, 12.5, 14.
    Well drawing a diagram and using Pythagoras got me 10.
    Q4. If you rearrange the letters in MANGERY, which of the following categories does it best fit into? Country, City, Animal, Plant, Ocean, Furniture, Garden, Conflict.

    Well I got Germany, so Country.
    Q5. Carlos has a box of apples. He eats one apple then gives half the remaining apples to Pete. Carlos then eats another apple and gives half the apples he has left to Sheila. There are five apples left in the box at the end. How many apples were there in the box at the start? 10, 11, 13, 16, 19, 21, 22, 23, 25, 29, 31.

    Simple algebra, I got 23.
    Q6. Your building company is working on two sites - a house and a shop. The company employs three people - Sam the Bricklayer, Monica the electrician, and a Plumber called Abdul. Only one employee works on each site at a time. All of the employees work on both sites at some point during the week. The bricklayer is the only one who works four days a week. Everyone takes Saturday and Sunday off. Abdul works for a different company on Tuesdays and Wednesdays. The shop is too far from the house for an employee to work at both sites on the same day. Sam only works on the house on Mondays, Tuesdays or Wednesdays. Monica takes four day long weekends.

    What type or types of work can you get done on the house on a Friday?
    Bricklaying, Plumbing, Electrical, Nothing, Any type.

    All I can get it down to is Electrical and Plumbing, dont know how to proceed.
    Q7. If the day before yesterday is one hundred and twenty hours before wednesday, what day is today?

    I get Sunday.
    Q8 is another pictorial question.
    Q9. The price of 144 turnips is *347* groats. The smallest denomination in this currency is one whole groat. The start and ending digits of the price are smudged. Which of the following choices is nearest to the price in groats of one turnip?

    40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240.

    I get 160. I got got a calculator and kept on adding 144 until i got a 5 digit number with 347 in the middle, then I divided that by 144, got 162 or something.
    Q10. Anneka buys jackets wholesale for 50 groats each and sells them in her shop for 100 groats each. One day, a customer comes in and buys one jacket using a 200 groat gift voucher. She doesn't have enough cash in the till to give the customer chance, so she goes to the shop next door and exchanges the voucher for 200 groats cash. Anneka then gives the customer the jacket and 100 groats cash as change. The next day the owner of the shop next door comes in and complains that the voucher is a fake, so she gives him 200 groats cash and takes the voucher back.

    How many groats has Anneka lost? (Assume she has no insurance, there are no other expenses and the customer is not caught)

    0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500.

    I don't know why I can't get this one, I just keep getting caught in loops. She loses 150 as soon as she gives the jacket and 100 groats change, but then gets 200 from the voucher so shes 50 up. Then When he comes back, she gives 200 so shes 150 down. Is that correct?
    Q11 is another pictorial one but I got it.
    Q12. You meet three people called Vlad, Jeremy and Bushra. You know that one of them is always honest and one of them always lies.
    Vlad says "Jeremy always responds with rectitude". Jeremy says " I don't respond in a homogeneous manner".
    Bushra says "Jeremy is always perfidious".

    Which of them are telling the truth and which are lying?

    Well in simpler terms, Bushra says "Jeremy always lies", Jeremy says " I don't respond in the same manner all the time" and Vlad says "Jeremy always tells the truth". And I don't know how to go further :(

    9. 27. 6
    19. 45. ?
    6, 21, 7

    Which of the following is the missing number? 0, 1, 3, 5, 7, 9, 12, 14, 21, 27, 36, 81.

    No idea for that one.
    Q14. Which of these is the odd one out?


    Q15. Arranged clockwise in a circle: A, ?, C, O, F. What is the missing Letter?

    Also dead stumped.

    Sorry I have no working on a lot of them, these just seem like the kind of problems where you either have them or you don't =[
  2. jcsd
  3. Aug 17, 2008 #2
    #Q15: Try to find a pattern between ever other letter, ie for the sequence ACF?O
  4. Aug 17, 2008 #3

    Gib Z

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    Ooh thanks! I get J by the way. How did you spot that?
  5. Aug 17, 2008 #4
    I dont know really, I noticed that A, C and F was close to each other and almost in chronological order, which gave me the idea :)
  6. Aug 17, 2008 #5
    Q6: I got plumber at the house and bricklayer at the shop

    Because if you just write it out like this its pretty simple
    M T W TH F

    H H H H H
    S S S S S

    You know where the bricklayer is on M,T,W so plug that in

    M T W TH F

    H-B H-B H-B H H
    S S S S S

    You know the plumber works somewhere else on T and W so add that and since someone else has to be at the shop you know it has to be the electrician.

    M T W TH F

    H-B H-B H-B H H
    S S-E S-E S S

    And since the plumber works three days and two of the days are full you know that he has to work at the shop on Monday. We know the electrician has a four day weekend and since she has to work at both places during the week and she worked at the shop on T and W she must work at the house on Thursday.

    M T W TH F

    H-B H-B H-B H-E H
    S-P S-E S-E S S

    Now we see that the plumber has only worked one day when he must work three, so he must work at the shop on TH and since he must also work at both places during the week he must work at the house on Friday. That leaves the bricklayer to work at the shop on Friday.

    M T W TH F

    H-B H-B H-B H-E H-P
    S-P S-E S-E S-P S-B

    How's that? Hope it makes sense since it wont let me leave the extra spaces between the letters.
  7. Aug 18, 2008 #6
    The first row simply subtracts one from the previous number

    The second row seems to work as follows:
    - The first digit is subtracted by 1
    - The middle digit is increased by 2
    - The last digit is subtracted by 1
    Which gives a difference of 81 between each number

    As for the last two lines, I am stumped. I can't see any patterns.

    I tried the numbers vertically as well, but couldn't find much.

    The second to last horizontal line seems to follow some sort of parabola with the peak at the third number. So presumably, so does the last line. Since 192 translates to 18 on both accounts, the parabola might be similar. Dividing the third line with the forth you get 10.5 for the first group of digits and 10.6 for the second / forth. Divide the third number by 10.6 and you get ~= 19, which is close to the option of 18, but this is really stretching it.

    I'd be interested in seeing the solution for this one.

  8. Aug 18, 2008 #7
    The ones where you fill in the missing numbers are stupid. It all depends on your ability to luckily spot the pattern.

    *I agree with your answers for #3, #5-7, and #10. For #10 her balance changes as follows: -50 (buys the coat), +200 (cash for voucher), -100 (hands the guy change), -200 (discovers voucher is fake). Sums to -150.

    *I don't have a clue for #1, #9, or #13.

    *My guess for #14 is that the digits in the tens place for all the numbers are all odd (and equal equal to each other), except for 781523 which has a different, even number, namely 2. Who knows, though; there could be some other wacky pattern we're missing, which is why I don't like those problems. By "odd one out" I assume they just mean the number different in pattern from all the other numbers.

    *For #15, I see the pattern you used. Once again, though, I'm not convinced that's the only solution. You arranged it as ACF?O. You saw the distance to AC was 1 letter (B), CF was 2 letters (D,E), and assumed there were 3 letters between F? (G,H,I) which would make ? = J. If they were arranged clockwise like the question said, it would be A?COF. If you looked at every other letter, AC is 1 letter (B), CF is 2 letters (D,E), and guess ?O would be 3 letters (L,M,N), making ?=K. This has no discernible pattern as far as I can tell, but I find it unlikely that your pattern would fit so perfectly (AC=1, CF=2, FJ=3, JO=4) if it wasn't the correct one.

    *For #4, there are thousands of combinations of those letters, and thousands of names to choose from among those categories, so I have no idea. I'm not aware of a way to check that nothing else fits without brute-force comparison of every permutation. Germany definitely works.

    *For #12, I'm not sure if there's a simpler way to do it, but I set up a preliminary truth table using the possible combinations of personalities and seeing whether contradictions emerge from their statements.

    T = always tells truth
    R = random truth value
    L = always lies

    V = Vlad
    J = Jeremy
    B = Bushra

    Our truth table is:
    T R L(1)
    T L R(2)
    R T L(3)
    R L T(4)
    L R T(5)
    L T R(6)

    We assume the values are the ACTUAL values determining whether they're telling the truth or not, and then we compare with their statements to see if it's possible to be true to their personality in making such a statement.

    The statements are:
    Vlad: Jeremy always tells the truth
    Jeremy: I answer randomly.
    Bushra: Jeremy always lies.

    For (1) and (2), if Vlad always tells the truth, then he must be right when he claims Jeremy always tells the truth, which is impossible since only one person can always tell the truth according to the question. For (3) and (6), if Jeremy always told the truth, his statement that he randomly tells the truth would be a contradiction. For (5), if Bushra always tells the truth, then she must be right in saying that Jeremy always lies, but she's not; Jeremy answers randomly in that scenario. For (4), there is no contradiction from Vlad because he may lie or tell the truth whenever he feels like it. If Jeremy always lies, that's consistent with him saying that he answers randomly, which is a lie. If Bushra always tells the truth, then she says that Jeremy always lies, which is a true statement. In (4), all their statements are consistent with their propensity to tell the truth, so Vlad answers randomly, Jeremy always lies, and Bushra always tells the truth.
    Last edited: Aug 18, 2008
  9. Aug 20, 2008 #8
    Your answer is correct for #9. A method which avoids the calculator is to use remainders (modular arithmetic). If x is the first missing digit and y is the second missing digit and z is the number of turnips sold, you can write:

    144z = 10000x + 3470 + y

    If you divide the left side by 144 you get an integer , z. So dividing the right side by 144 also results in an integer. So the sum of the remainders of the three terms must be divisible by 144.

    This gives:
    144n =64x + 14 + y

    Now you still have 3 unknowns and this equation cannot be solved by algebra. But x and y are both single digits and y is even, so x=2,y=2 can be found pretty quickly.

    This gives 23472 which is 144 * 163, so 160 is the closest choice.
  10. Aug 20, 2008 #9

    Gib Z

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    Geekchick, you're right, when you write it out like that it gets a lot easier =] Thanks heaps

    Jaeran - checking it out your solution is correct of course, though Im still wondering if theres a quicker way, these are meant to be sort of quick questions i think.

    ak1948- yes I knew i could use modular arithmetic, but the calculator was right next to me, i couldn't resist =P Though definitely a nice solution, thank you.

    So its pretty much just those stupid missing/odd number problems that were stuck on now :(
  11. Aug 20, 2008 #10
    The main reason it's so long is that I was giving a little exposition to go with it. I'm sure you can write out the truth table combinations in your sleep, and then I quickly noticed inconsistencies, like the fact that it's impossible for Vlad or Jeremy to always tell the truth (because of their statements), which immediately eliminate 4/5 of the incorrect possibilities.
  12. Aug 20, 2008 #11
    #14 - 781523 is the only prime number
  13. Aug 25, 2008 #12
    Q1: Don't look at the rows, look to the columns. 9*9*9 gives what?
  14. Aug 26, 2008 #13

    Gib Z

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    umm for 14, my friend suggested the same number, but because its the only number whose 10s column has 2 instead of 1. I don't really like these kind of questions because you could probably find some reason to justify any of them. Is there any particular way you happened to notice that lol, or used a calculator?

    lukas86 - nice observation! So its obviously 0, i feel a bit dumb now :( lol.

    Only one left is another stupid number question, and ive realised these don't really matter that much anyway, so im going to mark this solved now. Sorry for wasting some of your time lol, thanks for the help!
  15. Aug 26, 2008 #14
    I recognized there was a pattern across, but at first didn't see there was a pattern going down. Number 13 is still bugging me a bit because it's something easy that is being overlooked I'm sure lol. If you get a response to that question you should let me know.
  16. Aug 31, 2008 #15
    for this problem i only looked the last 3 digits of the last 2 rows

    192. 210. 192
    18. ? 18

    i noticed 192 + 18 = 210 and then it goes back to 192 so i thought maybe that 18 + 18 = 36?

    only thing i could see a pattern in the last 2 rows.
    Last edited: Aug 31, 2008
  17. Aug 31, 2008 #16

    Gib Z

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    lukas86 already solved that one in post 14 - its the product of the digits down the columns. That gives the solution to be zero.
  18. Aug 31, 2008 #17
    ohhh, i get it now.. must of overlooked it... sorry.:blushing:
  19. Aug 31, 2008 #18
    #13 the answer is 5.
    When you multiply the 1st and third numbers in each row together you get twice 2nd number.

    9. 27. 6 9x6=54
    19. 45. ? 19x5=90
    6, 21, 7 6x7=42
  20. Sep 2, 2008 #19
    While 781523 is the only prime number, given that the test is to be taken without a calculator, I would suggest 791615 to be the answer instead.

    Amongst the choices:

    It can be seen that
    5+7=12, 7+12=19 giving 5 7 12 19
    8+4=12, 4+12=16 giving 8 4 12 16
    4+7=11, 7+11=18 giving 4 7 11 18
    7+8=15, 8+15=23 giving 7 8 15 23
    And 7+9=16, 9+16=25, giving 7 9 16 25, not 7 9 16 15.

    Therefore I conclude that 791615 is the odd one out.
  21. Sep 2, 2008 #20

    I had what you had awhile ago, and thought I had it too... 19x5 does not equal 90, it gives 95. I am still lost on this as well haha.
  22. Sep 2, 2008 #21
    lukas- you are absolutely right. I can't believe I did that.

    Now I'm stumped again.
  23. Sep 3, 2008 #22
    Thats ok, I did it too Charmed. I still look at it every now and again, nothing really is jumping out at me though.
  24. Sep 9, 2008 #23
    Q14 - might also be 841216 since it's the only one without a 7 in it. There are many alternatives as always with these lists...Occam's Razor, anyone?
  25. Oct 5, 2008 #24

    Multiply the digits in the first row to
    get the number in the second row
    (example: 9x9x9=729); multiply the
    digits in the second row to get the
    number in the third row (7x2x9=126);
    multiply the digits in the third row to
    get the number in the fourth row
    (1x2x6=12). So the answer is 0.
  26. Jan 13, 2009 #25
    Hey there, I just did this test and on the version I have question #13 is different, in that the first number in the second row is 18, not 19. The answer then becomes 5. Thought it was worth mentioning given every other question is exactly the same.
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