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Thread: TestFunda Answers - Higher Maths

  1. #2001
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    Post TestFunda Answers - Higher Maths

    find the remainder when 13^27 is divided by 7?
    Options
    1) 
    -1
    2) 
    6
    Additional Notes: pl. explain

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    Post TestFunda Answers - Higher Maths

    Let N = 1327 = 13 x 16913
    Now 169 = 1Mod 7
    Thus 13 x 1 = 6 Mod 7
    Thus remainder would be 6..

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    Post TestFunda Answers - Higher Maths

    One man and six women working together can do a job in 10 days.The same job is done by two men in 'p' days and by eight women in p+5 days. By what percentage is the efficiency of a man greater than that  of a woman?
    Options
    1) 
    300%
    2) 
    500%
    3) 
    600%
    4) 
    700%
    Additional Notes: with detailed explanation,please do come up with shortcut also.

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    Post TestFunda Answers - Higher Maths

    Find the number of positive integer solutions of the equation 2/x +15/y=5
    Options
    1) 
    1
    2) 
    2
    3) 
    3
    4) 
    0

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    Post TestFunda Answers - Higher Maths

    N=7777..............7777,where the digit 7 repeats itself 429 times.What is the remainder left when N is divided by 1144?
    Options
    1) 
    913
    2) 
    1129
    3) 
    777
    4) 
    none of these

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    Post TestFunda Answers - Higher Maths

    How many factors of 20! (20 factorial) are there whose unit digit is 5?
    Options
    1) 
    2068
    2) 
    1868
    3) 
    1728
    4) 
    none of these

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    Post TestFunda Answers - Higher Maths

    A number N = 23335272 what is the number of factors of N that are not divisible by 6?
    Options
    1) 
    69
    2) 
    76
    3) 
    63
    4) 
    81

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    Post TestFunda Answers - Higher Maths

    total number of factors are 144 ( 4*4*3*3=144) 
    and factors that are divisible by 6 are 3*3*3*3 [ remove one 2 and one 3 from the factors given i.e 2*3*(2^2*3^2*5^2*7^2) ] 

    so factors that are NOT div by 6 are 144-81=63  
    Calls '10: XL-BM/HRM

  9. #2009
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    Post TestFunda Answers - Higher Maths

    total number of factors are 144 ( 4*4*3*3=144) 
    and factors that are divisible by 6 are 3*3*3*3 [ remove one 2 and one 3 from the factors given i.e 2*3*(2^2*3^2*5^2*7^2) ] 

    so factors that are NOT div by 6 are 144-81=63 

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    Post TestFunda Answers - Higher Maths

    As per divisibility rule of 11, the number 77777777.....777 for 429 digits should leave a remainder 7 when divided by 11. Similarly, this number leaves a remainder of 10 when divided by 13 and a remainder 1 when divided by 8.

    So the number is of the form: 11A+7 = 13B + 10 = 8C + 1.

    First take 11A+7=13B+10...(i)

    By Chinese remainder theorem, you get A = 5 and B = 4 (which give you 62 on both sides of the equation (i)). So the series of such numbers is given by 62+143D.

    Now take 62+143D = 8C+1....(ii)

    Again apply Chinese remainder theorem and you get C=97 and K=5 (giving you 777 on both sides of the equation (ii)). So the series of such numbers is given by 777+1144E. Hence remainder = 777. Option 3.

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    Post TestFunda Answers - Higher Maths

    20!=2^18 * 3^8 *5^4 *7^2 *11*13*17*19

    all odd multiples of 5 end in 5.

    So, [0-8]*[1-4]*[0-2]*2*2*2*2
    9*4*3*16
    =1728

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    Post TestFunda Answers - Higher Maths

    As per divisibility rule of 11, the number 77777777.....777 for 429 digits should leave a remainder 7 when divided by 11. Similarly, this number leaves a remainder of 10 when divided by 13 and a remainder 1 when divided by 8.

    So the number is of the form: 11A+7 = 13B + 10 = 8C + 1.

    First take 11A+7=13B+10...(i)

    By Chinese remainder theorem, you get A = 5 and B = 4 (which give you 62 on both sides of the equation (i)). So the series of such numbers is given by 62+143D.

    Now take 62+143D = 8C+1....(ii)

    Again apply Chinese remainder theorem and you get C=97 and K=5 (giving you 777 on both sides of the equation (ii)). So the series of such numbers is given by 777+1144E. Hence remainder = 777. Option 3.

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    Post TestFunda Answers - Higher Maths

    Let N = 1327 = 13 x 16913
    Now 169 = 1Mod 7
    Thus 13 x 1 = 6 Mod 7
    Thus remainder would be 6..or -1

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    Post TestFunda Answers - Higher Maths

    the equation can be reduced to :
    y= 15x/(5x-2)....... or
    y = 3+ 6/(5x-2)
    Now 5x-2 can take values as 1,2,3,6,-1,-2,-3,-4  
    this will only give inegral x as 0  or 1.
    But x can't be 0.
    So only 1 solution is possible. 

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    Post TestFunda Answers - Higher Maths

    Each 1*1 cube has 6 faces 
    Total 1*1 cubes = 2*5*5 + 2*3*5 + 2*3*3 = 98 
    Total faces of small cubes = 98*6 = 588 
    Now, four sides of the 5*5 cube is painted
    So, total small cube faces painted = 4*5*5 = 100 
    Desired answer = 588-100 = 488

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    Post TestFunda Answers - Higher Maths

    the equation can be reduced to :
    y= 15x/(5x-2)....... or
    y = 3+ 6/(5x-2)
    Now 5x-2 can take values as 1,2,3,6,-1,-2,-3,-4  
    this will only give inegral x as 0  or 1.
    But x can't be 0.
    So only 1 solution is possible.
    So, (x,y) = (1,5)

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    Post TestFunda Answers - Higher Maths

    The job is done by 2 men in 'p' days and by 8 women in 'p+5' days...
    If the amount of work done by a man in one day is 'm' and that of a woman in 'w',
    We get p(2/m)=1
               (p+5)(8/w)=1
    Solving above two equations,we get
         m=2p and w=8p+40
                          =4m+40
    Substituting the above values in 10(1/m+6/w)=1      {derived from first condition)
                      we get a quadratic equation
              w2 -140w+2400=0
    Solving the equation will give you w= 120,20
    For w=20 m gives a negative value so ruled out...
    Hence w=120 and m=20
    Implies M can finish the work in 20 days and w in 120 days i.e., in one day m can do 1/20th of work and w can do 1/120th of work.So efficiency of m over w is
    [(1/20)-(1/120)]/(1/120)=500%

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    Post TestFunda Answers - Higher Maths

    A gambler bets on the team of seven players ABCDEFG whose winning a-4 to 1 against b-4 to 1 against c-4 to 1 against d-4 to 1 against e-5 to 1 against f-6 to 1 against g. how should he bet on g to set 20% profit.

    Options
    1) 
    --------
    2) 
    -----------

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    Post TestFunda Answers - Higher Maths

    If in 100 miles race 8 person is running winner take 9.8sec and fifth man takes 10.4 sec the time of 8 man is in AP if in 4*100 meters realy of onside is 1,4,5,8 position then win by.

    Options
    1) 
    a).3 sec
    2) 
    b).1 sec
    3) 
    c).7 sec
    4) 
    d).5 sec
    5) 
    e)none

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    Post TestFunda Answers - Higher Maths

    In a straight highway 2 cars starts from the same point in opposite directions each travels for 8 Kms and take left turn then travel for 6 Kms what is the distance between them now
    Options
    1) 
    16
    2) 
    20
    3) 
    25
    4) 
    10

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