Quant Boosters - Learn Quest - Set 2

  • Learn Quest

    One day Vikram was out bicycling. After entering a one-way tunnel and after having ridden one-fourth of the distance through it, he looked back over his shoulder and saw a bus approaching the tunnel entrance at a speed of 80 miles/hr. Doing a quick mental exercise, Vikram realized that if he accelerated immediately to his top speed, he could just escape with his life, whichever direction he rode. What is Vikram's top biking speed in miles/hr?

    Bus .......... A....... Vikram ...B
    AB is a tunnel
    And suppose person is at point C
    AC : CB = 1:3
    Now the time at which bus reaches A
    Vikram would reach from point C to point A
    And the time at which bus reaches to B
    Vikram reaches from C to B
    Let assume
    Length of tunnel is 4km
    So if Vikram moves 1 km forward towards B
    Bus would reach at A
    So remaining distance covered by Vikram is 2km
    And bus covered the whole distance 4km(length of tunnel) in the same time with a speed of 80km/hr
    So speed of Vikram = 80/2 => 40km/hr

    Find the ten's place digit of 625^246 - 441^128

    (a5)^even ends with 25
    Last two digits
    => (81)^14
    => (61)^7
    => 21
    Or (41)^28
    => (4 * 8)1
    => 21

    So 25-21 = 04

    digit at tenth place = 0

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