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Math Help - Help needed with these two.

  1. #1
    Junior Member
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    Help needed with these two.

    A cube with edge length 2 metres is cut up into cubes each with edge lengths 5 centimetres. If all these cubes were stacked one on top of the other to form a tower, the height of the tower would be.
    a. 32km
    b. 160m
    c. 1600m
    d. 3.2km
    e. 320m

    ----------------------------------------------------------------

    A number of less than 2008. It is odd, it leaves a remainder of 2 when divided by 3 and a remainder of 4 when divided by 5. What is the sum of digits of the largest such number?

    a. 26
    b. 25
    c. 24
    d. 23
    e. 22
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  2. #2
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    Hello, 0110kim!

    A cube with edge length 2 metres is cut up into cubes
    each with edge lengths 5 centimetres.
    If all these cubes were stacked one on top of the other to form a tower,
    the height of the tower would be:

    . . (a) 32 km . . (b) 160 m . . (c) 1600 m . . (d) 3.2 km . . (e) 320 m

    The cube is 2 meters = 200 cm on an edge.
    It is cut into 5 cm cubes; each edge is cut into 40 parts.
    There are: .40 40 40 .= .64,000 cubes.

    A stack of 64,000 cubes, each 5 cm high, would be: .5 64,000 .= .320,000 cm high.

    And: .320,000 cm .= .3200 m .= .3.2 km . . . answer (d)




    A number of less than 2008; it is odd.
    It leaves a remainder of 2 when divided by 3
    and a remainder of 4 when divided by 5.
    What is the sum of digits of the largest such number?

    . . (a) 26 . . (b) 25 . . (c) 24 . . (d) 23 . . (e) 22
    I have a very primitive solution . . .


    Let the number be N.

    When N is divided by 5, the remainder is 4.
    . . Then N is of the form: .5a + 4

    For any integer value of a, 5a ends in 0 or 5.
    . . So: .N .= .5a + 4 .ends in 4 or 9.

    But we are told that N is odd . . . Hence, N ends in 9.


    Since N < 2008, the choices are: .1999. 1989, 1979, 1969, . . .

    Which of these has a remainder of 2 when divided by 3?

    . . 1999 3 .= .666, rem. 1

    . . 1989 3 .= .663, rem. 0

    . . 1979 3 .= .659, rem. 2 . . There!


    Therefore: .N = 1979, and the sum of the digits is 26 . . . answer (a)

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