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Difficult Math Problem #98 - Algebra

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800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Problem #98 - Algebra

Post Fri Feb 16, 2007 11:28 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?


    I. The units digit of x + y is greater than the units digit of either x or y.
    II. The tens digit of x + y equals 2.
    III. The hundreds digit of y is at least 5.

    A. II only

    B. III only

    C. I and II

    D. I and III

    E. II and III


    from diff math doc. oa coming after a few people reply. have a nice weekend!!

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    banona Senior | Next Rank: 100 Posts Default Avatar
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    Post Fri Feb 16, 2007 12:59 pm
    The numbers x and y are three-digit positive integers,
    this can be translated to : x = X1X2X3 ; AND y= Y1Y2Y3

    * AS x + y is a four-digit integer. This only means that (Y1+X1+1 ) > 10; PROVIDED that y>x; then hundreds digis of y is superior to hundreds digit of x; so the inequality in Blod becomes 2y>9. Then easily Y> ou equal to 5. ( III is true)

    * The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, we can not conclude that ten digits of the sum is 2 as it depends on the unit digits of x and y. So II is not true

    * Units digit of x + y can be greater than units digit of either x or y but it's not necessary. Fr this, consider three digit numbers x= 552 and y= 579 . It's obvious that the unit digit of the sum is 1 and is inferior to the unit digit of both numbers;

    III. The hundreds digit of y is at least 5. only this one is true


    B. III only s the naswer

    Looking for feedback

    _________________
    I appologize for my Frenchy-English.
    I am working on it.

    guynoor Senior | Next Rank: 100 Posts Default Avatar
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    Post Fri Feb 16, 2007 1:46 pm
    See Below



    Last edited by guynoor on Fri Feb 16, 2007 1:51 pm; edited 1 time in total

    guynoor Senior | Next Rank: 100 Posts Default Avatar
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    Post Fri Feb 16, 2007 1:51 pm
    guynoor wrote:
    800guy wrote:
    The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?


    I. The units digit of x + y is greater than the units digit of either x or y.
    II. The tens digit of x + y equals 2.
    III. The hundreds digit of y is at least 5.

    A. II only

    B. III only

    C. I and II

    D. I and III

    E. II and III


    from diff math doc. oa coming after a few people reply. have a nice weekend!!
    Suppose X = 275 and Y = 955
    X + Y = 1230
    Checking conditions in the answer choices........
    Hence Answer = B

    800guy Master | Next Rank: 500 Posts Default Avatar
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    Post Mon Feb 19, 2007 8:14 am
    oa:

    x= abc
    y= def

    x = a7c
    y= b5f

    x > y and x+y = wxyz.

    I. The units digit of x + y is greater than the units digit of either x or y.

    It can carryover one digit. False

    II. The tens digit of x + y equals 2.

    It can be 2 or 3. False

    III. The hundreds digit of y is at least 5.

    a+b+1 >= 10
    a >b so a at least 5. True.

    Ans: b

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