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Three-digits (OG)

This topic has 2 expert replies and 0 member replies
Anitochka Newbie | Next Rank: 10 Posts Default Avatar
Joined
01 Aug 2017
Posted:
4 messages

Three-digits (OG)

Post Sat Aug 12, 2017 6:26 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x,y, and z are three-digit positive integers and if x=y+z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?
    1) The tens digit of x is equal to the sum of the tens digits of y and z.
    2) The units digit of x is equal to the sum of the units digits of y and z.

    Answer: A

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    Post Sat Aug 12, 2017 6:30 am
    Quote:
    If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y & z?

    (1) the tens digit of x is equal to the sum of the tens digits of y and z.
    (2) the units digit of x is equal to the sum of the units digits of y and z.

    Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?

    Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z
    Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
    Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
    Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308

    Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.
    This rules out scenarios 2 and 3 (plus we already ruled out scenario 1).
    So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z
    Since we can answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: The units digit of x is equal to the sum of the units digits of y and z.
    This rules out scenario 3, but not scenario 2. Consider these two conflicting cases:
    Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z
    Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z
    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Answer = A

    Cheers,
    Brent

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    Post Sat Aug 12, 2017 7:28 am
    Quote:
    If x, y, and z are three-digit positive integers and if x = y+z, is the hundreds digits of x equal to the sum of the hundreds digits of y and z ?

    (1) the tens digit of x is equal to the sum of the tens digits of y and z.

    (2) the units digit of z is equal to the sum f the units digits of y and z.
    Let y = 2BC, z = 2EF, and x = HTU, so that the addition looks as follows:

    2BC
    2EF
    HTU

    When will it be true that H ≠ 2+2?
    When we have to CARRY A 1 FROM THE TENS PLACE TO THE HUNDREDS PLACE.
    To illustrate:

    259
    249
    508

    Here, because we have to carry a 1 from the tens place to the hundreds place, H = 2+2+1 = 5.

    Question rephrased:

    ABC
    DEF
    HTU

    In the addition problem above, do we have to a carry a 1 from the tens place to the hundreds place?

    Statement 1: The tens digit of x is equal to the sum of the tens
    digits of y and z.

    Since T = B+E, there is no need to carry a 1 to the hundreds place.
    SUFFICIENT.

    Statement 2: The units digit of x is equal to the sum of the
    units digits of y and z.

    Since U = C+F, we do not need to carry a 1 from the UNITS PLACE to the TENS PLACE.
    But it cannot be determined whether we have to carry a 1 from the TENS PLACE to the HUNDREDS PLACE.
    If T = B+E = 0+0 = 0, then there is no need to carry a 1 to the hundreds place:
    If T = B+E = 9+9 = 18, then we must carry a 1 to the hundreds place.
    INSUFFICIENT.

    The correct answer is A.

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    Thanked by: Anitochka
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