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If y is an integer and y = |x| + x, is y = 0?

This topic has 1 expert reply and 0 member replies
ahmedshafea Junior | Next Rank: 30 Posts
Joined
30 Aug 2017
Posted:
19 messages

If y is an integer and y = |x| + x, is y = 0?

Post Mon Sep 11, 2017 12:39 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If y is an integer and y = |x| + x, is y = 0?

    (1) x < 0
    (2) y < 1


    I rephrased the original question as Is x<0?
    Statement 1 : SF
    Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x
    - X<0 or,
    - 0<X<0.5
    Basis this II is insufficient.. Where am I going wrong ?


    Can some experts help me with this? How to come up with the correct answer?
    Need thorough explanation regarding this one. Thanks

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    Post Mon Sep 11, 2017 7:47 pm
    Hi ahmedshafea,

    We're told that Y is INTEGER and that Y = |X| + X. We're asked if Y = 0. This is a YES/NO question. Before we deal with the two Facts, we can certainly 'rewrite' the given question. Y would equal 0 under two circumstances:
    -If X is ANY NEGATIVE value.
    -If X is 0.

    Y would NOT equal 0 if X was a positive (in this situation, Y would equal 2X). Thus, the question is ultimately asking... "Is X less than OR equal to 0?"

    1) X < 0

    Fact 1 clearly defines X as negative, so the answer to the question is ALWAYS YES.
    Fact 1 is SUFFICIENT

    2) Y < 1

    The prompt tells us that Y is an INTEGER - and since Y cannot be negative, the only integer that's possible here is 0. Thus, the answer to the question is ALWAYS YES.
    Fact 2 is SUFFICIENT

    Final Answer: D

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