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# If Y is an integer and Y = |X| + X, is Y = 0 X<0 Y<1

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If Y is an integer and Y = |X| + X, is Y = 0 X<0 Y<1 [#permalink]  11 Mar 2009, 05:58
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If Y is an integer and Y = |X| + X, is Y = 0

X<0
Y<1

Senior Manager
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Re: DS - is Y = 0 [#permalink]  11 Mar 2009, 07:01
Allana25 wrote:
If Y is an integer and Y = |X| + X, is Y = 0

X<0
Y<1

Y = |x|+x

1. x<0
since x<0, then whatever values you take for x, y will always be 0.
e.g.
|-5|-5=5-5=0
|-1|-1=1-1=0
suffic.

2. y<1
since y can never be a negative number because y=|x|+x, then y>=0. Since it's given y<1, then y=0.
suffic.

Intern
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Re: DS - is Y = 0 [#permalink]  11 Mar 2009, 07:56
Thats what I got. But I saw this question at another forum and they said A. I think D is the correct answer.
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Re: DS - is Y = 0 [#permalink]  11 Mar 2009, 09:25
peraspera wrote:
Allana25 wrote:
If Y is an integer and Y = |X| + X, is Y = 0

X<0
Y<1

Y = |x|+x

1. x<0
since x<0, then whatever values you take for x, y will always be 0.
e.g.
|-5|-5=5-5=0
|-1|-1=1-1=0
suffic.

2. y<1
since y can never be a negative number because y=|x|+x, then y>=0. Since it's given y<1, then y=0.
suffic.

in second case, put x = 0.1 you get y = 0.2 which is less than 1 ..and put x = -0.1, y = 0. which is also less than 1 so case 2 is wrong.

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Re: DS - is Y = 0 [#permalink]  11 Mar 2009, 09:28
ugimba wrote:
peraspera wrote:
Allana25 wrote:
If Y is an integer and Y = |X| + X, is Y = 0

X<0
Y<1

Y = |x|+x

1. x<0
since x<0, then whatever values you take for x, y will always be 0.
e.g.
|-5|-5=5-5=0
|-1|-1=1-1=0
suffic.

2. y<1
since y can never be a negative number because y=|x|+x, then y>=0. Since it's given y<1, then y=0.
suffic.

in second case, put x = 0.1 you get y = 0.2 which is less than 1 ..and put x = -0.1, y = 0. which is also less than 1 so case 2 is wrong.

oh ...Y is integer here so ... didn't see that ... I guess you can't substitute 0.1 for x .. I think D should be good then.
Director
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Re: DS - is Y = 0 [#permalink]  11 Mar 2009, 10:22
when x<0, |x| = -x...so the first eq becomes
Y = -x + (-x) = -2x ?????
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Re: DS - is Y = 0 [#permalink]  11 Mar 2009, 16:02
1
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Economist wrote:
when x<0, |x| = -x...so the first eq becomes
Y = -x + (-x) = -2x ?????

When x is negative, you don't replace x with -x; if x is negative, then -x is a positive number. If x is negative, there is a negative sign 'inside' of x.

Now, if x is negative, you can replace |x| with -x, because if x is negative, -x will produce the 'positive equivalent' of x.
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Re: DS - is Y = 0 [#permalink]  15 Mar 2009, 01:35

But thanks Ian for this last bit. It made me see |x| in a different light. Never thought you could write |x| as -x when x is negative. Makes perfect sense.

Thanks.
Re: DS - is Y = 0   [#permalink] 15 Mar 2009, 01:35
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