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

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If y is an integer and y=|x|+x, is y=0? [#permalink]

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14 Dec 2010, 22:03
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If y is an integer and y=|x|+x, is y=0?

(1) x<0
(2) y<1
[Reveal] Spoiler: OA

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Re: tricky q from GMATPrep2 [#permalink]

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14 Dec 2010, 22:39
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Each of (1) and (2) are sufficient to answer the question. Thus the answer should be "D".
From(1), any value of X<0, whether it's integer or fraction will lead to Y = 0 because the mode function will result in positive value and positive value added to same negative value will result in Zero.
From (2), We can have Y as negative Integer ( -1,-2....) if and only if the Right hand side of equation is different. It's just adding the same X and it can't lead to the negative value.

Yes it can definitely lead to the Zero.

You can plug and play certain values ( numbers ) in order to verify the above.

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Re: tricky q from GMATPrep2 [#permalink]

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15 Dec 2010, 01:50
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Fijisurf wrote:
I am sure it is posted somewhere on the forum already , I just can't find it.

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

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

If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Note: as $$y=|x|+x$$ then $$y$$ is never negative. If $$x>{0}$$ then $$y=x+x=2x>0$$ and if $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$.

(1) $$x<0$$ --> $$y=|x|+x=-x+x=0$$. Sufficient.

(2) $$y<1$$, as we concluded y is never negative, and we are given that $$y$$ is an integer, hence $$y=0$$. Sufficient.

Also discussed in Inequality and absolute value questions from my collection: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it's clear.
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Re: tricky q from GMATPrep2 [#permalink]

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16 Dec 2010, 06:51
Fijisurf wrote:
I am sure it is posted somewhere on the forum already , I just can't find it.

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

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

A word of caution: When you read "If y is an integer and y=|x|+x", analyze it there and then. y can be a positive integer when x is positive, y will be 0 when x is negative and y will be 0 when x is 0."
Another important point to note here: When the author puts in extra effort to write "y is an integer" rather than "x and y are integers" , take special note that x may not be an integer. Not that it matters very much here but in many questions such a statement will have special significance.
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If y is an integer and y = |x| + x, is y = 0? [#permalink]

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21 Feb 2012, 22:07
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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 ?

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Re: If y is an integer and y = |x| + x, is y = 0? (1) x < 0 [#permalink]

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21 Feb 2012, 22:19
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2. If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Notice that since $$y=|x|+x$$ then $$y$$ is never negative. If $$x>{0}$$ (so if x is positive) then $$y=x+x=2x$$ and for $$x\leq{0}$$ then (when x is negative or zero) then $$y=-x+x=0$$.

(1) $$x<0$$ --> $$y=|x|+x=-x+x=0$$. Sufficient.

(2) $$y<1$$, as we concluded y is never negative, and we are given that $$y$$ is an integer, hence $$y=0$$. Sufficient.

For hard inequality and absolute value questions with detailed solutions check this: inequality-and-absolute-value-questions-from-my-collection-86939-40.html

Hope it helps.
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Re: If y is an integer and y = |x| + x, is y = 0? (1) x < 0 [#permalink]

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21 Feb 2012, 22:43
Bunuel,why didn't i get it with the way i solved it?
Am unable to understand where my approach is wrong . Thanks

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Re: If y is an integer and y = |x| + x, is y = 0? (1) x < 0 [#permalink]

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21 Feb 2012, 23:35
devinawilliam83 wrote:
Bunuel,why didn't i get it with the way i solved it?
Am unable to understand where my approach is wrong . Thanks

You forgot that it's given that y=integer. (2) says y<1, thus |x|+x must also be some integer less than 1: 0, -1, ... but if you refer to my solution you'll see that |x|+x can never be negative, so the only valid solution for |x|+x (or which is the same for y) is 0.

Hope it's clear.
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Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]

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04 Jul 2013, 01:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

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Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]

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07 Jul 2013, 19:30
If y is an integer and y = |x| + x, is y = 0?

(1) x < 0

y = |x| + x
y=-x+x
y=0
SUFFICIENT

(2) y < 1
TRICKYYYYYY
I originally said it was insufficient because it tells us nothing about the sign. However, if y is less than one and is an integer and it is equal to |x|+x then it must be zero!!
SUFFICIENT

(D)

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Re: If y is an integer and y=|x|+x, is y=0? [#permalink]

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07 Feb 2014, 17:23
If y is an integer and y = |x| + x, is y = 0?
y = 0, when x < 0; y = 2x, when x >=0
(1) x < 0 => y = 0
(2) y < 1 -> Because y is an integer, y has to be zero (y cannot be a negative integer because the least value of y is zero).

D

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Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]

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07 Sep 2014, 02:25
devinawilliam83 wrote:
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 ?

point to remember is y is an integer

if y<1 , then y could be 0, -1, -2 and so on .. here according to the second condition if x= 0 then y= 0 , if x = -ve then Y = 0 , if x = +ive like 1 then second choice only will fail, if x = 0.5 then y cant be less than one, if x=.2 or .3 then y cant be integer.

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Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]

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19 Jan 2015, 01:14
stat 1: X<0 => y = -x+x =0
suff
stat 2:y is in integer & y<1 => y<=0 ...y can be less than zero only when x is less than zero => y = -x+x = 0 and for y=0...ntn to calculate
suff
=> Ans D

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Re: If y is an integer and y=|x|+x, is y=0? [#permalink]

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08 Oct 2016, 03:35
Bunuel wrote:
Fijisurf wrote:
I am sure it is posted somewhere on the forum already , I just can't find it.

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

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

If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Note: as $$y=|x|+x$$ then $$y$$ is never negative. If $$x>{0}$$ then $$y=x+x=2x>0$$ and if $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$.

(1) $$x<0$$ --> $$y=|x|+x=-x+x=0$$. Sufficient.

(2) $$y<1$$, as we concluded y is never negative, and we are given that $$y$$ is an integer, hence $$y=0$$. Sufficient.

Also discussed in Inequality and absolute value questions from my collection: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it's clear.

the only place i'm stuck is
if $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$

if x is negative why arent we taking the other x as negative:$$y=-x-x=-2x$$

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Re: If y is an integer and y=|x|+x, is y=0? [#permalink]

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08 Oct 2016, 03:48
nishantdoshi wrote:
Bunuel wrote:
Fijisurf wrote:
I am sure it is posted somewhere on the forum already , I just can't find it.

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

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

If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Note: as $$y=|x|+x$$ then $$y$$ is never negative. If $$x>{0}$$ then $$y=x+x=2x>0$$ and if $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$.

(1) $$x<0$$ --> $$y=|x|+x=-x+x=0$$. Sufficient.

(2) $$y<1$$, as we concluded y is never negative, and we are given that $$y$$ is an integer, hence $$y=0$$. Sufficient.

Also discussed in Inequality and absolute value questions from my collection: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it's clear.

the only place i'm stuck is
if $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$

if x is negative why arent we taking the other x as negative:$$y=-x-x=-2x$$

Knowing that x is a negative number does not mean that you should replace it with -x, this just does not make any sense.
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Re: If y is an integer and y=|x|+x, is y=0? [#permalink]

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08 Oct 2016, 04:00
nishantdoshi wrote:
Bunuel wrote:
Fijisurf wrote:
I am sure it is posted somewhere on the forum already , I just can't find it.

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

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

If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Note: as $$y=|x|+x$$ then $$y$$ is never negative. If $$x>{0}$$ then $$y=x+x=2x>0$$ and if $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$.

(1) $$x<0$$ --> $$y=|x|+x=-x+x=0$$. Sufficient.

(2) $$y<1$$, as we concluded y is never negative, and we are given that $$y$$ is an integer, hence $$y=0$$. Sufficient.

Also discussed in Inequality and absolute value questions from my collection: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it's clear.

the only place i'm stuck is
if $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$

if x is negative why arent we taking the other x as negative:$$y=-x-x=-2x$$

No, you are missing something here.

We are given y = |x| + x, take the value of x as -2 and see the result.

Note that |x| is always positive,

When we say |x| = -x, we mean x will hold a negative value which when multiplied by -ve sign before will give a positive result. NEVER EVER take the values of mod like the way you have taken. I would suggest go through the mod concepts again.
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Re: If y is an integer and y=|x|+x, is y=0? [#permalink]

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08 Oct 2016, 04:42
hey t hanks for the reply

When we say |x| = -x, we mean x will hold a negative value which when multiplied by -ve sign before will give a positive result. NEVER EVER take the values of mod like the way you have taken. I would suggest go through the mod concepts again.

i couldnt understand the above sentence

but my point is when we take x as -2,we get, y=|-2|-2 => y=-2-2 just like we do in the "Critical Points method" (if we get -ve value inside the mod we mult. the mod with the -ve sign.)

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If y is an integer and y=|x|+x, is y=0? [#permalink]

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08 Oct 2016, 04:51
nishantdoshi wrote:
hey t hanks for the reply

When we say |x| = -x, we mean x will hold a negative value which when multiplied by -ve sign before will give a positive result. NEVER EVER take the values of mod like the way you have taken. I would suggest go through the mod concepts again.

i couldnt understand the above sentence

but my point is when we take x as -2,we get, y=|-2|-2 => y=-2-2 just like we do in the "Critical Points method" (if we get -ve value inside the mod we mult. the mod with the -ve sign.)

No Dude, your reasoning is 100% incorrect. As I said above |x| is always positive, so |-2| is always 2. Note that MOD means MAGNITUTE irrespective of sign.

Now, I can confidently say you are not aware of Mod concept used in mathematics.

Please go through the below link and try solving as many questions as you could.

http://magoosh.com/gmat/2012/gmat-math- ... te-values/
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Re: If y is an integer and y=|x|+x, is y=0? [#permalink]

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08 Oct 2016, 05:16
Break into 2 cases
a) x>0
then
y = 2x,
and y >=1 as y is an integer

b) x<= 0
then
y = 0

therefore
1) is sufficient as for x <0, y is 0
2) is sufficient as only possible value of y <1 is 0, coming from the case b).

Hence, an is D

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Re: If y is an integer and y=|x|+x, is y=0? [#permalink]

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10 Nov 2016, 16:38
Fijisurf wrote:
If y is an integer and y=|x|+x, is y=0?

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

haha, what a classic trap!
i knew it when i saw 50% correct rate...
1. sufficient. x is negative, therefore y=0
2. y<1. sufficient. y must be zero. y can't be a decimal, since we are given the fact that y is an integer.

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Re: If y is an integer and y=|x|+x, is y=0?   [#permalink] 10 Nov 2016, 16:38

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