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

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

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New post 11 Sep 2017, 07:55
Bunuel wrote:
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.

Answer: D.

For hard inequality and absolute value questions with detailed solutions check this: http://gmatclub.com/forum/inequality-an ... 39-40.html

Hope it helps.


Hi Buneal

In stmt 1, we are given that x is negative. Then how does the second x remain positive. Should it not become -x-x=-2x ?

Kudos [?]: 2 [0], given: 3

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

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New post 11 Sep 2017, 07:58
sinhap07 wrote:
Bunuel wrote:
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.

Answer: D.

For hard inequality and absolute value questions with detailed solutions check this: http://gmatclub.com/forum/inequality-an ... 39-40.html

Hope it helps.


Hi Buneal

In stmt 1, we are given that x is negative. Then how does the second x remain positive. Should it not become -x-x=-2x ?


Let me ask you: say x = -1. Knowing that x is negative do you change x there to -x and write -x = -1?
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

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Collection of Questions:
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What are GMAT Club Tests?
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Kudos [?]: 128459 [0], given: 12173

Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 78

Kudos [?]: 2 [0], given: 3

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

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New post 11 Sep 2017, 08:19
Bunuel wrote:
sinhap07 wrote:
Bunuel wrote:
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.

Answer: D.

For hard inequality and absolute value questions with detailed solutions check this: http://gmatclub.com/forum/inequality-an ... 39-40.html

Hope it helps.


Hi Buneal

In stmt 1, we are given that x is negative. Then how does the second x remain positive. Should it not become -x-x=-2x ?


Let me ask you: say x = -1. Knowing that x is negative do you change x there to -x and write -x = -1?


Interesting point. No. That will be incorrect. But in algebra, we understand that a variable can take any sign ie positive or negative unless given explicit. So in stmt 1, is it that |x|+x is actually -x-(-x)?

Kudos [?]: 2 [0], given: 3

Expert Post
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User avatar
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Joined: 02 Sep 2009
Posts: 41875

Kudos [?]: 128459 [0], given: 12173

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

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New post 11 Sep 2017, 08:37
sinhap07 wrote:
Interesting point. No. That will be incorrect. But in algebra, we understand that a variable can take any sign ie positive or negative unless given explicit. So in stmt 1, is it that |x|+x is actually -x-(-x)?


That's totally wrong. A variable can stand for positive or negative number and you should not change it because you know its sign.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128459 [0], given: 12173

Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 78

Kudos [?]: 2 [0], given: 3

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

Show Tags

New post 11 Sep 2017, 10:00
Bunuel wrote:
sinhap07 wrote:
Interesting point. No. That will be incorrect. But in algebra, we understand that a variable can take any sign ie positive or negative unless given explicit. So in stmt 1, is it that |x|+x is actually -x-(-x)?


That's totally wrong. A variable can stand for positive or negative number and you should not change it because you know its sign.


Thanks Bunuel. Guess I mixed it up for mod function.

Kudos [?]: 2 [0], given: 3

Re: If y is an integer and y = |x| + x, is y = 0?   [#permalink] 11 Sep 2017, 10:00

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