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Is x < w ?

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Is x < w ?  [#permalink]

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New post 10 Jul 2016, 01:52
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Question Stats:

75% (01:11) correct 25% (01:41) wrong based on 332 sessions

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Is x < w ?

(1) x - w < x

(2) x + w < w

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Re: Is x < w ?  [#permalink]

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New post 10 Jul 2016, 08:34
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Re: Is x < w ?  [#permalink]

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New post 10 Jul 2016, 02:06
1
1. x-w<x
= -w<0
= w>0

2. x+w<w
= x<0

combining both
x<w
C answer.
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Re: Is x < w ?  [#permalink]

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New post 10 Jul 2016, 08:28
is x < w ?

1) x - w < x

2) x + w < w


Can someone please explain the OA along with the process of solving such sums?
Thanks in advance

Ok i got it now

1) x - w < x
subtract x from both sides :

-w < 0
w > 0 but no clue about x ------> insufficient

2) x + w < w
subtract w from both sides :
x < 0 =====> no clue about w ---> insufficient

C) 1 + 2
w > 0 and x < 0 hence x < w ------> sufficient

Can some one please confirm whether my reasoning is correct.
I believe dividing or multiplying by an expression (such as w and or x) in this case is wrong, Since it is not mentioned whether x & or w is +ve/-ve and or int or a fraction
But subtraction should be ok.
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Re: Is x < w ?  [#permalink]

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New post 10 Jul 2016, 15:10
1
Top Contributor
aniketm.87@gmail.com wrote:
is x < w ?

1) x - w < x

2) x + w < w


Can someone please explain the OA along with the process of solving such sums?
Thanks in advance

Ok i got it now

1) x - w < x
subtract x from both sides :

-w < 0
w > 0 but no clue about x ------> insufficient

2) x + w < w
subtract w from both sides :
x < 0 =====> no clue about w ---> insufficient

C) 1 + 2
w > 0 and x < 0 hence x < w ------> sufficient

Can some one please confirm whether my reasoning is correct.
I believe dividing or multiplying by an expression (such as w and or x) in this case is wrong, Since it is not mentioned whether x & or w is +ve/-ve and or int or a fraction
But subtraction should be ok.


IMO,
    You are absolutely correct since both side of the inequities in Statement(1 and (2) have same expression.Their subtructions are ok

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Re: Is x < w ?  [#permalink]

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New post 20 Jan 2017, 08:34
1
Bunuel wrote:
Is x < w ?

(1) x - w < x --> w > 0. Not sufficient.

(2) x + w < w --> x < 0. Not sufficient.

(1)+(2) x < 0 < w. Sufficient.

Answer: C.


Hi Bunuel
As per GMAT Club Math Book - "When you divide both sides by a variable (or do operations like "canceling x on both sides") you implicitly assume that the variable cannot be equal to 0, as division by 0 is undefined."
Does this apply only for division. Is it allowed to add, subtract or multiply without knowing the sign (+ve or -ve) for that variable in an inequality.
Please explain or share any link which addresses this confusion.
In both the case above you have subtracted one of the variable from both sides.
Thanks
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Re: Is x < w ?  [#permalink]

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New post 21 Jan 2017, 03:19
2
2
Nightfury14 wrote:
Bunuel wrote:
Is x < w ?

(1) x - w < x --> w > 0. Not sufficient.

(2) x + w < w --> x < 0. Not sufficient.

(1)+(2) x < 0 < w. Sufficient.

Answer: C.


Hi Bunuel
As per GMAT Club Math Book - "When you divide both sides by a variable (or do operations like "canceling x on both sides") you implicitly assume that the variable cannot be equal to 0, as division by 0 is undefined."
Does this apply only for division. Is it allowed to add, subtract or multiply without knowing the sign (+ve or -ve) for that variable in an inequality.
Please explain or share any link which addresses this confusion.
In both the case above you have subtracted one of the variable from both sides.
Thanks


We are concerned about the sign of a number when multiplying/dividing an inequality by that number. However we can safely add/subtract a number from both sides of an inequality.

Inequalities Made Easy!

Solving Quadratic Inequalities - Graphic Approach
Inequality tips
Wavy Line Method Application - Complex Algebraic Inequalities

DS Inequalities Problems
PS Inequalities Problems

700+ Inequalities problems

inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html

Hope this helps.
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Re: Is x < w ?  [#permalink]

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New post 22 Jan 2017, 04:10
Is x < w ?

(1) x - w < x

-w < 0 ...........W>0.......No info about X

Insufficient

(2) x + w < w

x< 0......No info abut W

Insufficient

Combining 1 & 2

x< 0 <w

Answer: C

Alternatively, we can sum up 2 inequalities :

2x-w+w<x +w.............2x<x+w.............2x-x<w...............x<w
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Re: Is x < w ?  [#permalink]

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New post 15 Jul 2018, 05:23
Bunuel wrote:
Is x < w ?

(1) x - w < x --> w > 0. Not sufficient.

(2) x + w < w --> x < 0. Not sufficient.

(1)+(2) x < 0 < w. Sufficient.

Answer: C.



Can x<w be re-written as x-w<0?
If not, then why?
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Re: Is x < w ?  [#permalink]

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New post 15 Jul 2018, 05:58
Shbm wrote:
Bunuel wrote:
Is x < w ?

(1) x - w < x --> w > 0. Not sufficient.

(2) x + w < w --> x < 0. Not sufficient.

(1)+(2) x < 0 < w. Sufficient.

Answer: C.



Can x<w be re-written as x-w<0?
If not, then why?


You can add or subtract a value from both parts of an inequality freely. So, you can subtract w from x < w and get x - w < 0.
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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.


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Re: Is x < w ? &nbs [#permalink] 15 Jul 2018, 05:58
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