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What is the value of y ?

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What is the value of y ? [#permalink]

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New post 07 Oct 2017, 08:50
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What is the value of y ?

1) \(\frac{4xy+2y}{6x+3} = y-3\)

2) \(x=2\)
[Reveal] Spoiler: OA
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What is the value of y ? [#permalink]

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New post 07 Oct 2017, 08:53
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kunal1608 wrote:
What is the value of y ?

1) \(\frac{4xy+2y}{6x+3} = y-3\)

2) \(x=2\)



Bunuel

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Re: What is the value of y ? [#permalink]

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New post 07 Oct 2017, 09:50
Expert's post
What is the value of y ?

(1) \(\frac{4xy+2y}{6x+3} = y-3\);

Factor our 2y from the numerator and 3 from the denominator: \(\frac{2y(2x+1)}{3(2x+1)} = y-3\);

Reduce by 2x+1: \(\frac{2y}{3} = y-3\);

Cross-multiply: \(2y = 3y - 9\);

Solve to get y =9.

Sufficient.

(2) \(x=2\). Nothing about y. Not sufficient.

Answer: A.
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Re: What is the value of y ? [#permalink]

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New post 07 Oct 2017, 10:00
@bunuel,

For reducing by 2x+1, shouldnt we be sure that x is not equal to -1/2.


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Re: What is the value of y ? [#permalink]

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New post 07 Oct 2017, 10:03
Expert's post
kunal1608 wrote:
Bunuel,

For reducing by 2x+1, shouldnt we be sure that x is not equal to -1/2.


Sent from my iPhone using GMAT Club Forum


If 2x + 1 were 0, then the whole faction (\(\frac{4xy+2y}{6x+3}\)) would be undefined and could not equal to y - 3.
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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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What is the value of y ? [#permalink]

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New post 07 Oct 2017, 10:10
Bunuel wrote:
kunal1608 wrote:
Bunuel,

For reducing by 2x+1, shouldnt we be sure that x is not equal to -1/2.


Sent from my iPhone using GMAT Club Forum




If 2x + 1 were 0, then the whole faction (\(\frac{4xy+2y}{6x+3}\)) would be undefined and could not equal to y - 3.


@Bunuel,

So if a variable is present in the denominator, we can be sure that it’s not equal to zero. But if a variable is in the numerator in the LHS or RHS in cross multiplication, we have to ensure that it’s not equal to zero.

I know this all is very basic but please clarify.


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Re: What is the value of y ? [#permalink]

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New post 07 Oct 2017, 10:27
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Expert's post
kunal1608 wrote:
Bunuel wrote:
kunal1608 wrote:
Bunuel,

For reducing by 2x+1, shouldnt we be sure that x is not equal to -1/2.


Sent from my iPhone using GMAT Club Forum


Bunuel,

If 2x + 1 were 0, then the whole faction (\(\frac{4xy+2y}{6x+3}\)) would be undefined and could not equal to y - 3.


So if a variable is present in the denominator, we can be sure that it’s not equal to zero. But if a variable is in the numerator in the LHS or RHS in cross multiplication, we have to ensure that it’s not equal to zero.

I know this all is very basic but please clarify.


Sent from my iPhone using GMAT Club Forum mobile app


If it's given that xy/y = 1, we can says that y ≠ 0, and thus can reduce to get x = 1.

If the question asks: does xy/y = 1? This can be translated as does x = 1 AND y ≠ 0. For example:

Does xy/y = 1 ?

Here we cannot simply reduce and translate this as "does x = 1?"

Say (1) says: x = 1. Here this would not be sufficient because if y =0, the xy/y would be undefined, and not equal to 1.

Hope it's clear.
_________________

New to the Math Forum?
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Resources:
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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?
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Joined: 11 Jun 2016
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Re: What is the value of y ? [#permalink]

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New post 07 Oct 2017, 10:31
Bunuel wrote:
kunal1608 wrote:
Bunuel wrote:
[quote="kunal1608"]Bunuel,

For reducing by 2x+1, shouldnt we be sure that x is not equal to -1/2.


Sent from my iPhone using GMAT Club Forum


Bunuel,

If 2x + 1 were 0, then the whole faction (\(\frac{4xy+2y}{6x+3}\)) would be undefined and could not equal to y - 3.


So if a variable is present in the denominator, we can be sure that it’s not equal to zero. But if a variable is in the numerator in the LHS or RHS in cross multiplication, we have to ensure that it’s not equal to zero.

I know this all is very basic but please clarify.


Sent from my iPhone using GMAT Club Forum mobile app


If it's given that xy/y = 1, we can says that y ≠ 0, and thus can reduce to get x = 1.

If the question asks: does xy/y = 1? This can be translated as does x = 1 AND y ≠ 0. For example:

Does xy/y = 1 ?

Here we cannot simply reduce and translate this as "does x = 1?"

Say (1) says: x = 1. Here this would not be sufficient because if y =0, the xy/y would be undefined, and not equal to 1.

Hope it's clear.[/quote]

Crystal !

Thanks a lot !

Million Kudos to you !!!!


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What is the value of y ? [#permalink]

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New post 08 Oct 2017, 00:10
Bunuel wrote:
What is the value of y ?

(1) \(\frac{4xy+2y}{6x+3} = y-3\);

Factor our 2y from the numerator and 3 from the denominator: \(\frac{2y(2x+1)}{3(2x+1)} = y-3\);

Reduce by 2x+1: \(\frac{2y}{3} = y-3\);

Cross-multiply: \(2y = 3y - 9\);

Solve to get y =9.

Sufficient.

(2) \(x=2\). Nothing about y. Not sufficient.

Answer: A.



Bunuel
I ddi not notice the common factor or I was afraid to have zero. So I proceeded as follows:

\(4xy+2y = (6x+3) (y-3)\)

\((y-1) (2x+1) =0\)

\(y =0 or x =-1/2\)

Should I check my solution in original statement to prove if x = -1/2 would make denominator undefined ??
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Re: What is the value of y ? [#permalink]

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New post 08 Oct 2017, 04:33
Expert's post
Mo2men wrote:
Bunuel wrote:
What is the value of y ?

(1) \(\frac{4xy+2y}{6x+3} = y-3\);

Factor our 2y from the numerator and 3 from the denominator: \(\frac{2y(2x+1)}{3(2x+1)} = y-3\);

Reduce by 2x+1: \(\frac{2y}{3} = y-3\);

Cross-multiply: \(2y = 3y - 9\);

Solve to get y =9.

Sufficient.

(2) \(x=2\). Nothing about y. Not sufficient.

Answer: A.



Bunuel
I ddi not notice the common factor or I was afraid to have zero. So I proceeded as follows:

\(4xy+2y = (6x+3) (y-3)\)

\((y-1) (2x+1) =0\)

\(y =0 or x =-1/2\)

Should I check my solution in original statement to prove if x = -1/2 would make denominator undefined ??

___________________________
Yes.
_________________

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?
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Re: What is the value of y ?   [#permalink] 08 Oct 2017, 04:33
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