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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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07 Oct 2017, 08:50
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Difficulty:

55% (hard)

Question Stats:

48% (00:39) correct 52% (00:52) wrong based on 66 sessions

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What is the value of y ?

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

2) $$x=2$$
Manager
Joined: 11 Jun 2016
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GMAT 1: 680 Q49 V35
GMAT 2: 690 Q49 V34
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What is the value of y ?  [#permalink]

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07 Oct 2017, 08:53
1
kunal1608 wrote:
What is the value of y ?

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

2) $$x=2$$

Bunuel

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Joined: 02 Sep 2009
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Re: What is the value of y ?  [#permalink]

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07 Oct 2017, 09:50
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.

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

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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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07 Oct 2017, 10:03
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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What is the value of y ?  [#permalink]

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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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07 Oct 2017, 10:27
1
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.
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Re: What is the value of y ?  [#permalink]

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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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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.

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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Joined: 02 Sep 2009
Posts: 47967
Re: What is the value of y ?  [#permalink]

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08 Oct 2017, 04:33
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.

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