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# If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 54696
If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?  [#permalink]

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04 Apr 2016, 07:13
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Difficulty:

35% (medium)

Question Stats:

69% (01:45) correct 31% (02:26) wrong based on 119 sessions

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If $$\frac{4t}{3x} = \frac{2}{3y} +\frac{2}{5y}$$ and xy is not equal to 0, is t equal to 1?

(1) y = 5

(2) $$x = \frac{5y}{4}$$

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Re: If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?  [#permalink]

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04 Apr 2016, 17:15
I simplified the equation to $$t = 4x / 5y$$. Also note that neither x nor y will be 0.
1) Given $$y = 5$$, when we substitute this value into the simplified equation we get $$t = 4x / 25$$. When $$x = 25/4$$ the answer will be yes, if x is any other value the answer will be no => INSUFFICIENT

2) Given $$x = 5y/4$$, this value substituted into the simplified formula yields $$t = 1$$, so the answer is yes => SUFFICIENT

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Joined: 09 Oct 2015
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Re: If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?  [#permalink]

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22 Jul 2016, 11:07
Bunuel wrote:
If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?

(1) y = 5

(2) x = 5y/4

Hi Bunuel

I was wondering if we could take the LCM of 5y and 3y which i thought will be 15 y. with this approach we end up eliminating y from the equation and to know the value of t, we only need the value of x. However using this method i am getting the incorrect answer. Can you help me understand why exactly we cant do this ?

Regards,
Math Expert
Joined: 02 Sep 2009
Posts: 54696
Re: If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?  [#permalink]

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22 Jul 2016, 11:22
sgrover18 wrote:
Bunuel wrote:
If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?

(1) y = 5

(2) x = 5y/4

Hi Bunuel

I was wondering if we could take the LCM of 5y and 3y which i thought will be 15 y. with this approach we end up eliminating y from the equation and to know the value of t, we only need the value of x. However using this method i am getting the incorrect answer. Can you help me understand why exactly we cant do this ?

Regards,

How are you reducing y in $$\frac{4t}{3x} = \frac{2}{3y} +\frac{2}{5y}$$? Please show your work.
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Re: If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?  [#permalink]

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22 Jul 2016, 14:07
Bunuel wrote:
sgrover18 wrote:
Bunuel wrote:
If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?

(1) y = 5

(2) x = 5y/4

Hi Bunuel

I was wondering if we could take the LCM of 5y and 3y which i thought will be 15 y. with this approach we end up eliminating y from the equation and to know the value of t, we only need the value of x. However using this method i am getting the incorrect answer. Can you help me understand why exactly we cant do this ?

Regards,

How are you reducing y in $$\frac{4t}{3x} = \frac{2}{3y} +\frac{2}{5y}$$? Please show your work.

Hi Bunuel,

I realised that while taking 15y as the LCM, I was still multiplying the numerators by 5y and 3y respectively, which was a mistake. This led to one 'y' in the numerator and one the denominator and I ended up cancelling them. Thanks for your time and sorry for the inconvenience !

Regards,
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Re: If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?  [#permalink]

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08 Sep 2017, 21:55
Bunuel wrote:
If $$\frac{4t}{3x} = \frac{2}{3y} +\frac{2}{5y}$$ and xy is not equal to 0, is t equal to 1?

(1) y = 5

(2) $$x = \frac{5y}{4}$$

This is another cumbersome "C" trap question- what this question is testing is your ability to manipulate fractions- a basic rule of thumb whenever you have a whole integer divided by a fraction a faster way to rewrite is

8 / (2/4) =

8 (4) /2 = 32/2 =16

Just multiply the numerator by the bottom most denominator. And always try to rewrite the stimulus

4t/3x = 10y +6y/15y
4t/3x =16y/15y

St 1

No inf about Y or any relative values or anything like that

insuff

St 2

Basically

4t/ 15y/ 4=
16t/15y = 16y/15y

And because X and Y cannot be 0 the only choice is 1

B
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Re: If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?  [#permalink]

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08 Sep 2017, 22:17
Bunuel wrote:
If $$\frac{4t}{3x} = \frac{2}{3y} +\frac{2}{5y}$$ and xy is not equal to 0, is t equal to 1?

(1) y = 5

(2) $$x = \frac{5y}{4}$$

As we need to find the value of $$t$$, it will be good to simplify the equation with $$t$$ as the dependent variable and $$x$$ & $$y$$ as the independent variable before looking at the statements
$$\frac{4t}{3x} = \frac{2}{y}(\frac{1}{3}+\frac{1}{5})$$, or
$$t = \frac{3x}{2y}*\frac{8}{15}$$----------$$(1)$$
so to find the value of $$t$$ we need a relationship between $$x$$ & $$y$$

Statement 1: provides only the value of $$y$$ but not of $$x$$. Hence Insufficient

Statement 2: provides the relationship between $$x$$ & $$y$$ and on putting the value of $$x$$ in equation $$(1)$$ we will get a definite value of $$t$$. Hence Sufficient

Option B
Re: If 4t/3x = 2/3y + 2/5y and xy is not equal to 0, is t equal to 1?   [#permalink] 08 Sep 2017, 22:17
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