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

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New post 04 Apr 2016, 07:13
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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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New post 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

Answer: 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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New post 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,
Shradha

Kudos [?]: 12 [0], given: 15

Expert Post
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Joined: 02 Sep 2009
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Kudos [?]: 128459 [0], given: 12173

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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New post 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,
Shradha


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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New post 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,
Shradha


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,
Shradha

Kudos [?]: 12 [0], given: 15

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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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New post 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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New post 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

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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] 08 Sep 2017, 22:17
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