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If 4x/7y = 1, then what is the value of 3x + 5y ?

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If 4x/7y = 1, then what is the value of 3x + 5y ?  [#permalink]

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New post 31 Oct 2017, 23:02
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D
E

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  25% (medium)

Question Stats:

77% (01:16) correct 23% (01:13) wrong based on 96 sessions

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Re: If 4x/7y = 1, then what is the value of 3x + 5y ?  [#permalink]

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New post 01 Nov 2017, 00:28
1
Bunuel wrote:
If 4x/7y = 1, then what is the value of 3x + 5y ?

(1) x + 4y = 23

(2) y^3 = 64



x = 7y/4

(1) 7y/4 + 4y = 23
23y = 23*4
y=4
then x = 7
3x +5y = 41..sufficient

(2) y = 4
then x = 7
3x +5y = 41..sufficient

D
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Re: If 4x/7y = 1, then what is the value of 3x + 5y ?  [#permalink]

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New post 01 Nov 2017, 19:35
\(\frac{4x}{7y}\)=1; x=\(\frac{7y}{4}\)

Put this value in (1)

\(\frac{7y}{4}\)+4y=23

\(\frac{7y+16y}{4}\)=23

y=4, then x=7

3x+5y= 3(7)+5(4)= 41 [Suff]

(2) \(y^3\)=64; y=4, then x=7

3x+5y= 3(7)+5(4)= 41 [Suff]

Answer: D.
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Re: If 4x/7y = 1, then what is the value of 3x + 5y ?  [#permalink]

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New post 01 Nov 2017, 20:43
Since 4x/7y=1 => 4x-7y = 0 (*)
1/ From 1 and from (*), we can find y = 4, x=7 => 3x+5y = 41 => Suff
2/ From 2 => y = 4 => x=7 =>3x+5y = 41 => Suff

Answer D
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If 4x/7y = 1, then what is the value of 3x + 5y ?  [#permalink]

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New post 27 Mar 2019, 10:39
In this DS, No need to calculate values.

It's required to keep in mind that values of two unknown variriables can easily be found from two different equations with the condition that TWO EQUATIONS ARE NOT THE SAME EQUATION.

How to find out whether two equations are the same or different:
(1) X+2y =7 & (2)7x +14y=49
Here, (since 7x is 7 times x) if I multiply each variables of EQUATION 1 by 7, equation 1 will become exactly the same thing written in equation 2.

(1) X+2y =7 & (2)7x +8y=41
Here, (since 7x is 7 times x) if I multiply each variables of EQUATION 1 by 7, equation 1 will BE DIFFERENT FROM equation 2.

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Re: If 4x/7y = 1, then what is the value of 3x + 5y ?  [#permalink]

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New post 27 Mar 2019, 10:54
STATEMENT 1: SUFFICIENT
Prompt says:
4x=7y
Or, 4x-7y=0....(1)
Statement 1: x+4y=23....(2)
Here, (1)TWO EQUATIONS & TWO VARIABLES
(2) BOTH EQUATIONS ARE THE SAME EQUATION.
So, I can easily find out the individual value of x and y.

If I have individual value of x and y, I can easily figure out anything with unknown variriable of x and y.
Thus, I can easily find out the value of 3x +5y.

STATEMENT 2:
Y= 4
[NB: ODD POWER DOESN'T CHANGE THE POSITIVE/NEGATIVE NATURE OF INPUT (BASE) AND OUTPUT (RESULT)]
Now the prompt (4x=7y) becomes (4x=7*4) "ONE EQUATION WITH ONE UNKNOWN VARIRIABLE" from which the value of unknown variriable can be found without calculation.

Now, I have individual value of x and y. So, I can easily figure out anything with unknown variriable of x and y.
Thus, I can easily find out the value of 3x +5y.

So. THERE IS NO NEED TO CALCULATION.

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Re: If 4x/7y = 1, then what is the value of 3x + 5y ?   [#permalink] 27 Mar 2019, 10:54
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