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If \(\frac{4x}{7y} = 1\), then what is the value of 3x + 5y ?
(1) x + 4y = 23
(2) y^3 = 64
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(1) x + 4y = 23
(2) y^3 = 64
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Last visit: 31 Mar 2026
Posts: 510
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
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Bunuel
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
\(\frac{4x}{7y}\)=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.
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.
Posts: 46
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
Please hit kudos if it helps.
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
Please hit kudos if it helps.
BelalHossain046
Joined: 11 Feb 2013
Last visit: 05 Apr 2023
Posts: 193
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
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.
Posted from my mobile device
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.
Posted from my mobile device
BelalHossain046
Joined: 11 Feb 2013
Last visit: 05 Apr 2023
Posts: 193
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
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.
Posted from my mobile device
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.
Posted from my mobile device
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