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03 Nov 2021, 08:00
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B
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Difficulty:
55%
(hard)
Question Stats:
59% (02:05) correct
41%
(02:00)
wrong
based on 106
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If \(x + y + z = 8\) and \(3x + 2y + 4z = 25\), what is the value of z ?
(1) \(12z = 75 − 9x − 6y\)
(2) \(6yz = y^2 + 9z^2\)
(1) \(12z = 75 − 9x − 6y\)
(2) \(6yz = y^2 + 9z^2\)
03 Nov 2021, 08:23
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Statement 1 is just rephrasing of 3x+2y+4z = 25 Hence insufficient( Only one variable can be eliminated 2 eq 3 unknowns)
St 2 gives y=3z
Eliminating X from given 2 eq we have
Z-Y=1
Z= -1/2
Ans: Option B
Posted from my mobile device
St 2 gives y=3z
Eliminating X from given 2 eq we have
Z-Y=1
Z= -1/2
Ans: Option B
Posted from my mobile device
03 Nov 2021, 10:23
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Bunuel
Given: \(x + y + z = 8\) and \(3x + 2y + 4z = 25\)
Target question: What is the value of z ?
Statement 1: \(12z = 75 − 9x − 6y\)
This equation is equivalent to the given equation \(3x + 2y + 4z = 25\).
Here's why:
Take: \(12z = 75 − 9x − 6y\)
Divide both sides by \(3\) to get: \(4z = 25 − 3x − 2y\)
Add \(3x\) and \(2y\) to both sides of the equation: \(4z + 3x + 2y = 25\)
IMPORTANT: Data Sufficiency target questions are always impossible to answer without any additional information.
Since statement 1 doesn't add any additional information, we know that statement 1 is NOT SUFFICIENT
Statement 2: \(6yz = y^2 + 9z^2\)
Do you see the special product hiding in this equation?
Subtract \(6xy\) from both sides of the equation: \(0= y^2 - 6yz+ 9z^2\)
Factor to get: \(0= (y-3z)(y-3z)\)
From this we can conclude that \(y - 3z = 0\)
Now let's see if we can fiddle with the given equations to create another equation with \(y\) and \(z\)
We have:
\(3x + 2y + 4z = 25\)
\(x + y + z = 8\)
Create an equivalent equation by multiplying both sides of the bottom equation by \(3\) to get:
\(3x + 2y + 4z = 25\)
\(3x + 3y + 3z = 24\)
Subtract the bottom equation from the top equation to get: \(-y + z = 1\)
We now have the following system of equations:
\(y - 3z = 0\)
\(-y + z = 1\)
Add the two equations to get: \(-2z = 1\)
Solve to get: \(z = -\frac{1}{2}\)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
