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03 Mar 2021, 14:37
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
75% (01:02) correct
25%
(00:50)
wrong
based on 109
sessions
History
Date
Time
Result
Not Attempted Yet
If 2x = 2y – 3z, what is the value of z?
(1) y = x + 2
(2) x = y – 2
(1) y = x + 2
(2) x = y – 2
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
04 Mar 2021, 23:32
Kudos
Bookmarks
Bunuel
First, rewrite the equation, so that we have z on one side:
2x = 2y - 3z
3z = 2y - 2x
Statement 1:
y = x + 2
One way is picking numbers:
y = 4 --> x = 2 --> 3z = 2*4 - 2*2 = 4
y = -2 --> x = -4 --> 3z = 2*-2 - 2*-4 = 4
The solution of 3z will always be 4, therefore z = \(\frac{4}{3}\)
Additionally, you can solve this with Algebra:
y = x + 2
2y = 2x + 4
2y - 2x = 4
You can plug this into the stem: 3z = 2y - 2x = 4 --> z = \(\frac{4}{3}\)
SUFF
Statement 2:
x = y – 2
If you realize that this is the same as statement 1, you can be done in a few seconds.
But again, you can pick numbers:
x = 4 --> y = 6 --> 3z = 2*6 - 2*4 = 4
x = -2 --> y = 0 --> 3z = 2*0 - 2*-2 = 4
Again, 3z will always be 4, therefore z = \(\frac{4}{3}\)
The Algebra-way:
x = y - 2
2 = y - x
4 = 2y - 2x
You can plug this into the stem: 3z = 2y - 2x = 4 --> z = \(\frac{4}{3}\)
SUFF
Answer D
12 Apr 2021, 01:45
Kudos
Bookmarks
Bunuel
MAGOOSH OFFICIAL SOLUTION
Whenever the question stem presents you with an equation with multiple variables and asks you to solve for one of them, you should immediately rewrite the equation to find a more useful question. Specifically, you should isolate the variable you’re asked to solve for and then focus on the expression equal to that variable.
Here’s what that would look like for this problem:
2x = 2y – 3z
Add 3z and subtract 2x from each side of the equation to isolate the z term.
3z = 2y – 2x
Factor the two from the right-hand side of the equation.
3z = 2(y – x)
Divide each side of the equation by 3.z
z = 2/3*(y – x)
Because this is Data Sufficiency, ask, “What do I need to know to know the value of 2/3*(y – x)?" The answer to that question is simply “y -x.”
Turn to Statement (1) and try to isolate y – x.
y = x + 2
Subtract y from each side of the equation.
y – x = 2
Statement (1) is sufficient. Eliminate B, C, and E.
Turn to Statement (2) and try to isolate y – x.
x = y – 2
Subtract x from and add 2 to each side of the equation.
y – x = 2
Statement (2) is sufficient. Eliminate A. The correct answer is D.
