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04 Apr 2018, 23:43
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
85% (01:18) correct
15%
(01:08)
wrong
based on 130
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of x?
(1) \(8^{(x + 2)} = 16^{(4 + y)}\)
(2) \(3^{(x − y)} =27^{(y + 6)}\)
(1) \(8^{(x + 2)} = 16^{(4 + y)}\)
(2) \(3^{(x − y)} =27^{(y + 6)}\)
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
05 Apr 2018, 00:40
Kudos
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Bunuel
Before explicitly solving, we'll first look for a property-based approach without calculation.
This is a Logical approach.
(1) , (2) Each of these gives only one equation with two variables and so has infinite solutions.
Insufficient.
Combined:
We can translate (1) and (2) into two distinct linear equations with two variables, which has one solution!
No need to actually calculate.
(C) is our answer.
If it is unclear if the given expressions do in fact give distinct linear equations, then basic simplification can help:
We'll rewrite \(8=2^3\), \(16=2^4\) and \(27=3^3\). This gives the following:
(1) \(2^{3(x + 2)} = 2^{4(4 + y)}\)
(2) \(3^{(x − y)} =3^{3(y + 6)}\)
Then (1) gvies 3(x+2)=4(4+y) and (2) gives (x-y)=3(y+6).
Now it should be clear that these are 2 distinct linear equations with two variables which is sufficient.
05 Apr 2018, 05:17
Kudos
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Bunuel
Statement 1: \(8^{(x + 2)} = 16^{(4 + y)}\)
i.e. \(2^{3(x + 2)} = 2^{4(4 + y)}\)
i.e. \({3(x + 2)} = {4(4 + y)}\)
i.e. \(3x + 6 = 16 + 4y\)
i.e. \(3x-4y = 10\)
NOT SUFFICIENT
Statement 2: \(3^{(x − y)} =27^{(y + 6)}\)
i.e. \(3^{(x − y)} =3^{3(y + 6)}\)
i.e. \(x-y = 3y+18\)
i.e. \(x-4y = 18\)
NOT SUFFICIENT
Combining the two statements
WE HAVE TWO EQUATIONS IN TWO VARIABLES AND OSLVING GTHEM WILL GIVE US UNIQUE VALUES OF X AND Y HENCE
SUFFICIENT
ANSWER: OPTION C
