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14 May 2020, 09:35
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:47) correct
31%
(02:11)
wrong
based on 45
sessions
History
Date
Time
Result
Not Attempted Yet
Given 2x + 3y + 4z > 2, can z be equal to zero?
(1) 4x + 6y < -3
(2) 9y + 12z > 4
(1) 4x + 6y < -3
(2) 9y + 12z > 4
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
14 May 2020, 18:27
Kudos
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Given 2x + 3y + 4z > 2, can z be equal to zero?
Addition: We can add two inequalities when they have the same inequality signs.
Subtraction: We can subtract two inequalities when they have opposite inequality signs.(we take the sign of the inequality we subtract from).
(1) 4x + 6y < -3
or, 2x + 3y < -1.5
now, 2x + 3y + 4z > 2 ---(1)
& 2x + 3y < -1.5 ---(2)
(1) - (2)
4z > 2 - (-1.5)
or, z > 3.5/4
so, z cannot be zero. sufficient
(2) 9y + 12z > 4
or,3y+4z>4/3
so, z can be zero or cannot be zero. insufficient
correct answer A
Addition: We can add two inequalities when they have the same inequality signs.
Subtraction: We can subtract two inequalities when they have opposite inequality signs.(we take the sign of the inequality we subtract from).
(1) 4x + 6y < -3
or, 2x + 3y < -1.5
now, 2x + 3y + 4z > 2 ---(1)
& 2x + 3y < -1.5 ---(2)
(1) - (2)
4z > 2 - (-1.5)
or, z > 3.5/4
so, z cannot be zero. sufficient
(2) 9y + 12z > 4
or,3y+4z>4/3
so, z can be zero or cannot be zero. insufficient
correct answer A
15 May 2020, 00:48
Kudos
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Bunuel
Solution
Step 1: Analyse Question Stem
- • \(2x + 3y + 4z > 2 ……………(i)\)
• We need to find if z = 0
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: 4x + 6y < -3
- • \(4x + 6y < -3\)
• Dividing both sides by 2, we get,
- o \(2x + 3y < -\frac{3}{2}\)
• Thus, z ≠0
Statement 2: 9y + 12z > 4
- • \(9y + 12z > 4\)
• Dividing both sides by 3 we get,
- o \(3y + 4z > \frac{4}{3} ........(ii)\)
o This does not tell if z is zero or not. For example, consider the following two cases:
- Case 1: y can be 1 and z can be 0.
- • In this case z = 0 and \(3y + 4z = 3 + 0 > \frac{4}{3}\)
- • In this case z ≠0 then also \(3y + 4z = 0 + 4*1 > \frac{4}{3}\)
Thus, the correct answer is Option A.
