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Updated on: 17 Aug 2019, 11:17
Originally posted by freedom128 on 17 Aug 2019, 10:08.
Last edited by freedom128 on 17 Aug 2019, 11:17, edited 3 times in total.
Last edited by freedom128 on 17 Aug 2019, 11:17, edited 3 times in total.
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
42% (01:56) correct
58%
(02:05)
wrong
based on 45
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(X - Y - Z\) even?
(1) \((X + Y + Z)/Z\) is even
(2) \(XYZ\) is even
Source: adapted from GMAT Club Test
+1 kudo if you like the question
(1) \((X + Y + Z)/Z\) is even
(2) \(XYZ\) is even
Source: adapted from GMAT Club Test
+1 kudo if you like the question
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
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17 Aug 2019, 10:11
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Note that X, Y and Z are not necessarily integers.
Q: is (X - Y - Z) even?
(1) (X + Y + Z)/Z = even
If all variables are integers, X - Y - Z will be even BUT if they are not, i.e. X=8, Y=0.5, Z=0.5 then (X + Y + Z)/Z is even and X - Y - Z = odd.
NOT SUFFICIENT
(2) XYZ is even
If all variables are integers, X - Y - Z will be even BUT if they are not, i.e. X=8, Y=0.5, Z=0.5 then XYZ is even and X - Y - Z = odd.
NOT SUFFICIENT
Combining (1) and (2),
X - Y - Z may be odd or even (again if variables are integers: YES but if X=8, Y=0.5, Z=0.5 answer is NO).
NOT SUFFICIENT
Answer is (E)
+1 kudo if you like this explanation
Q: is (X - Y - Z) even?
(1) (X + Y + Z)/Z = even
If all variables are integers, X - Y - Z will be even BUT if they are not, i.e. X=8, Y=0.5, Z=0.5 then (X + Y + Z)/Z is even and X - Y - Z = odd.
NOT SUFFICIENT
(2) XYZ is even
If all variables are integers, X - Y - Z will be even BUT if they are not, i.e. X=8, Y=0.5, Z=0.5 then XYZ is even and X - Y - Z = odd.
NOT SUFFICIENT
Combining (1) and (2),
X - Y - Z may be odd or even (again if variables are integers: YES but if X=8, Y=0.5, Z=0.5 answer is NO).
NOT SUFFICIENT
Answer is (E)
+1 kudo if you like this explanation
17 Aug 2019, 10:46
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chondro48
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.
In this question, \(x\), \(y\) and \(z\) do not need to be integers.
Since we have 3 variables (\(x\), \(y\) and \(z\)) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2)
If \(x = 1\), \(y = 2\) and \(z = 1\), which satisfy both conditions 1) & 2), then \(x - y - z = -2\) is an even number and the answer is 'yes'.
If \(x = 8\), \(y = \frac{1}{2}\) and \(z = \frac{1}{2}\), which satisfy both conditions 1) & 2), then \(x - y - z = 8 - \frac{1}{2} - \frac{1}{2} = 7\) is an odd number and the answer is 'yes'.
Since both conditions together don't yield a unique answer, they are sufficient.
Therefore, the answer is E.
In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
