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11 May 2016, 03:19
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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:
45%
(medium)
Question Stats:
60% (01:12) correct
40%
(01:16)
wrong
based on 245
sessions
History
Date
Time
Result
Not Attempted Yet
Are the integers x, y and z consecutive?
(1) The arithmetic mean (average) of x, y and z is y.
(2) y-x = z-y
(1) The arithmetic mean (average) of x, y and z is y.
(2) y-x = z-y
11 May 2016, 04:41
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St1: The arithmetic mean (average) of x, y and z is y.
y = (x + y + z)/3
y = (x + z)/2
If x, y, z = 1, 2, 3 then x, y and z are consecutive
If x, y, z = 2, 4, 6 then x, y and z are not consecutive
Not Sufficient
St2: 2y = x + z
This statement is a replica of St1. Not Sufficient
Answer: E
y = (x + y + z)/3
y = (x + z)/2
If x, y, z = 1, 2, 3 then x, y and z are consecutive
If x, y, z = 2, 4, 6 then x, y and z are not consecutive
Not Sufficient
St2: 2y = x + z
This statement is a replica of St1. Not Sufficient
Answer: E
11 May 2016, 20:28
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In the original condition, there are 3 variables (x, y, and z). In order to match the number of equations to the number of variables, we need 3 equations. However, since the condition 1) and the condition 2) each has 1 equation, we lack 1 equation. Therefore, there is high chance that E is the correct answer. Using both the condition 1) and the condition 2), from x+z=2y, we get x=1, y=2 and z=3. The answer is yes. However, when we get x=1, y=5 and z=9. The answer becomes no. Hence, the conditions are not sufficient. Therefore, the correct answer is E.
- For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
- For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
