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22 Dec 2015, 01:38
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Difficulty:
75%
(hard)
Question Stats:
60% (02:54) correct
40%
(02:46)
wrong
based on 294
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The range of the set {60, 120, − 30, x, 0, 60} is 210. If a is the median, b is the mode, and c is the average (arithmetic mean), is a = b?
(1) abc > 0
(2) b = 60
(1) abc > 0
(2) b = 60
22 Dec 2015, 01:59
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The 5 known elements of set are -30 , 0 , 60 , 60 , 120
Since range is 210 , x can either be - 90 or 180 .
Mode , b = 60
Average,c for this set will always be positive
The 2 sets can be -90 , -30 , 0 , 60 , 60 , 120 . Median = 30 .=> a ≠ b
or -30 , 0 , 60 , 60 , 120 , 180 . Median = 60 => a= b
In either case median will be positive
(1) abc > 0
=>Median , a is positive
Not sufficient.
(2) b = 60
We have no new information .
Not sufficient.
Combining , Not sufficient.
Answer E
Since range is 210 , x can either be - 90 or 180 .
Mode , b = 60
Average,c for this set will always be positive
The 2 sets can be -90 , -30 , 0 , 60 , 60 , 120 . Median = 30 .=> a ≠ b
or -30 , 0 , 60 , 60 , 120 , 180 . Median = 60 => a= b
In either case median will be positive
(1) abc > 0
=>Median , a is positive
Not sufficient.
(2) b = 60
We have no new information .
Not sufficient.
Combining , Not sufficient.
Answer E
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22 Dec 2015, 02:07
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Bunuel
Tricky one. So, what we have from the questions stem: is a=b
Range = 210, means that either we need a new min. value or a new max. value => -90 or 180
min=-90 or max=180
Median: 30 or 60
Average: 20 or 70
Mode is 60 (is independant from the new range values, in each case it's 60)
(1) abc>0 we already know this from the manupulated question stem. NOT SUFFICIENT
(2) b=mode=60 we already know this from the manipulated question stem. NOT SUFFICIENT
(1) + (2) we already know this from the manipulated question stem. NOT SUFFICIENT
Answer E
