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The range of the set {60, 120, − 30, x, 0, 60} is 210. If a is the me

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Bunuel
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The range of the set {60, 120, − 30, x, 0, 60} is 210. If a is the me [#permalink] New post   22 Dec 2015, 01:38
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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
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Re: The range of the set {60, 120, − 30, x, 0, 60} is 210. If a is the me [#permalink] New post   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
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The range of the set {60, 120, − 30, x, 0, 60} is 210. If a is the me [#permalink] New post   22 Dec 2015, 02:07
Bunuel wrote:
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


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
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Re: The range of the set {60, 120, − 30, x, 0, 60} is 210. If a is the me [#permalink] New post   27 Dec 2015, 16:39
Bunuel wrote:
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



SOLUTION:

To get the range 210, we will have two cases.

Case 1) {-90, -30, 0, 60, 60, 120}

Case 2) {-30, 0, 60, 60, 120, 180}

Now the Question is, is Case two possible where we have median(a)=mode(b)=60.

In Both cases mode(b)=60, In both cases median is positive and In both cases Average is positive.

Statement 1) abc > 0 . Insufficient as mentioned above.

Statement 2) b = 60 . Insufficient as mentioned above

Statement 1 and statement 2 together.

No Addition information.

Hence Ans E.
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Re: The range of the set {60, 120, 30, x, 0, 60} is 210. If a is the me [#permalink] New post   19 Dec 2023, 04:08
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Re: The range of the set {60, 120, 30, x, 0, 60} is 210. If a is the me [#permalink]
19 Dec 2023, 04:08
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