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02 Sep 2022, 00:34
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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:
55%
(hard)
Question Stats:
71% (02:31) correct
29%
(02:33)
wrong
based on 313
sessions
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Consider seven integers; whose range is 80 and median is 240. The median for the three smallest integers is 180. What is the possible range for the largest three integers?
I. 75
II. 24
III. 0
A. I only
B. II only
C. I and III only
D. II and III only
E. III only
I. 75
II. 24
III. 0
A. I only
B. II only
C. I and III only
D. II and III only
E. III only
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02 Sep 2022, 01:52
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The range of the seven integers is 240. As the number of integers is odd, the range is a member of the set.
So the set is as follows
X _ _ 240 _ _ Y
Its also given that Y - X = 80
We know that the median of three smallest integer is 180. Let's incorporate this information in our set -
X 180 _ 240 _ _ Y
We know that the range (difference between Y and X) is constant. Hence Y to be maximum, we have to have X as 180.
Therefore Y = 180 + 80 = 260
We need the range of the largest three.
The maximum range possible = 260 - 240 = 20.
Hence the only option that fits in is III.
Option E
So the set is as follows
X _ _ 240 _ _ Y
Its also given that Y - X = 80
We know that the median of three smallest integer is 180. Let's incorporate this information in our set -
X 180 _ 240 _ _ Y
We know that the range (difference between Y and X) is constant. Hence Y to be maximum, we have to have X as 180.
Therefore Y = 180 + 80 = 260
We need the range of the largest three.
The maximum range possible = 260 - 240 = 20.
Hence the only option that fits in is III.
Option E
General Discussion
03 Sep 2022, 00:32
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carcass
Median for \(x\) number of terms where \(x\) is odd = Term No. \(\frac{(x+1)}{2}\)
So, median for group of 7 integers = \(\frac{(7+1)}{2} = 4\)th term
Similarly, median for the first 3 integers = \(\frac{(3+1)}{2} = 2\)nd term
As per the question, given information is as follows:
Median (of all 7 integers) = 240
Median (first 3 integers) = 180
So, we can safely write the numbers in the following ascending order (blank spaces are currently unknown)
__ 180 __ 240 __ __ __
Let the terms be denoted as \(x_1, x_2, x_3, x_4, x_5, x_6, x_7\)
\(x_4 = 240\)
\(x_2 = 180\)
Range overall = 80 => \(x_7 - x_1 = 80\)
To determine: Range of last 3 numbers or \(x_7 - x_5\)
__ 180 __ 240 __ __ __
\(x_1\) and \(x_3\) can be equal to 160 and 180 respectively and terms \(x_5\) to \(x_7\) can equal 240 and still maintain the medians and overall range properties in the question stem
160 180 180 240 240 240 240 : Range (Last 3) or \(x_7 - x_5\) = 0
Now, we know that the overall range of the series has to be 80 and also that \(x_1\) cannot be greater than 180 because \(x_2 = 180\) (as part of the question stem)
So, the maximum that \(x_1\) can be is 180 and similarly \(x_7\) has to be 260 for range to match, even in this scenario
180 180 180 240 240 240 260 : Range (\(x_7 - x_5\)) = 20 It cannot exceed 20
So other options are ruled out, only 0 from the options remains
Answer - E
