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10 Jul 2019, 00:57
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (02:22) correct
26%
(02:34)
wrong
based on 80
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The median of the set of values a, b, a + 2b, a - 3b, ab and 3b where a < b and b > 4, \(a>\frac{8}{3}\) is
A. \(\frac{(a-3b)}{2}\)
B. \(\frac{(a+3b)}{2}\)
C. \(\frac{(2a+b)}{2}\)
D. \(\frac{(2a-b)}{2}\)
E. \(\frac{(3a+b)}{2}\)
A. \(\frac{(a-3b)}{2}\)
B. \(\frac{(a+3b)}{2}\)
C. \(\frac{(2a+b)}{2}\)
D. \(\frac{(2a-b)}{2}\)
E. \(\frac{(3a+b)}{2}\)
10 Jul 2019, 02:10
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Bunuel
The median of the set of values a, b, a + 2b, a - 3b, ab and 3b where a < b and b > 4, \(a>\frac{8}{3}\) is
A. \(\frac{(a-3b)}{2}\)
B. \(\frac{(a+3b)}{2}\)
C. \(\frac{(2a+b)}{2}\)
D. \(\frac{(2a-b)}{2}\)
E. \(\frac{(3a+b)}{2}\)
A. \(\frac{(a-3b)}{2}\)
B. \(\frac{(a+3b)}{2}\)
C. \(\frac{(2a+b)}{2}\)
D. \(\frac{(2a-b)}{2}\)
E. \(\frac{(3a+b)}{2}\)
Least value = a - 3b (Negative)
We can see a - 3b < a < b (Given a < b)
Between a + 2b & 3b ; 3b is higher (since a < b)
To decide between a + 2b & ab;
Assume least value of a = 8/3 (approx)
--> 8/3 + 2b & 8/3b
--> 8/3 + 2b & 2/3b + 2b
--> Since b > 4, 2/3b is always greater than 2*4/3 = 8/3
--> ab > a + 2b
In ascending order,
Possible set 1 = {a - 3b, a, b, a + 2b, ab, 3b}
Possible set 2 = {a - 3b, a, b, a + 2b, 3b, ab}
Note: We can also see the options DO NOT have 'ab' in them. so, we can assume the above order
From both the possible sets, Median = average of 3rd & 4th term
--> Median = (b + a + 2b)/2 = (a + 3b)/2
IMO Option B
Alternate Method:
Assume a = 3, b = 5
a, b, a + 2b, a - 3b, ab and 3b
--> 3, 5, 3 + 2*5, 3 - 3*5, 3*5, 3*5
--> 3, 5, 13, -12, 15, 15
--> -12, 3, 5, 13, 15, 15 (Ascending order)
Median = (5 + 13)/2 = 9
Only Option B satisfies!
Pls Hit Kudos if you like the solution
17 Jul 2019, 08:09
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A smart approach to solve this question with less effort is to take b = 4 and a = 3 to calculate the values of the individual terms. Once we know the terms, knowing the median is just a couple of steps away.
If a = 3 and b =4, the values in the set will be { 3, 4, 11, -9, 12, 12}.
To find the median, we have to first arrange these values in ascending order. We get,
{-9, 3, 4, 11, 12,12}.
The median in this case will be the average of the 3rd and the 4th values i.e. 4 and 11.
Median = 7.5
Substituting the values of a and b in the options, we see that option B gives us 7.5
Therefore, answer option B is the correct answer.
When the question and options both consist of variables, plugging in simple values is the best and the fastest approach.
Hope this helps!
If a = 3 and b =4, the values in the set will be { 3, 4, 11, -9, 12, 12}.
To find the median, we have to first arrange these values in ascending order. We get,
{-9, 3, 4, 11, 12,12}.
The median in this case will be the average of the 3rd and the 4th values i.e. 4 and 11.
Median = 7.5
Substituting the values of a and b in the options, we see that option B gives us 7.5
Therefore, answer option B is the correct answer.
When the question and options both consist of variables, plugging in simple values is the best and the fastest approach.
Hope this helps!
