The median of the set of values a, b, a+2b, a-3b, ab and 3b where a

Question

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}

CareerGeek · Answer

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

CrackverbalGMAT · Answer

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!

ScottTargetTestPrep · Answer

Since we have six values, we need to find the middle two values (when their values are ordered from smallest to largest) to determine the median.

Since a < b, b > 4 and a > 8/3, we can let a = 3 and b = 5, so the six values are:

3, 5, 13, -12, 15, and 15.

In order, they are:

-12, 3, 5, 13, 15, 15

We see that two middle values are 5 and 13, or in terms or a and b, they are b and (a + 2b). Therefore, the median is:

(b + a + 2b)/2 = (a + 3b)/2

Answer: B

bumpbot · Answer

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The median of the set of values a, b, a+2b, a-3b, ab and 3b where a<b

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