a, b, and c are integers in the set {a, b, c, 51,85,72}.

Question

a, b, and c are integers in the set {a, b, c, 51,85,72}. Is the median of the set greater than 70? (1) b>c>69 (2) a

Bunuel · Accepted Answer

a, b, and c are integers in the set {a, b, c, 51, 85, 72}. Is the median of the set greater than 70?

The median of 6 integers is the average of the middle two, when arranged in ascending/descending order.

(1) b > c > 69 --> the least values of c and b are 70 and 71, respectively. Even if a is the smallest of the numbers the median = (70 + 71)/2>70 (the set in this case is{a, 51, 70, 71, 72, 85}). Sufficient.

(2) a < c < 71. If a=69, c=70, and b is the smallest number, then the set is {b, 51, 69, 70, 72, 85} and the median is less than 70 but if a=69, c=70, and b is the largest number, then the set is {51, 69, 70, 72, 85, b} and the median is greater than 70. Not sufficient.

Answer: A.

nikhilsehgal · Answer

Well, Bunnel i have a question over here - As the question does not specify whether the integers are different or not - in that case if we take 70 and 70 in the first statement than in that case answer will be different - am i right?

Bunuel · Answer

(1) says that b > c > 69.

nikhilsehgal · Answer

Yeah !!! Missed that one

One has to be greater than 69. Well, thanks.

AccipiterQ · Answer

came here to post about that very question. Sloppiness kills on this test! It got me too on this question

Kritisood · Answer

Hi
I am not understanding how to solve this question at all. Why did we take the least values of b and c? and if a could be any value then how can we be sure?

Bunuel · Answer

The question asks whether the median of the set greater than 70? For (1) we tried to make the median as small as possible, and got that even in this case it must be more than 70.

swadhakamal · Answer

Bunuel

Hello Bunuel,

Hope you are doing well.

I have a confusion.
For option A why did you not take a as the highest number? like in option B, b is tested with both high and low.

Thanks.

Bunuel · Answer

For (1) we considered the worst case scenario. So, minimized everything and got that even in this case the median turns out to be greater than 70. Naturally for all other cases, the median must be greater than 70, thus no need to consider them at all.

gagan543 · Answer

Why do we have to make the set in ascending order ?

Bunuel · Answer

It's according to the the definition of the median: 
The median of a set with even number of terms is the average of the middle two, when arranged in ascending/descending order. 
The median of a set with odd number of terms is the middle term, when arranged in ascending/descending order.

AnshBatra · Answer

Hi Bunuel

DOUBT 1
since we know nothing about 'a' in the first statement cant we take 'a' as 70??
then the median will not be greater than 70 and the statement will be insufficient

DOUBT 2
b and c take any value above 69 and we are not told that they are less than 72. c can be 70,71,72 and b will be more than that making the set {a,51,72,73(c),74(b),85} and then in this case median will be more than 70.

Can you please help me out

Bunuel · Answer

From (1), every possible case gives a YES answer to the question. For example, the case you considered gives a median of 72.5, while the case in the solution gives the smallest possible median of 70.5.

If a = 70, which is possible, the smallest possible median is still greater than 70. We’d have the set {51, a = 70, c = 70, b = 71, 72, 85}, resulting in a median of 70.5.

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a, b, and c are integers in the set {a, b, c, 51,85,72}.

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a, b, and c are integers in the set {a, b, c, 51,85,72}.

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