Is 'b' the median of three numbers a, b, and c? 1) |a-b|=|b-c| 2) bc

Question

Is ' b ' the median of three numbers  a, b,  and  c ?

(1)  |a-b|=|b-c| 
(2)  b>c

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 3 variables ( a , b and c ) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) If a = 3 , b = 2 , c = 1 , then b is the median of a , b , c and the answer is 'yes'. If a = 1 , b = 2 , c = 1 , then b is not the median of a , b , c and the answer is 'no'. Therefore, E is the answer. In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Kinshook · Answer

Asked: Is ' b ' the median of three numbers  a, b,  and  c ?

1)  |a-b|=|b-c| 
a---------------b----------------c
{c,a}-----------------b
or 
b--------------------{c,a}
NOT SUFFICIENT

2)  b>c 
c---------------b
a---------------c---------------b
c-----------a-----------b
or
c-----------b-----------a
NOT SUFFICIENT

Combining (1) & (2)
1)  |a-b|=|b-c| 
a---------------b----------------c
c---------------b----------------a
{c,a}-----------------b
or 
b--------------------{c,a}
2)  b>c 
{c,a}-----------------b
c-----------------b----------------a
b may or may not be median of a, b & c
NOT SUFFICIENT

IMO E

ccooley · Answer

The trap here is assuming that all three numbers are different.

Statement 1 tells you that the distance between a and b is the same as the distance between b and c. ("|x - y|" is the same as "the distance between x and y on a number line.") If all three numbers are different, that means b would have to be halfway in between a and c. However, we don't know that the numbers are different. a and c could be equal, in which case b is definitely the same distance from both of them, no matter what its value is.

Same thing with statement 2 - this tells you that b and c aren't equal, but if a and c are equal, b could be anything! So, we don't know whether it's the median.

TheBipedalHorse · Answer

Numbers assumed are in the format (a,b,c)

Statement 1 says magnitude of the difference between a,b and b,c are the same. Series can be 1,2,3 or 1,2,1 or 3 2,1 or 3,2,3

Statement 2 says b>c. Not sufficient as numbers can be 1,2,0 or 3,2,1

Combining both
Not sufficient as series could be 3,2,1 or 1,2,1

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Is 'b' the median of three numbers a, b, and c? 1) |a-b|=|b-c| 2) b>c

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