If ab=c, what is the median of a,b,c? 1) a=1 2) c=1

Question

If  ab=c , what is the median of  a,b,c ?
1)  a=1 
2)  c=1

chetan2u · Answer

1)  a=1 
so ab=c means 1*b=c or b=c.
We require to know the value of b and c, as the median will be value of b/c..
If b=c=1, the median = 1
If b=c=3, the median is 3
Insuff

2)  c=1 
This means ab=1..
If a and b were positive, answer will be 1 as c will be the median always for example  \frac{1}{2}*2  or  \frac{2}{3}*\frac{3}{2} 
If negative then any of a or b can be median, for example -\frac{1}{2}*-2 .. median of -2, -1/2, 1 is -1/2 or  -\frac{2}{3}*-\frac{3}{2} .. median of -3/2, -2/3, 1 is -2/3 OR -1*-1=1.. median is -1
Insuff

Combined 
all are 1, so median is 1

C

MathRevolution · Answer

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have 3 variables ( a ,  b  and  c ) and 1 equation,  ab = c , C 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)
Since we have  ab = c ,  a = 1  and  c = 1 , we have  b = 1 .
Thus, their median is  1 .
Since both conditions together yield a unique answer, they are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If  a = 1 ,  b = 1 ,  c = 1 , then their median is  1 .
If  a = 1 ,  b = 2 ,  c = 2 , then their median is  2 .
Since condition 1) does not yield a unique answer, it is not sufficient.

Condition 1)
If  a = 1 ,  b = 1 ,  c = 1 , then their median is  1 .
If  a = 2 ,  b = 2 ,  c = 1 , then their median is  2 .
Since condition 2) does not yield a unique answer, it is not sufficient.

Therefore, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

Coggi · Answer

I am confused, in this question it is asked which letter is the median or what is the value of the median ?

Bunuel · Answer

What is the median = What is the value of the median.

This is a value DS question, so a statement to be sufficient you must get a single numerical value of the median.

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If ab=c, what is the median of a,b,c? 1) a=1 2) c=1

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GMAT Data Sufficiency (DS) Questions

If ab=c, what is the median of a,b,c? 1) a=1 2) c=1

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