Is b the median of 3 numbers a, b, and c?

Question

(1) b/a = c/b
(2) ab < 0

Kurtosis · Accepted Answer

St1: b^2 = ac
2^2 = 2 * 2 --> b is the median
2^2 = -2 * -2 --> b is not the median
St1 is not sufficient

St2: ab < 0. We have no information about c and hence insufficient

Combining St1 and St2, we know that a and b should be of opposite signs and b^2 = ac
But since b^2 is a positive value, a and c should have the same signs
Suppose b = -ve then a = +ve and c = +ve
Suppose b = +ve then a = -ve and c = -ve
By this we know that b either occurs at the beginning or at the end and hence b cannot be the median. --> Sufficient

Answer: C

AyeMon · Answer

I am confused with St.1.
The question asked whether b is the median or not ... so I understand whether b is the middle value, bigger than one number and lower than another number.
So; either a>b>c or c>b>a

State 1: b/a = c/b
if a > b, b must be > c ... then a>b>c
if a < b, b must be < c ... then a<b<c

So ... Statement 1 seems sufficient to me :'(
Someone please help me to clarify this

Kurtosis · Answer

I am not sure how you arrived at the solution a > b > c or a < b < c, but you can try to plug in few values for a, b and c. If a = 1, b = 1 and c = 1 then b is the median. If a = 1, b = -1 and c = 1 then b is not the median. Posted from my mobile device

TestPrepUnlimited · Answer

Analyzing the question: We would need to prove either a >= b >= c or a <= b <= c . Note it is easier to prove this sufficient by answering "no" to the question. For example if we are given that b is the biggest, it would be sufficient since b cannot be in the middle. (1) b^2 = a*c . We can have b between a and c if a, b, c are positive, or we can have negative b with positive a and c . Therefore this is insufficient. (2) Nothing on c , insufficient. This tells us a and b have opposite signs however. (3) Combining with b^2 = a*c , a and c must have same signs in order to have a*c >= 0 . Then since b always has opposite signs from a and c , b is never in the middle. Therefore this is sufficient. Answer: C

Cellchat · Answer

IMO, when dealing with most fractions, it's always clearer to make one variable the subject.

(1)  \frac{b}{a }= \frac{c}{b}  -->  b^2 = ac 
Now you can more easily test cases. If b is any negative number, you can make a and c any positive number for b not to be the median.
If b = 2, a = 1 and c = 4, then b is the median. Therefore, insufficient.

Thekingmaker · Answer

A provides the information b^2 =ac however it could 6,6,6 so answer yes, 12,6,3 answer no .
B provides a<0 or b<0 clearly insufficient
when combined B^2 = ac which means a>o , C>0 , b could be positive or negative however second option provides B is negative (ab<0) therefore b is not the median yes the information are IMO C

IanStewart · Answer

There are good solutions above. I looked at things slightly differently:

For Statement 1 alone, the letters can all equal 1, and then b is the median. But if b = -1 and a = c = 1, then b is not the median, so Statement 1 is not sufficient. Statement 2 is clearly not sufficient alone.

Using both Statements:

From Statement 2, we know ab is negative. If ab is negative, then b/a is automatically negative. But Statement 1 tells us b/a equals c/b, so c/b must be negative too, which means bc is negative.

So we know ab is negative and bc is negative. If b is positive, then a and c must both be negative, and b is the largest thing in the set. If b is negative, then a and c must both be positive, and b is the smallest thing in the set. So it is impossible for b to be the median, and the answer is C.

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is b the median of 3 numbers a, b, and c?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is b the median of 3 numbers a, b, and c?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards