If a 0, b 0, and (a^2)b = a, then which of the following MUST equa

Question

If a > 0, b > 0, and (a^2)b = a, then which of the following MUST equal a?

A. 1/(b^2)
B. 1/b
C. b
D. b^2
E. b^2 – 2b +1

nalinnair · Answer

(a^2)b = a 
Subtract  a  from both sides
 (a^2)b - a = a - a 
 a(ab - 1) = 0 
As  a>0 ,  ab-1  must be equal to 0
 ab - 1 = 0 
 ab = 1 
 a = 1/b 
Hence, the correct answer is  B

chetan2u · Answer

Hi,
 although it is always safer to take variables on one side and then factor, but we can avoid here since it is given that both a and b are >0.. 
so (a^2)b = a...
or (a^2)b/a=1,
ab=1 or a=1/b
B

nipunjain14 · Answer

A^2b=A
A^2b-A=0
A (Ab-1)=0
Since A >0 then
Ab-1=0
A=1/b

Ans:B

TeamGMATIFY · Answer

(a^2)b = a
Since both a and b are greater than 0, we can directly cancel out the powers of a from both sides
Therefore, ab = 1
Or a = 1/b
Option B

dmod14 · Answer

Would this work?

(a^2)b=a
divide both sides by a^2
b=a/a^2
b=1/a
a=1/b

abhimahna · Answer

Hey  dmod14  ,

Yes, this will work. You can divide by  a^2  only if you know that a is non zero. Since this question explicitly mentions that, you are good but don’t divide if it is not given.

Does that make sense?

BelisariusTirto · Answer

I'm a bit confused by the working out... The solutions posted reach the consensus that because a > 0, ab - 1 = 0.. Does this just mean that it cannot be anything BELOW 0? Thus we assume ab - 1 = 0? (because of a > 0) From all the solutions listed I feel like I should instantly grasp it but I had to re-read the solutions a few times..

Like how do we go from  a(ab-1) = 0  , oh  a > 0 , and  b > 0 , so it must be that  ab - 1 = 0  then  ab = 1  ... tada  a = 1/b  (to clarify the last part I do understand, I just have trouble with the general thought process to reach there, trying to wrap my head around it.)

Bunuel · Answer

Don't overcomplicate it. This is a fairly easy question. The condition a > 0 implies a ≠ 0, allowing us to reduce (a^2)b = a by dividing both sides by a, giving ab = 1. Similarly, the condition b > 0 implies b ≠ 0, allowing us to divide by b, resulting in a = 1/b. That's it!

Answer:" B.

BelisariusTirto · Answer

Bunuel, thank you for making it so clear for me. I couldn't see it until you explained it.

If a > 0, b > 0, and (a^2)b = a, then which of the following MUST equa

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