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Since ab = a b = 1
from condition 1 by = 2 so y = 2
from condition 2 2xy = 4 so x = 1
going back to condition 1 ax = by = 2 since x = 1 a = 2
we know a,b,x and y
So C is the answer

I was not questioning his explanation. I didn't understand it at the first sight. Now, I see b = 1 from the given the problem. So, the answer should be C.

Friends, I would agree with the answer but a little different opinion on the explanation.
Given,

ab = a => ab - a = 0 => a(b-1) = 0

=> a = 0 & b <> 1 OR a = 0 & b = 1 OR a <> 0 & b = 1

(Here <> stands for "not equal to")

What do we need to find? (axb) (ayb)

Since ab = a, this can be simplified to (ax) (ay) = (a^2)xy = ?

Statement 1:

ax=by=2 => Since ax = 2, a can NOT be 0. So the only possibility is the third one above (in bold). That is b = 1 => y = 2. This does not help us find the value of (a^2)xy.

Statement 2:

2xy = 4 => xy = 2 => This information along with the possible values of a and b above (in bold) will not help us find the value of (a^2)xy

TOGETHER

ax = 2
by = 2
xy = 2
=> (2/a) (2/b) = 2 => 4/ab = 2 => ab = 2 => a = 2 (because ab = a is given)

So we have value of a and xy hence,we can find out (a^2)xy

I attended a portfolio workshop hosted by Business Design club today. Competing against thousands of MBA students with the entire world, you need more than your resume and coverletter...

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