GMAT Math

This is from the GMAT800, page 246 Q5:

if x=3 and y=4, what is (xy)/(1/x + 1/y)

Plugging in the values you get:

12 / (1/3 + 1/4)

Since you can divide by multiplying by the inverse, I multiplied 12 by (3 + 4). (12 x (3/1 + 4/1)). This gives you 84.

This is wrong. The correct answer is to simplify the denominator first before doing that. You get 12 / (7/12), then multiply by the inverse gives you 144/7.

I understand the right answer completely, but I don't see where the error in reasoning lies in my original answer.

Thanks if anybody can point it out for me.

Inversion is not distributive, unlike multiplication. You cannot add the inverses, because

1/(1/x + 1/x) is not equal to (1/1/x+ 1/1/y)=(x+y)

what you need to do is multiply by 1, in the form xy/(xy), to get

xy/(y+x)

Multiplication IS distributive; eg a(b + c) = ab + ac; this is probably why you are confused.

BTW - you can find a longer explanation of this and some other operations stuff here: https://mathforum.org/dr.math/faq/faq.pr ... ssary.html

And some more sample questions here:
https://www.testsandtutors.com/course/view.php/GMAT

Thanks for the clarification, I'll do some additional reading on those pages.