Algebra - why is this wrong?

[jmagnuss]

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.

[praxis]

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.

[praxis]

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

[jmagnuss]

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