OG2016 - fractions

boomgoesthegmat wrote:1/(1+1/3) - 1/ (1+1/2) =

A) -1/3
B) -1/6
C) -1/12
D) 1/12
E) 1/3

USEFUL/IMPORTANT rule: 1/(a/b) = b/a
So, 1/(3/2) = 2/3
And 1/(5/6) = 6/5
etc...

Now onto the question....
1/(1 + 1/3) - 1/ (1+1/2) = 1/(4/3) - 1/ (3/2)
= 3/4 - 2/3
= 9/12 - 8/12
= 1/12
= D

Cheers,
Brent

boomgoesthegmat wrote:1/(1+1/3) - 1/ (1+1/2) =

A) -1/3
B) -1/6
C) -1/12
D) 1/12
E) 1/3

The first term can be simplified as: 1/(1 + 1/3) = 1/(4/3) = 3/4

The second term can be simplified as: 1/(1 + 1/2) = 1/(3/2) = 2/3

Thus, 3/4 - 2/3 = 9/12 - 8/12 = 1/12.

Answer: D

Hi All,

We're asked for the value 1/(1+1/3) - 1/ (1+1/2). Most Test Takers would use standard Arithmetic to answer this question (which is fine). By 'converting' the fractions though, you can get the solution with a little logic and not that much math...

1/(1+1/3) = 1/1.333
1/ (1+1/2) = 1/1.5

The first fraction is BIGGER than the second fraction (because it has the smaller denominator). Since we're subtracting a smaller fraction from a larger fraction, we're looking for an answer that is POSITIVE. Since those fractions are fairly close to one another, the answer won't be that much bigger than 0. There's only one answer that matches.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich