Today’s SAT question of the day is an algebra question about adding fractions.  Before you break out your calculator or tell me how much you hate adding fractions, check out the strategy for this one – it will save you quite a bit of time.

If s = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 and t = 1 + s/2, then t exceeds s by how much?

We are looking for the difference between t and s, or t – s. Algebraically, if we substitute in the equivalency of s for t, that’s:

1 + s/2 – s

Now we can put in the value of s – it’s going to look ugly for a minute, but bear with it and fight the urge to tap all of this into your calculator to make it go away:

1 + (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32)/2 – (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32)

Simplifying a bit:

1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 – 1 – 1/2 – 1/4 – 1/8 – 1/16 – 1/32

Look at all the things that disappear when we perform the next round of subtraction. 1-1, 1/2 – 1/2, etc. – everything has a partner except for 1/64.

So, there’s your answer. t is 1/64 greater than s.

Fraction (and exponent) problems that are better solved on paper than on your calculator occur frequently on the SAT. As you saw from this one, it’s worth writing out the full problem on paper and seeing if anything can easily be simplified!